Our Learning Curve

Can Computers Revolutionize Education?

2011-04-10T23:44:00.000-07:00

I remember a long, long time ago (late '70s? '80s?) reading a book about how microcomputers were going to revolutionize the world. At the time, from 1979 to probably 1984, I was the only person I knew who owned a microcomputer—an Apple II—oh, yeah, this was long before PC, the Mac and iEverything!—and most of my friends and coworkers scoffed as I talked to them about the exciting ideas I'd read in that book. The idea that intrigued me the most was how computers could revolutionize education and learning.

Individualized instruction? Computers are obviously ideal for providing self-paced, learner-driven material.

Drill made fun? Computers can, with endless patience, provide language or math drill—and in entertaining game formats, too!

Simulations? Computers, with great visuals, interactivity, and number-crunching power, can offer everything from virtual dissections and physics labs to Sim amusement parks and empires.

Of course, my much-read, quite-bedraggled paperback book about the microcomputer revolution didn't say anything about the Internet and Google, Wikipedia and YouTube—because the Internet was tiny and not much known when the book was written, and none of these other things had been invented yet. As much as the book's author strove to imagine the future, he didn't tumble to some of the biggies that were coming. Now we see that educators and learners can use computers to access a vast amount of information (and mis-information).

With all this going for computers, we can firmly say that of course they are revolutionizing education. Students can write better because word processors make it easy to find and fix mistakes, to reorganize or edit for clarity, and to produce neat final drafts. Students can research from the privacy of their homes and find up-to-the-minute information. Kids in remote areas can take correspondence courses with much quicker “correspondence”—including real-time interaction.

And yet...despite computer labs, school websites, and online courses, by and large schooling looks very much like it did in the '50s and the '70s and the '90s: a teacher talking in front of a bunch of students, textbooks and a set curriculum, paper assignments and tests (no cheating allowed!), letter grades that are vague about actual achievement and learning.

Are computers really revolutionizing education?

Here are some recent research studies I turned up with a little Googling:

The National Research Council reports that computer games and simulations are worthy of future investigation as tools for learning science, since research on their effectiveness remains inconclusive. (published 12/2010)

University of Missouri researchers have found that, since there is no clear definition of e-learning, online learning, and distance learning, it is difficult to study the efficacy of these educational techniques. (published 4/2011)
A North Carolina State University economist analyzed research studies about computers and education; he reports that computers appear to help elementary students learn—but not high school students. (published 8/2006)

Computers' impact on education doesn't sound all that revolutionary, does it?

After so many years of computers infiltrating and upending our lives, it's not at all clear that they have infiltrated schools all that deeply, let alone upended them! Why?

I would argue that most classroom teachers who utilize computers at all (and I mean for more than computing grades) use them in limited ways under the familiar and traditional paradigm of teacher-led, group-paced instruction. Even many researchers limit themselves to testing the efficiency of computers to teach concepts chosen by curricula-developers, and evaluate learning via traditional tests. I would argue that, if computers are to revolutionize education, we would have to allow them to drastically change the paradigm and leave back in the dust traditional evaluations and practices.

Students asking their own questions, exploring their own interests, developing their own projects—those kids will be able to use computers to find answers, to create visuals and movies and music and writings that express their ideas, and to analyze data and interact with the world and produce materials as they complete their own projects. Most students will work collaboratively, at least some of the time, and they will benefit from feedback, suggestions, and material help from caring and enthusiastic adults.

So far, in most school situations, computers have been revolutionary like the British colonies asking King George and Parliament if they could lower the tax on tea by a halfpenny per pound, please. Pretty please?

Which is not to say that computers have not and are not revolutionizing education for some...Not all education goes on in schools!

Learning from Our Mistakes

2010-10-15T18:53:00.000-07:00

It is a truism that we can learn from our mistakes as well as—or perhaps even better than—from our successes. But is it always true?

What we need in order to learn from our mistakes is accurate, timely, and appropriate feedback.

Without feedback, we are quite likely to go gallumphing off with mistaken ideas in our heads, perhaps even self-reinforcing mistakes. Every time we say or remember a mistaken idea (basically, a falsehood that we think is a fact) as long as we don't receive feedback, it becomes more solid in our heads as truth.

An example: my daughter's charming roommate grew up speaking Japanese but studied English. Then she became an English teacher to preschool-aged children. For several years she taught the English words for zoo animals—and of course, these little kids didn't know enough to correct her one tiny mistake—so now who knows how many Japanese children think that the long version of the word rhino is rhinosaur?

Learning from Artificial Intelligence

We can learn some things about human learning by studying efforts to program robots and computers to learn. A new project called NELL (Never-Ending Language Learning system) is programmed to teach itself natural language. The computer scientists seeded NELL with some starter facts about various categories of knowledge and then turned NELL loose to read hundreds of millions of Web pages. The computer uses the starting facts and pre-programmed relations to make inferences about other facts and has achieved a high rate of accuracy—with around 87% of inferred facts being correct.

But what happens when NELL makes a mistake? Apparently the category “baked goods” had been seeded with the terms pies, cakes, and cookies. By noticing that the words tortes, tarts, and coffee cake are used in the same sorts of sentences as pies, cakes, and cookies, NELL could correctly assign those additional items to the category as well. However, NELL didn't have enough background knowledge about the Internet to realize that Internet cookies were most definitely NOT baked goods. Having erroneously assigned the phrase Internet cookies to the category baked goods, NELL looked for sentences with similar contexts. “I deleted all my Internet cookies” came up somewhere, and later NELL spotted a very similar sentence: “I deleted all my files.” As usual, NELL made an inference based on her previously learned facts and so assigned files to the category of baked goods as well.

And then there was an entire cascade of mistaken inferences that left the baked goods category pretty much a hot mess!

A human had to wade into that mess, figure out and fix the initial mistake, and restart the learning in that category. NELL learns a lot on its own—but it still needs feedback from time to time.

Kids need feedback, too...

Little kids, when learning to talk, make mistakes, too. For example, a toddler might overgeneralize the word dog to include non-canine four-legged animals of medium size. Older kids and adults automatically correct them (usually by simply restating the child's sentence using the correct word)—and so provide the appropriate, prompt feedback.

Kids need feedback when they are learning to read. I remember one of my daughters, when she was learning to read, asked me to sit with her and help her whenever she asked for a word. One of the education books I'd read stated that parents and teachers shouldn't correct a new reader's mistakes but rather should allow him or her to self-correct, so I decided I would ONLY answer questions, never give corrections.

But it didn't work. I quickly discovered that my daughter wasn't very good at phonics but was quite brilliant at utilizing context clues. In an early reading session, my daughter came to the word garage. She looked at the beginning of the word and made a stab at it, saying garden. As planned, I didn't correct her. The esteemed education author had assured me that the next few words would tell my daughter she'd made a mistake and would cause her to go back and find it on her own. But my daughter used the mistaken context of garden to figure out the following words—all wrong, of course!—and soon there was an avalanche of "mistakes." My daughter was no longer reading—she was inventing her own story!

“Hold on!” I finally said. “You read a word wrong back here.” I gave my daughter the feedback she apparently needed—and she firmly told me to correct her mistakes from then on, thank you very much—and we went on with the reading. She learned through her mistakes and successes, and I learned through my own mistake to both answer questions and give feedback.

Research backs it up...

A recent study of college students confirms what we already know: students do better and feel more connected to coursework when they get prompt and personalized feedback.

Cheating:

2010-10-04T15:18:00.000-07:00

It's Reported as a Problem that's Getting Worse

...but Is It?

I see occasional news items bemoaning the scandal that cheating in schools has become. Journalists and educators tend to say, with the gravitas that implies speaking in capitalized words, that The Problem of Cheating is Getting Worse!

However, when I look back at my own high school days, I seem to remember that cheating was rampant then, too. Students everywhere seemed to assume that every other student would either cheat or would at least allow and support cheating—in other words, if asked, it was expected that we would allow our homework to be copied or our test answers to be shared. I guess large-scale and formal cheating scandals were few and far between, back then—but aren't they still?

I am willing to grant that cheating might be worse nowadays due to teachers' and schools' reliance on all-too-hackable computers (not to mention students' use of the internet and copy-paste—but I think that plagiarism is a separate topic). I think it's hard to know how many people cheated then or now, because it is in people's best interest to lie about cheating to themselves as well as to researchers...However, suffice to say that, despite all the hand-wringing, I am a bit skeptical that cheating is really getting much worse, since it seemed to be ubiquitous back in the day.

I even wonder if “cheating” is a problem...

If an assignment is worth doing, it's because either a worthwhile product is created (think shop class) or a concept or skill is learned (think, say, algebra). If a student doesn't do an assignment that is worth doing, then the natural consequence is that the student doesn't have the product or know the concept or skill. If the student mindlessly copies an assignment and therefore merely seems to have done the assignment, but doesn't know the material, then that student is really just cheating him or herself.
If an assignment is not worth doing, but is just busywork, then who cares if the student did or did not do it? It's not worth doing, so it's not worth assigning. Right?

One might even make the point that it takes character to not waste time on something not worth doing.

Finally, why is asking others for help or for answers considered cheating? In most work situations outside of school, what matters is getting stuff done. Yes, there are times in the world of work when it matters who does that stuff—and there are social rules about giving others credit when it is due them. Yes, sometimes people break those rules. But because adult work is structured around getting real stuff done, things like asking questions, cooperating, delegating, and sharing ideas are all considered important tools – certainly not cheating!

To solve the “problem” of cheating on assignments, make fewer assignments, but make each one a great opportunity to make a valuable product or to learn valuable concepts and skills. Encourage sharing and brainstorming on assignments, and give attention to accomplishments and feedback for results. Encourage group critique and self-evaluation, but don't grade the assignments.

And voila! There will be no reason to cheat!

How about cheating on tests?

I remember reading an anecdote in a book by education writer William Glasser. He related that one night he caught his high-school student son preparing a cheat sheet for his U.S. History class test. Glasser of course protested, but the son scornfully told him that the teacher wanted the students to memorize the list of all the U.S. presidents in order, with dates served as president—and, the son said, that was just dumb!

Glasser agreed with his son. If that was the type of test the teacher was going to give—just a mindless recitation of a list of names and dates, in the correct order (and, it turned out, it was that kind of test), Glasser felt that that teacher deserved any cheating that occurred.

Glasser pointed out that memorizing such a list is difficult and not very useful. If we need to know what ordinal number President Andrew Jackson was, we can easily look it up. If we need to know what year Andrew Johnson stepped down from the presidency, we can look that up, too. Even the students who perfectly recall the names and dates in order, while taking the test, will undoubtedly forget much of the information in short order.

Glasser went further than stating that such a simple-minded test deserved cheating. As I recall, he said something to the effect that a teacher should never give a test that is even open to cheating.

What would a non-cheatable test look like?

Actually, it would look quite familiar. Essay tests and math tests on which students are required to show all their work are pretty hard to cheat on. In the case of a unit on U.S. presidents, a non-cheatable test item might be something like this: Which of the presidents of the first half of the nineteenth century weakened the Union and pushed the country toward Civil War? Back up your answer with reasons or specific examples.

A teacher who gives tests with just a few short-answer or essay questions will quickly realize whether or not a student has listened during class, read the text, and thought about the chapter's topic. The student's understanding or lack of understanding will be apparent.

Glasser stated that all tests should be open-book and open-note. This suggestion is based on the philosophy that education is not memorizing facts that can be looked up, but instead learning to see connections and cause-and-effect relationships, analyzing concepts, generalizing from data, and other higher-order thinking skills. This kind of test makes cramming unnecessary.

Isn't all this just ivory-tower thinking?

Thousands of homeschooled kids demonstrate that grades and test scores aren't necessary in education. They have even shown by example that students without graded transcripts can get into colleges and universities and thrive there. Since “cheating” is such a “problem,” it makes sense to adopt Glasser's ideas and eliminate cheatable tests and to adopt the world-of-work paradigm that makes cooperation and sharing answers a good thing.

1. Kids Teach Themselves, 2. My Teacher the Machine, and 3. The Method of the Grandmother

2010-09-26T10:40:00.000-07:00

The TED talk by education scientist Sugata Mitra is well worth hearing in its entirety, but these three topics are to me the heart of his message.

1. Kids Teach Themselves

Mitra does many experiments in which he installs a computer with a high-speed internet connection somewhere, such as a slum in New Delhi, and leaves it there unsupervised (apart from a camera). This experiment is called “Hole in the Wall.” By themselves, with no adult help, the kids learn how to do remarkable things. They not only learn to do searches and to access games, they are even able to learn new speech patterns, absorb difficult material, and answer difficult questions—even questions in a different language! Mitra even ran tests that demonstrated that much of this learning is deep and long-lasting.

Unsupervised kids have learned so much so well in Mitra's experiments, that he has had some difficulty publishing findings because outsiders considered them “too good to be true.”

Mitra quotes the late science/science fiction writer and intellectual Arthur C. Clarke, who said, “Where there is interest, there is education.”

We can benefit from Mitra's research by providing computers, not one per student as many homes and schools do, but one computer for every, say, four students. Mitra points out that the kids in groups at a computer tend to discuss what they've discovered, show off what they've learned, and otherwise interact with each other as well as the computer.

If there are already multiple computers in a home, I bet having them in the same room tends to facilitate this sort of showing-off, discussing, interacting learning, even if each kid has his or her own machine.

Certainly schools and teachers, homeschools and parents—everyone concerned about education—should remember that kids can learn remarkable things on their own IF THEY ARE INTERESTED. Kids will learn what they want to learn.

2. My Teacher the Machine

Obviously, Mitra's experiments assume the availability of computers with internet access. The central problem he first addressed was how to provide education to poor children and children in out-of-the-way places where good teachers and schools don't exist. It is far cheaper to provide some computers to these communities than to build schools staffed with teachers!

Again, Mitra quotes Arthur C. Clarke:

A teacher who can be replaced by a machine should be.

This is not to say that there should be no human teachers anymore. As Mitra's work shows, people are natural teaching as well as learning animals—some kids set themselves up as teachers, for example. However, teachers should not try to replicate the kinds of tasks that computers can do—they should do the things that computers can't do (at least not yet).

What are those things?

A teacher can go out into the world and gather interesting resources that pertain to the things their students are interested in, the things they want and need to learn. Kids can find data on computers—and, Mitra shows us, often without adult guidance. But actual 3-dimensional materials, living things, stuff to mess around withn and non-virtual objects to manipulate--all enrich kids lives and learning.

A teacher can pose interesting questions that the students wouldn't come up with on their own. Mitra poses some challenging questions in the course of his experiments, and a teacher who knows his or her students can help kids go further with their own interests and ideas by pushing a bit here, questioning something there, daring kids to try something hard over there.

And then, of course, a teacher can use the method of the grandmother...

3. The Method of the Grandmother

Mitra shows that people can help kids learn even if they don't know what the kids are learning themselves! This can be accomplished using what he calls the method of the grandmother:

Stand behind them and admire them all the time. Say, “That's cool! That's wonderful! Can you do that again? Show me some more!”

This furthers the learning-through-interaction noted in Point 1 above. Kids don't just like showing off to each other, they also enjoy attention and admiration from adults, especially adults they know and care about.

Mitra actually uses volunteer grandmothers in Skype sessions with kids elsewhere in the world to further the learning of children who don't have access to good schools and teachers. He calls this a “granny cloud” that he can aim anywhere he wants!

Why grandmother rather than mother or father? Often it is grandparents who have the time and patience to really listen to or watch kids. But any of us can use the method of the grandmother.

Paying Attention and Being Distracted

2010-09-19T23:21:00.000-07:00

Some school practices are built around the idea that we have to lure students to do assignments and to learn lessons. We often use rewards (think everything from prizes and pizza parties to good grades and gold stars), punishments (such as extra homework, low grades, and dreadful threats of not being promoted or graduated), and even “edutainment” type interest-grabbing techniques (one example might be use of the latest celebrity or pop-culture item to jazz up a multiplication lesson)—and, in so doing, we often act as if students would have no interest in learning school subjects for their own sake.

Which I fear is quite the self-fulfilling prophecy.

And we know from long experience that, at least to some extent, students who can pay attention to our lessons and who can focus on their homework do better in school. Kids with so-called Attention Deficit/Hyperactivity Disorder often struggle in school. We labor to provide ADHD kids—well, to be truthful, all kids—with non-distracting environments so that they can concentrate on reading, writing, doing math, and thinking deep thoughts.

Concentration good. Distraction bad.

However, a recent study from scientists at Harvard and the University of Toronto informs us that distractible students are often creative students.

S. H. Carson and others have published a study about latent inhibition, that is, the ability to tune out distractions. They found that people who aren't very good at tuning things out—in other words, the people who are more easily distractible—are often people who are more creative than those who score high in latent inhibition. And people ranked as eminent creative achievers are seven times more likely to “suffer” from low latent inhibition.

Seven times!

Wired Science Blog's Jonah Lehrer writes that these low-latent-inhibition/creative types have more data pouring into their brains—which by definition makes them more open-minded—and are therefore more likely to see unlikely connections or to “think outside the box.” However, they cannot just let tons of stuff in and, in Kierkegaard's words, drown in possibilities. Creative /distractible people must be willing to analyze all the extra thoughts and sensations and ruthlessly toss out the useless stuff.

Do kids with ADHD have an actual deficit? Do they lack whatever it is that allows us to pay attention?

Actually, just about anyone who knows a child diagnosed with ADHD will tell you that the kid can focus just fine on something that interests him or her. It's usually an inability to focus on something ADHD sufferers have to do but don't want to do that runs them into trouble.

As I have already reported, the neurotransmitter dopamine can be considered the currency of the brain, which assigns “price tags” to pieces of sensory information. As Lehrer writes, there is a “highway of nerves connecting the dopamine reward pathway to the prefrontal cortex, a crucial fold of tissue that controls the spotlight of attention.” What this really means is that dopamine helps us to pay attention to whatever is important to us and motivates us to move, learn, or otherwise act.

Apparently kids with ADHD need a higher threshold interest to pay attention to something. Drugs for ADHD work by increasing the amount of dopamine in the synapse, so that the worlds seems full of interesting thoughts and sensations, and even something like a lesson on fractions is likely to be passed along to the prefrontal cortex.

I don't know a ton about ADHD and even less about the drugs used to treat it. However, it is my guess that some (perhaps a small percentage) kids truly need medication but many do not. My guess is that, in a world of unschooling or alternative education designed around kids' needs rather than adult convenience, way fewer kids would be diagnosed with an attention disorder. But I bet some still would.

At any rate, it is heartening to reflect on the fact that being distractible has its good points and that even those of us with an attention “deficit” are able to pay attention to things that truly interest us!

My own distractions...

I haven't written a post for this blog for several months. My husband just retired, we took three splendid trips, and other family matters pressed for time and attention. Plus there's this cool thing called Facebook...However, I am this week back to work and consider myself “back” to my blog as well.

Your Brain on Computers –

2010-06-15T00:16:00.000-07:00

Perhaps Not What You Think!

I have seen this New York Times article posted in several places. It warns us that our use of technology—computers, video games, I-Pads, I-Pods, smart phones, the internet, Facebook—may be rewiring our brains and making us into a bunch of multi-taskers with no ability to focus.

It's good to question modern lifestyles (it's good to question everything!), and advice to seek balance and moderation is always win-win. However, I still felt a bit restive with the somewhat dire tone of the article's warning. I have noticed the changes in my own life before and after internet, before and after cell phones, before and after computers: there are some problems to watch out for, sure, but most of the effects of these technologies have been great!

That's why I'm so grateful for the perspective given by Jonah Lehrer in his post “Tradeoffs.” He points out that a group of University of Michigan scientists identified walking down a city street as having a much MORE dramatic bad effect on working memory, self-control, visual attention and positive affect than does multi-tasking on the internet with a computer.

Where, oh where are the articles warning “This is your brain on a walk”?

The University of Michigan study concludes that time spent in nature can be restorative, leading to “improvements in directed-attention abilities.” It carefully explains that a walk in nature is usually filled with things to see, smell, feel, and hear, but these stimuli only modestly grab our attention in a bottom-up way. The city walk, on the other hand, is filled with sights, sounds and smells that dramatically vie for attention and that require top-down thinking—directed attention—to stay safe from traffic and to deal with the confusing urban grid.

The study doesn't seem to deal with all the in-between situations that describe the bulk of my life: the city walks that feature little or no traffic, no jostling crowds, and are very, very familiar. I find myself not thinking too much about the here-and-now on many of my city walks, and since I am walking a well-known course, I certainly don't think for a moment about where I am or where I am going. Instead, I can concentrate on a good conversation, watch the sun set, or enjoy the chirping of birds. Another situation that seems to be in-between is walking in nature on full alert. When we've just spotted fresh bear scat, and there were reports about a bear getting into a camper's food supply the night before, I am definitely directing my attention to every little sight and sound!

The main point of the study—the restorative qualities of being in nature—is one I can fully embrace. But only because the scientists didn't warn us to avoid cities. As Lehrer points out, “we also know that cities are enormously valuable.” All the stimulation and interaction provided by an urban setting can benefit us, although we can and should still take time out for nature.

Likewise, the internet provides incredible benefits, and (Lehrer writes) “the value it provides far outweighs the cognitive costs (which may or may not exist.)”

Yes, let's study brain function as we use new technologies. Yes, let's continue to avail ourselves of old technologies—like boardgames and jump ropes and paperback books—even as we invent the latest great thing. Yes, let's live by balance and moderation in all things, including moderation itself. Yes, let's keep questioning our choices and our values, and let's keep up the society-wide conversation about all these issues.

But let's do this, too: let's keep our conclusions in proportion to our data.

Skipping Grades

2010-05-25T08:57:00.000-07:00

One thing that unschoolers* get right is not buying into the myth that “grade level” has some inherent meaning.

We can arbitrarily assign a grade level to a student, of course, in the sense of “first year of schooling / homeschooling / unschooling,” “second year,” and so forth—but somehow this simple label has taken on so much extra weight:

Children's reading ability is often expressed by “grade level” (supposedly measured to the year and month), and people worry if a child is reading “below” grade level, when we should be concerned about other aspects of reading and learning to read.

Children's curricula are often organized according to traditional “grade level” assignments, and people tend to plop kids into materials and subjects that they simply aren't ready for or interested in because of the grade-level label.

Children are assumed to learn better with children who share the number labels of age and “grade level,” rather than in groups with shared interests and similar abilities, and rather than taking advantage of multi-level classrooms in which older children can teach younger children.

Learning to Read in Lockstep with our Peers

Babies don't learn to walk and talk at the same age. Toddlers don't achieve toilet training at the same age. Is it realistic to expect all children to learn to read at the same age?

The long-term results sought by parents and educators should be young adults who can read critically and who enjoy reading for entertainment and education. Although awareness of problems along a child's way to this goal of course is helpful to alleviating those problems, it is not necessary or even helpful to constantly compare children to one another or to some arbitrary idea of exactly what “level” they have achieved at any given moment in their school career.

Rather than worrying about reading “level,” we should be asking questions such as, does the child feel that he is being welcomed into the reading “club”? Does she enjoy reading? Why is he or she reading?

Some schools hold to rigid curricula based on imparting knowledge largely through reading and measuring knowledge largely through written tests, and late readers in such schools often fall farther and farther behind. Education professor Laura Justice worries because one-third of all fourth graders in the U.S. “lack basic reading skills,” with a much higher percentage of poor children facing this lack. She posits that early intervention is necessary because these kids can never catch up.

However, homeschoolers, particularly unschoolers, are a giant experiment in allowing children to learn to read with their own timetable, as children learn to talk and walk and so many other important things in their own time. Although I was unable to find a scientific study about the topic, every single one of the many, many homeschooled children I know or have read about have successfully learned to read, although at ages ranging from three to eleven, and the late bloomers have in every case successfully “caught up” in reading ability to the early readers.

(I am certain that there are some homeschoolers with disabilities who run into reading problems that aren't just “late blooming,” but I don't personally know any. The “every single one” I do know includes kids who have been diagnosed with dyslexia, which has impacted the kids' ability to spell more than to read.)

The success of homeschoolers allowing children to learn to read at their own pace depends, of course, on the ability to individualize learning and teach one-on-one. Most homeschool parents read aloud to their children, and this practice can (and should) go on for years, even after children have started to read on their own. Because of all this reading aloud, children who are late bloomers still enjoy and learn from books and literature.

New research backs up the idea that later readers aren't at a disadvantage: University of Otago researcher Dr. Sebastian Suggate has shown that children who begin to learn to read at age seven soon catch up to children who begin to learn to read at age five. Other studies have shown that many reading difficulties can crop up when reading is taught before a child is ready, so an earlier start date in school is a bad idea. Finally, education critics point out that developing lifelong readers is very different from just teaching a child to read; despite all the emphasis in school on the three R's, research shows that 20 million people in the U.S. can't read, another 40 million cannot read well enough to keep up with current events through reading, but far more prevalent are the millions and millions of adults who can read but don't read.

Measuring Reading Grade Level

Of course, if we allow our children to learn to read at their own pace, that will make a mockery of the so-called grade-level measurements on their reading ability, but those measurements are questionable in any case. The precision with which “reading grade level” is reported belies the methodology of the measurement.

A reading evaluation that is actually useful is having a child read material silently and then discussing it with him or her. Of course, this evaluation is a bit harder to achieve in mass factory-schooling situations, and a lot harder score with a number—but I've been a classroom teacher and a parent, and I know that teachers and parents can develop a pretty good sense of how well kids are understanding what they read.

Besides, firm numbers are really good for comparing kids. But comparing kids is really bad for nurturing true learning.

Graded Curricula

Homeschoolers are lucky in that they can easily follow kids' interests rather than rigid curricula, and I understand that interest-based learning is harder to achieve in large classrooms. Still, schools can and should move away from rigid graded curricula by looking to preschool and university models. In preschool, lots of materials and activities are strewn about, available to children, and kids enjoy free time to choose among them. At other times during the preschool day, the kids are all gathered together for group activities. Few preschools spend time on "evaluation," instead, emphasis is on exposure, exposure, exposure... In universities, courses and seminars have prerequisites but (usually) not grade labels. It makes sense to ask kids to take Elementary Algebra before taking Advanced Algebra, but it doesn't make sense to ask all kids of a particular age to take Elementary Algebra. (As a private tutor, I have worked with kids who don't truly understand fractions, percents, or even multiplication and division, and they have been placed willy-nilly into Algebra classes!)

Must Classmates Be Agemates?

Parade magazine recently ran a report called “The End of Grade Levels?” Elementary and middle-school students in a Colorado school district will not be assigned to grade levels based on age, but will instead fall into multi-age levels based on what they already know. They will move up as they master new material.

According to the article, education experts say that this system works better with how children actually learn, and the system has already been proven a success in Alaska. However, the article states, many administrators and district personnel in other cities and states are afraid to try this “radical” “new” idea.

To them, I say:

(1) It's not radical. Multi-age groups are more common than not. Again, look at many preschools and universities. Look at families and clubs and scout troops.

(2) It's not new. In the small schools of the past, multi-age classes were common (think of the one-room schoolhouse).

(3) It's not necessarily going to unpopular with parents (as apparently many educators worry). The poll that accompanies the Parade article reports that 77% of all people think that ending grade levels (or adopting multi-age levels) is a good idea.

(4) Even if some parents are nervous to try a new educational practice, surely it is the job of educators to educate parents, tell them it is the better choice for learning, and explain why.

I have seen many, many good ideas pop up in education, only to fade away (or be stomped down by the system). But any one school or district can use ideas that work and make good choices for its students!

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*Unschoolers are those homeschoolers who do not generally use the methods or materials of schools.

This Just In: TV Doesn't Rot Brains!

2010-05-12T22:17:00.000-07:00

For several decades, experts on parenting urged us to limit our children's television viewing. Many criticisms have been leveled at that most ubiquitous source of information and entertainment: TV is supposed to lead to unhealthy, under-exercised, materialistic children hooked on eating the sugariest cereals and the sloppiest (AKA juiciest) burgers, hooked on owning the latest toys and electronics gear, hooked on passive reception rather than active participation.

No doubt about it, TV can lead to or at least exacerbate an unhealthy lifestyle or a materialistic worldview. But a lot of other things can, too. And, let's face it, many people of all ages manage to enjoy TV and still stay physically active... many manage to tune out the commercials and hold onto their own values.

Another charge levied at television is that it rots our (or at least our children's) brains.

For years, this idea seemed to be backed up by scientific studies. As Misty Harris of Canwest News Service points out, the negative link between TV viewing and performance on cognitive tests has been shown many times over. However, a new research study proves, once again, that correlation does not necessarily mean causation.

Harris reports that the new study looked at more than 3,000 children between ages five to ten. Co-authors Abdul Munasib and Samrat Bhattacharya took into consideration parental ambition, family structure, and household income, as well as television viewing. When adjusted for these factors, the correlation between TV viewing and test scores vanished. Munasib and Bhattacharya conclude that it is parenting, not TV, that negatively or positively affects children's scores.

BBM Canada and A.C. Nielsen Company track children's viewing; recent statistics state that North American kids ages two to eleven average about three hours of TV per day. Many pediatricians, education experts, and other adults point out that, even if the viewing itself isn't harmful, they are concerned about what the kids AREN'T doing, that they COULD be doing, instead. That is a good point—although a lot of kids probably multi-task during some of those hours. (Whether or not multi-tasking is a good thing is an entirely new discussion topic!)

Some families who strictly limit TV time manage to churn out adults who watch enormous amounts of television (perhaps, in some cases, in a kind of backlash against the strict rules of their childhood), and some families who have no limits on television viewing manage to churn out active, involved adults. Clearly, as in so many things, there are no easy answers—and no substitute for good parenting.

Sleep, Baby, Sleep

2010-04-27T08:13:00.000-07:00

Many parents worry about getting their infants to “sleep through the night,” probably genuinely worried about the child's well-being along with their own good night's sleep. People reason that they want to train their children to sleep at night and wake in the day, rather than allow them to mix up the two. Some people even worry about “spoiling” their babies!

One tool used by some parents to achieve this goal is letting their babies “cry it out.” I know that, when I was a young parent, I was advised to let my babies cry. “It works!” I was told. If I answered my baby's cries, I was warned, I would be “training” her to cry MORE at night.

Another school of thought has always been that we should answer our infants' cries and at least attempt to soothe them. Attachment parenting, breast feeding “on demand,” the family bed—all these time-honored and widely-used (by which I mean world-wide) practices are touted as being better for baby and parents. (This is the route I took.)

A new study has been released that claims one of the two viewpoints as clearly better for baby. According to Penelope Leach, babies should not be allowed to cry themselves to sleep, because high levels of the stress hormone cortisol develops in infants when nobody answers their cries. When babies are left alone to cry repeatedly, over long periods of time, Leach says, the cortisol can become toxic to their brains.

There are times when babies cannot be soothed. This seems to be particularly true of “colicky” babies. I was lucky enough not to have this problem very often—there were only a handful of times parenting my three daughters when teething pain (or something) made them inconsolable. However, my understanding of Leach's writing is that a baby crying while being held, sang to, and soothed is much better off than a baby crying alone, unanswered, and learning that she or he will not be answered.

Still, it is incredibly stressful for the parents to hold a screaming baby. I remember the advice given by John Holt, education reformer and writer: he suggested that, if a baby's fed, burped, clean and dry, but is still crying, the tending parents could wear earplugs so that she or he can hold the baby with a calmer demeanor, which is inevitably better for both parent and child.

Value of Sleep to Memory

Jonah Lehrer and Ed Yong report that dreaming (REM sleep) is very important to the process of storing long-term memory. Apparently we replay our memories as we sleep, which reinforces them. However, as you know, dreams are always different from real life—and odder. Speculation among scientists is that the weird vibe of our dreams may be from our attempts to make new connections between various events and knowledge.

Erin Wamsley from Harvard Medical School did a study in which 99 volunteers worked with a complicated visual maze. They learned to reach a specific landmark after being dropped into the maze in a random spot. Five hours later, the volunteers were retested. Generally speaking, the volunteers did better in the retest, but those who stayed awake tested on average only 28 seconds better. The volunteers who took a 90-minute nap averaged 188 seconds better! And those volunteers who reported that they had dreamed about the maze did better than average.

These results speak to the contrasts between school systems I explored in my last post. I reported that students in Finland score highest in the world in most subjects although they attend school fewer years, days, and hours than other students, and have less homework. South Korean students score well, too (and best the Finns some years, in one or two subjects), but they have much more stressful lifestyles. One study showed that South Korean students average one hour less sleep than their American counterparts. I assume that Finnish students, with their more relaxed schedules, get plenty of sleep.

It seems to me that Wamsley's research findings show one reason why Finland's more relaxed system works so well: although we know that we can learn by consciously practicing, rehearsing, and self-testing (and South Korean students get good results with lots of extra studying), we are now finding that we learn even better when we give our brains time off to sort through concepts and events—and we give our brains time off by sleeping.

By the way, Yong reported on two similar research studies that showed that creative problem solving improved if subjects had a chance to “sleep on it.” Non-REM sleep didn't help too much, he reported; it was REM sleep (dreaming) that helped subjects draw connections between ideas and leap to a novel solution.

What to Do

It's clear that parents should pick up, sing to, or otherwise try to soothe a crying baby. It seems that a stressed-out older child who is trying to cram before a test or solve a complex math problem may need the same soothing message: Sleep, baby, sleep.

Finnish Education in the News

2010-04-09T23:13:00.000-07:00

Recently I read two different articles—and watched some video clips—about the high test scores of Finland's students, including their math and science scores. Apparently, the people at the Wall Street Journal and at the BBC are wondering why the Finns score so high.

The counter-intuitive findings include the fact that Finns start school later than do most countries' students. Kids in Finland don't start school until age 7, and much of the rest of the developed world starts students off at age 6, 5, or even earlier. (A majority of American kids, around 64%, go to pre-school by age 4. And many pre-school programs are more like "real" school than U.S. kindergarten programs were ten years ago, let alone 40 years ago. That means that most American kids go to school at least 3 years before Finnish kids.)

After starting late, Finnish schools also have the fewest class hours in the developed world. They assign less homework than schools in most countries, and they have far less standardized testing.

And wait, there's more:

Schools in Finland are more informal and relaxed than schools elsewhere, with kids walking around in their stocking feet, addressing teachers by first name, and even occasionally being allowed to sleep in class. Primary and secondary school levels are combined so that students don't change schools at ages 11 and again at 13, and they don't even change teachers often—the teacher interviewed had had her students for five years.

Perhaps most important, schools in Finland are based on a collaborative model that has little or no competition. Children are not separated by talent, and kids who have conquered topics are encouraged to help those who are struggling. (With multiple teachers in the classroom, kids who struggle also get extra help from teachers.) In Finnish schools, no child IS left behind.

All of this makes the Finnish public schools sound more like American homeschools than American public schools. Fewer hours, more informality, stronger relationships with fewer adults (one teacher even said she was like her students' "school mother"), more sharing and caring, less competition.

And Finland's students are at the top of world rankings.

One of the headlines claimed "Less is more." But of course, that depends on less what! As we have seen in various research studies, creativity flourishes in environments with collaboration, and wilts with competition, learning occurs more deeply when there is opportunity to teach as well, and is stifled by constant evaluation through standardized testing. The Finns have arranged their society and education system to have less of the negatives—but also more of the positives.

Other benefits of Finnish schools emphasized in the articles and videos are trust and independence. The school directors and teachers feel that their society values and trusts them. They aren't beholden to politicians, and they don't have to prove themselves constantly to non-educators.

Again, this is more like American homeschools than American public schools. I would also point out that Finnish teachers apparently trust their students and their students' parents more than most teachers in the U.S. trust theirs—which demonstrates once again that trust engenders trust in a two-way-street or even in a pay-it-forward phenomenon.

South Korean Schools in the News

Another, very different, sort of school system that made the news recently is the South Korean schools. Apparently, when President Obama visited the country in November, he had high praise for the nation's high-scoring students.

Yet both government officials and parents interviewed on the BBC program said that they were surprised by the praise, because in their minds, there is a problem with South Korean schools. The students are so highly stressed by academics, after school academic tutoring and classes, a lot of additional homework, and little sleep. All of it is high stakes as the students struggle to get into the best universities and therefore the best careers. Literally, the rest of their lives rest on their exhausted young shoulders. There seems to be some concern that the kids will max out on all this study—that maybe, eventually, there will be a kabloo-ey moment.

Of even more concern, apparently, is that most of the work and effort is going into mere memorization of information. Some South Koreans worry that students are not being challenged with higher-level thinking, creative problem-solving, and real-world critical thinking skills. These students may not be the innovators, the shapers of tomorrow. Some worry that all that work, and no play...will be for nothing.

Myths of Creating Creativity

2010-04-06T17:58:00.001-07:00

In an earlier blog post, I explored several studies about creativity and concluded that children should have lots of opportunities to play in unstructured ways outdoors and with traditional toys such as blocks and art materials, and that they shouldn't be hurried into formal academics such as reading instruction and paper-and-pencil math. Creative thinkers need situations in which they can uninhibitedly brainstorm ideas and make mistakes.

Pictured here are creative tributes
paid to creative musicians.

Today I will look at a research study that was done with adult subjects (some time ago). Not only does it confirm the same findings, it also shows us that many of us hold onto certain myths about creativity.

Teresa Amabile of Harvard Business School headed up the ambitious study, which dealt with 12,000 daily journal entries from 238 people working on creative projects for a variety of companies. The companies were in industries such as high-tech consumer products and chemical industries. None of the study participants knew that her focus was creativity.

For her report in her own words, you can read Fast Company, but I sum up her myth-busting findings here and then relate them to children and education.

Myth 1: Some people are creative, others aren't. And that's just fine.

Amabile says that many adults, including business managers, assume that, although people in the arts and in fields like advertising need to be creative, people in, say, accounting don't. However, Amabile finds that, in reality, all professions benefit from creativity. Further, she points out that anyone with normal intelligence is capable of creativity.

My last post confirms the ubiquity of creativity in children. Teachers and parents should know that all kids are creative geniuses and that all jobs and hobbies benefit from creativity. Amabile warns against “ghettoizing” creativity, but I would further warn against “pedestal -izing” creativity. That is, we shouldn't think, “Oh, so and so is so creative. I would never be able to think of that!” or “Such-and-such's child is so creative. Well, it's no wonder, with parents that are artists! My kids aren't so lucky!” When we categorize creativity as out of our own reach (which it isn't), we easily slip into the idea that it may well be out of our child's reach as well.

Myth 2: Extrinsic rewards motivate creativity.

Amabile reports that adults assume that they themselves are directly motivated by money to work hard, be creative, and solve problems. Also, managers tend to operate on the assumption that the almighty dollar has this motivational power. However, although adults are more creative when they work in an environment that makes them feel valued (and being underpaid may well erode this feeling), day-to-day work is not tied to thinking about extrinsic rewards.

She further finds that adults who do think a lot about rewards—people who are worried about their bonuses, for instance, or about a potential raise—aren't doing creative thinking. They tend to get risk-averse, which is definitely a creativity killer. If you can't risk making a mistake, you can't risk having new ideas.

Kids in traditional schools are generally rewarded with grades rather than money (although some parents and even the occasional school tie cash rewards to grades). These extrinsic rewards do not motivate greater creativity. In fact, worry about grades, like worry about bonuses, distracts from creativity and even directly lessens it by making students risk averse.

Myth 3: People are more creative when working under time pressure.

People tend to say about themselves that they work best under deadline pressure. They even claim that such pressure makes them able to be their most creative selves. But the 12,000 days of journaling proved that the opposite was true: people were least creative when under time pressure. There was, in fact, a lingering effect of deadlines: people were less creative during times of great time pressure plus two days afterward.

According to Amabile, creativity requires “an incubation period.” People need to “soak” in a problem, need time for their unconsciousness to grapple with it, need time to allow ideas and possible solutions to “bubble up.” This is why a really tough problem can often be conquered only after a time period of working on it that is followed by a rest or break—sleeping on it, or taking a walk and coming back refreshed.

Amabile notes that, when there does have to be a deadline, if the deadline is genuinely important rather than arbitrary, people can rise up to the occasion and act creatively to solve problems, even under the gun.

Children, too, need to be doing work they feel is important, with either no deadlines or genuine deadlines. They should be able to settle into a project, steep in a subject, soak in a problem...and take the sort of breaks that help all of us.

Myth 4: Fear and sadness often give rise to creativity.

Although there is some research that indicates a somewhat higher incidence of depression in creative geniuses, Amabile's research an association between positive emotions—joy, happiness, and love—and creativity. On the other hand, she found that fear, anger, and anxiety tend to tamp down creativity.

When people feel happy one day, they tend to make creative break-throughs the next day (after the overnight incubation period we discussed).

Although educators don't, I'm sure, set out to cultivate fear and anxiety in their students, a study of traditional school policies does indicate that, in actual fact, schools focus their motivational efforts on fear and anxiety more than on happiness and love.

Myth 5: Competition helps bring out creativity.

Amabile reports that many companies deliberately foster internal competition in order to motivate excellence, creativity and problem solving. Especially in high-tech industries, she says, managers often believe than innovation is the result of such competition. However, her research shows the exact opposite: it is collaboration, not competition, that encourages creativity.

During collaboration, people share and debate ideas, but within a competitive structure, people usually stop sharing information. The result? Fewer problems are solved, less creativity is expressed, fewer discoveries are made.

By and large, traditional school policies encourage competition, not collaboration. There is a common word used for student collaboration within schools: cheating. Grades, GPAs, and class standings are the trappings of a system of competition...and the focus on competition is even more clear when we realize that no teacher is encouraged or even allowed to give every student an A. What if an excellent teacher is able to motivate all his or her students to master the curriculum? They all deserve As, right? Apparently not. Apparently there must be some way to discriminate between the students. Grading on a curve makes sure that some kids' gains are other kids' losses.

Myth 6: Streamlining, downsizing, and restructuring foster creativity.

In the businesses that Amabile studied, downsizing was often an economic reality. However, creativity does take a hit during the process, despite what PR departments and managers often say. This is an obvious result of Myth 4, above: fear and anxiety tamp down creativity and distract from problem-solving. Amabile found out that the actual negative effect is even worse than she imagined, because anticipation of the downsizing was worse than the actual downsizing, and because the effect lingered long after the event. (For example, five months later, creativity was still down.)

There is no strong correlation between downsizing in the business world and the education world. However, we talked earlier about anxiety about bonuses and raises. Surely downsizing and the resulting worry about keeping a job at all represent “high stakes” for adults. These days, education is filled with high-stakes testing such as high-school-exit-exams. Could it be that we are creating higher stakes, and therefore higher anxiety, with the result that creativity and education actually go downhill?

Enough with myths. What should parents and teachers do?

According to my reading of Amabile's results, it looks as if traditional schools were engineered to diminish creativity rather than maximize it. Amabile's recommendations to business managers and CEOs provide a blueprint for improving education, too.

She writes, “People are most creative when they care about their work and they're stretching their skills. If the challenge is far beyond their skill level, they tend to get frustrated; if it's far below their skill level, they tend to get bored.”

She goes on: “[W]hen people are doing work that they love and they're allowed to deeply engage in it -- and when the work itself is valued and recognized -- then creativity will flourish.”

Smart Babies and Genius Toddlers

2010-04-04T09:45:00.000-07:00

For some reason, there has been a common thread running through my life the past few months. In discussions with adults on internet forums and in real life, my idea that all kids are born “learning machines” has met with disagreement. People don't say it right out loud, but their hundreds of words seem to boil down to the idea that many kids just aren't smart.

Yeah, there are genetic differences among people. Yeah, we all have our own talents and weaknesses—we are not just born as blank slates, ready to be programmed by parents and teachers.

But I keep going back to what I know: I have never (or at least almost never) met a baby or a toddler that didn't seem very, very smart.

NOTE: Presumably some babies are born with the sort of genetic glitch or birth trauma that really impairs their ability to learn and function. I may have met one such, although watching him made me think that he might be learning quite a bit but unable to express it through action or language because of his physical disabilities.

Little kids learn language, or languages, in great big gulps. As they learn about how things and creatures and people act in the world, they create a sort of folk biology, physics, and psychology. They say incredible things that show just how much they absorb of adult words and attitudes—this is the little-kids-as-sponges theory—AND that show how fresh and original their thinking can be—this is the little-kids-as-one-of-a-kind-potential-geniuses theory. All of them (or almost all of them) are, I maintain, unbelievably good at what they do: learning.

Here is an old, old study (well, not as old as I am!) that is still quoted as relevant:

In the 1960s, educators George Land and Beth Jarman gave 1,600 3- to 5-year-old kids a creativity test used by NASA. They retested the same kids five years later and again ten years later. At the same time, they gave the same test to a large group of adults over the age of 25.

Here's what Land and Jarman found (according to their findings published in 1968):

3 – 5 year olds – 98% scored at genius level

8 – 10 year olds – 32% scored at genius level

13 – 15 year olds – 10% scored at genius level

adults – 2% scored at genius level

We are born creative. Pretty darn near all of us are born creative geniuses. We either learn not to be creative, or something in our mental or social development shuts off our creativity.

I touch on this with an earlier post on creativity studies. Soon I will post some additional studies that deal with creativity among adults. But for now, I leave you with one simple, and hopeful, finding:

According to Johah Lehrer, undergraduate college students were asked to imagine school being canceled and a whole unplanned, uninterrupted day of freedom stretching before them. They are asked, “What would you do? Where would you go? Who would you see?”

One group was given this scenario with the first sentence, “You are seven years old.” Their imagining of a free day is as their childish self. The second group was given the exact same scenario without the harkening back to age seven; presumably these students imagined their day of freedom at their current age, 18 to 20 or so.

Ten minutes after the imagination task, the subjects were given tests of creativity. The young adults who had a few minutes earlier imagined themselves at age seven scored far higher in creativity!

This study was done by psychologists Darya Zabelina and Michael Robinson of North Dakota State University. To sum up their findings in one simple recommendation:

To unleash your creativity, just imagine yourself as a little kid.

Top Ten Reasons to Minimize (or Even Get Rid of) Standardized Testing

2010-03-19T14:23:00.000-07:00

10.Standardized tests are said to be “objective” but are not.

Even on a multiple-choice test that is scored by a machine, the decision of what to include on a test, how to word test items and possible answers, and which answer is correct, is very much subjective. Some tests or test sections are not machine-scored fill-in-the-bubble; the scores on these are not only subjective, they are scored by poorly paid, under-trained temporary and part-time workers who are under major time pressure to score items quickly. Read about one scorer's experiences here.

9. Minorities and females under-perform.

According to Stanford University's “Stereotype Threat” study (among others), females and minority students perform worse than their actual achievement or ability would warrant, when compared to white males. (White males perform less well on math tests when they are told that their scores will be compared to Asian males' scores.) This under-performance is not because the tests are biased (although they are)—but because of anxiety caused by the stereotype that these groups perform at a lower level. Read more here.

8. Students from lower socio-economic groups under-perform.

No matter how carefully a test is constructed, it is going to have biases. Children with a lot of experiences outside of school and a lot of attention from parents score higher because they bring so much more previous learning to the classroom and the test. And kids with a lot of experiences and involved parents tend to be from middle-class and upper-class families—for the simple reason that adults in such families have more money to spend on their kids—art, music, and dance classes; travel; sports—plus more time and energy to spend with their kids. To find out more, read here.

7. Bad test items punish the most thoughtful and the most creative thinkers.

It is really hard to make multiple choice questions that are challenging, fair, and have only one unambiguous answer. Quite a few test items, therefore, have more than one answer that could be considered correct—especially for those students who “think outside of the box.” For more on this, read here.

6. Standardized tests have little predictive power.

Many colleges and universities give SAT results and other test scores very little attention, because there is only a very small correlation between higher scores and success in college. Some colleges and universities see so little value in test scores that they do not require testing, and almost all colleges and universities drop their test requirements for transfer students. Read more here.

5. High-stakes tests encourage cheating—even from teachers and administrators.

Many standardized tests are high-stakes. With school funding and ranking on the line, administrators tend to put pressure on teachers so that they will put pressure on the students. In some districts, teacher salaries and even their jobs get “left behind” if test scores don't go up. With money concerns tied up with the tests, there is temptation to cheat. Read more here.

4. Standardized testing takes up too much time out of schools' instructional year and out of kids' educations and lives.

It used to be that there was very little standardized testing, and most of it was of older students. Even today, many countries do little testing at lower grade levels. However, in the U.S., standardized testing starts early and is frequent, with some districts testing even 6 year olds, and some yearly tests taking up to two weeks at a time—and that's just for the administration of the test! (Test prep takes more time.) Even SAT tests take way more time, these days, than they used to, because it is common for students to sign up for test-prep courses and to take the SAT test several times. Mind you, all the hours spent taking tests could be used in other ways. Read more here.

3. High-stakes testing causes stress and anxiety for all involved.

In #5 above, we mentioned that tests can be high stakes (think money) for schools, administrators, and teachers, but what about students and their parents? In addition to the pressure put on students by schools and teachers, they often face high stakes like graduation, college acceptance, college credits, and scholarships (which can be translated into money, money, money, and money). With high stakes, test anxiety is natural—but anxiety not only causes lower scores (see #9 above) but also gets in the way of true learning. Read more about negative emotional effects of testing here.

2. Standardized tests—particularly those that use multiple-choice format—don't measure the most important facts, concepts, or abilities.

Because test scoring mandates that students are differentiated from one another, the test items do not cover just the most important facts that most teachers focus on—because “too many” students get those items correct. Therefore, tests include many less-important facts. Unfortunately, some teachers and schools, in an effort to boost test scores, then start to teach those facts as if they were important. This teaching to the test can water down curricula in unintended ways.

Also, standardized tests are almost useless in measuring true understanding, positive or negative attitudes about a subject, problem-solving abilities, and upper-level thinking skills. Because test scores have become very important to schools, teachers, parents, and kids, true understanding, problem-solving, and high-level thinking have all been reduced in importance in education.

Read more about this topic here, or in the PDF file “The Case Against Standardized Testing,” by Alfie Kohn. (Linking doesn't work for a PDF file, but you can Google it.)

Finally, here is the Number 1 reason to limit or eliminate standardized testing:

1. Low test scores rarely lead to improvements, and the very structure of testing ensures lots of low scores.

One rationale for giving tests in the first place is to hold schools accountable for educating children, and to show teachers and parents weak areas that need improvement in individual children. Given that reasoning, we would expect to see the feedback of low scores in certain academic areas motivating the school to experiment with new instructional methods and the government or school district to provide extra help to the school in that area. In the case of just one particular student, we would expect to see remediation, again by changing the learning situation, trying new modalities and techniques, and by providing additional time, effort, or personnel to address the deficit.

However, low scores really just become an excuse to punish. Schools with low scores tend to lose resources rather than gain support. Students are often put into “lower” classes with less accomplished students and (often) teachers, thus perpetuating the lack of success.

We do not see feedback from standardized tests used for improvements in schooling, teaching, or learning because, it turns out: Tests are just a way of ranking students and schools.

The very design of these tests as norm-referenced instruments requires that half of the students taking the test are judged “below average”—no matter how accomplished they may be! The need to appear useful, to seem to be measuring something worth knowing, pushes test makers to deliberately make tests that will create a wide range of scores, and of course these scores are arranged on a bell curve of success at one end, failure at the other, and mediocrity a large bulge in the middle. Read here to find out more.

What good does it do to find out where children are ranked? There aren't many good results from ranking kids, but there are plenty of bad results for individuals and therefore society: Anxiety. Low self-esteem. Lack of motivation.

Some of the worst problems come from the simple fact that testing begins so early—when many of the students being tested are not ready to do the tasks on the test. The age of reading readiness varies, and the ability to conceptualize number does not necessarily coincide with readiness for paper-and-pencil arithmetic. Young children who aren't developmentally ready for formal academics are pushed into a downward spiral of negative expectations by early and frequent evaluation.

As a thought experiment, imagine kids facing “standardized tests” about walking and speech when they are just babies and toddlers. How would it be helpful to rank the babies and infants according to their accomplishments at age 9 months, and 11 months, and 13 months, say, for walking, and 16 months, 20 months, and 24 months, for talking? Would that help parents and babies or only lead to more stress and quite possibly walking and talking “disorders”?

***

Standardized testing has grown to be big business! It has taken on a life of its own in the minds of politicians and journalists and society at large—but it is based on an outmoded theory of learning rather than the latest findings in child development, psychology, cognition, and education.

Standardized testing as it exists today does more harm than good, and it should be greatly limited. Or even, quite possibly, abolished.

Research About Generosity and Fairness—

2010-03-13T08:51:00.000-08:00

What's the Connection with Grading?

It has been well documented that praise and other rewards can detract from learning. I deal with the down side of praise a bit in my post on “Mindset”; books and articles by Alfie Kohn go into much deeper analysis of praise and all sorts of rewards, detailing research carried out by Mary Budd Rowe, W. U. Meyer, and others.

Some recent findings by researchers from Caltech and Trinity College deal with people's perceptions of fairness, but when considered along with earlier findings, I think there are some implications for educational practices such as evaluating kids with letter grades.

Bear with me...

The Background

First, the new research is designed in response to research on what is called the ultimatum game. In this game, one person (the proposer) is given $10 and is told to share it with another person (the responder). The proposer can offer any amount of money (even just $1), but if the responder does not accept the offer, neither of them gets any of the money. Apparently this game has been done many times with many different populations, and the results are nearly always the same: almost everyone offers around $5 (an even split), and responders are happy to receive that even split. In the rare cases that proposers offer less, responders almost always reject an unfair split—even though they know that they will end up with no money at all. In other words, although it would make sense to accept $2 rather than to reject it and get nothing, almost everyone faced with such a choice acts irrationally; we apparently value fairness even more than a chance to get “free” money.

There are several possible reasons for the overwhelming popularity of even splits in the ultimatum game, and no doubt a variety of conscious and subconscious considerations go into people's behavior. One suggested reason is that we have a hard-wired wish for equality and fairness. The new research tests this idea.

A New Experiment

Subjects were chosen randomly to either get a $50 endowment at the start of the experiment or to get no money to start with. All the subjects were placed into brain scanners and then given cash rewards of $5 to $20; furthermore, the subjects were told about rewards that were given to a stranger--sometimes more money than they themselves received, and sometimes less.

The results were read from the brain scanner—specifically, the researchers recorded the reaction of the reward circuitry of the brain (the ventral stratium and VMPFC). In earlier research, scientists recorded what people said and did—fully knowing that these words and behaviors were at least partially under people's conscious control. In this new research, scientists were able to see what people's “brains liked,” perhaps getting a glimpse at how humans are “wired.”

What were the findings?

The subjects who started with $50 were not as excited when given another $20 as those who started with nothing. That makes sense; we all know that money is relative. However, those who started with $50 were very excited when a stranger who started with nothing was given $20.

In other words, people who were already assured of money themselves were happier to see a stranger go from nothing to $20 than for they themselves to go from $50 to $70.

It is possible that most of us feel uncomfortable in the face of inequality—if, that is, we know that the inequality is due to random chance. That would suggest that humans are naturally motivated by fairness, aside from any social norms. I've known a lot of little kids in my life, and little kids often seem VERY interested in fairness, even at a seeming cost to themselves.

The Selfish Side of "Fairness"

Here's the twist that may have import regarding the educational practice of giving letter-grade evaluations: if people are given a test (any sort of test) BEFORE they play the ultimatum game, the proposers act much more selfishly. They are much less likely to offer an even split; they assume that they were given the role of the proposer based on the test results, so they assume that they deserve more money than the responder.

Over the years I have noticed that letter grades, numerical scores, and test scores get kids riled up if unfairness is perceived—even if what they perceive as “unfairness” doesn't affect them personally, and even if it would seem to benefit them. For example, education reformer John Holt noticed the bad effects low grades had on student motivation and also the bad effects that grades of any kind had on intrinsic motivation; yet Holt was required by the school system he worked in to give grades. Holt decided to effectually rid his classroom of grades by informing all of the students at the beginning of the term that they would all receive As in the course. One might guess that the students would all be dancing on their desks with joy at this news, but most of the students expressed unhappiness or even outrage at the idea. Everyone getting A's, no matter what, they said, would be totally unfair.

I have found that people who are (or were) “winners” in the school system—those who get good grades and high test scores—often get very upset when faced with evidence that grades and grade-point averages do not demonstrate true learning, do not communicate nuanced evaluations of strengths and weaknesses, and do not predict future success. They have very much “bought into” the idea that grades have meaning and that the system that rewards them does so because they deserve the rewards.

The corollary of this, of course, is believing that poor students deserve their bad grades, too. I'm pretty sure many readers are nodding their heads and thinking, “Well, they do.”

But I think of how the whole process starts: how little kids come to school as amazing learners, having already learned a language or two, having figured out stuff about numbers and physics and a kind of folk psychology—and I think about how these kids are socialized, not only by classroom rituals and teachers and classmates, but also by tests and scores and grades.

Little kids like a girl named Jacqui.

Jacqui's weekly reading tests were given by computer. The test program would ask her a question about a story she had read earlier, giving several possible answers in a multiple-choice format. When Jacqui selected an answer, the computer would go on to ask the next question, not giving her any kind of feedback.

Sometimes Jacqui was a little bit slow to read the question and possible answers, or to figure which answer was best. Whenever she was too slow, the computer automatically marked the question wrong and went on to the next item.

At the end of the test, the computer reported her score to her teacher. Even at this point, Jacqui was not told which questions she got right or wrong—in other words, in the entire experience, there was no helpful feedback at all. There was just a numeric score and a letter grade.

And the teacher would look at that grade—an F!—and announce it in front of the whole class, “Jacqui, you got an F on the reading test today! You must do better than that!”

Jacqui, not surprisingly, quickly developed a reading problem. She was only 6.

I maintain that Jacqui didn't deserve her low grades, not one little bit!

The Upshot

I can't help thinking that, if schools had no letter grades and fewer scores of all sorts, things like “group projects” wouldn't be greeted with groans, cooperation would increase as both competition and cheating dwindled, and schools would be nicer places to be.

TV Talk

2010-03-02T21:55:00.000-08:00

In my last post, I discussed some of the research that indicates that babies don't learn language from television, but rather from interactions with people.

In an excellent article on the same topic, Dr. Gwen Dewar explains that any form of one-way communication (adult monologues and storytelling, for example) is less effective than two-way conversations in fostering language learning. The Center for Applied Linguistics reports that even one-way communication, specifically reading aloud, fosters more language learning when done live rather than by way of tape, CD, DVD, or television (Patterson, 2002).

Dr. Dewar goes on to point out that research demonstrates that babies who watch a lot of television in their own native language acquire that language slower than babies who don't. This does not indicate that television somehow makes babies more stupid;* the findings can be explained by the fact that babies with a lot of screen-time have fewer interactions with parents and other people. Dimitri Christakis of the Seattle Children's Research Institute reports that, for ever hour in front of the TV, parents speak 770 fewer words to children (the study dealt with children ages 2 months to 4 years). Children speak less while in front of the TV, too. (June issue of Archives of Pediatrics & Adolescent Medicine.)

And yet...

A woman named Sonja wrote to me from Serbia, reporting that her students often pick up fluent German just from watching TV. This seems to go against the research—but the research I discussed is specific to babies. It seems that toddlers and older children, who already use language fluently (in Sonja's experience, the kids are already bilingual, having learned Valachian and Serbian from infancy**), can and do pick up foreign languages from television.

Is there any research that can back up Sonja's experience?

Yes!

Jaana Jylha-Laide did a case study on a 6-year-old Finnish girl who learned English through cartoons on video (note: it was not television—she had control over repetition and pausing). This girl had no contact with English speakers and no formal instruction. (“Learning by Viewing: Cartoons as Foreign Language Learning Material for Children,” Journal of Educational Television, Volume 20, Number 2, 1994.)

An empirical study of 374 Flemish students found a correlation between more time spent watching English-language television and movies and higher scores on an English proficiency test. On the other hand, listening to music with English lyrics and playing English-language video games did not lead to improved English scores.

By the way, the TV programs and movies those Flemish students watched were subtitled in their own language, which makes me wonder...

Do subtitles help?

An article called “Children's vocabulary acquisition in a foreign language through watching subtitled television programs at home, “ by Cees M. Koolstra and Jonannes W. J. Beentjes, shows that Dutch children in Grades 4 to 6 learn more English vocabulary while watching an English-soundtrack program with Dutch subtitles than by watching the same English-language program without subtitles. (There was also a control group who watched a Dutch television program.)

There is no indication in the abstract about the age of these students and whether or not they had already learned some English in school. In the U.S., students in Grades 4 to 6 are usually 9 to 11 years old. However, in the Netherlands, Groups 4 and 5 include 7- and 8-year-old students. According to AngloInfo, English instruction generally begins in Group 7 (age 10). From this I would guess that the majority of students in the study knew little or no English from previous schooling. (This article appeared in Educational Technology Research and Development, Volume 47, Number 1, March, 1999.)

But subtitles are more useful to adults...

Another study done in the Netherlands was meant to compare children's language learning from subtitled television to previous findings about adult learning from subtitled programming. This study worked with Danish and French as the foreign languages, and students ages 8 to 12. Although children generally learn languages more easily than adults, this study showed less learning in the children than in a previous study with adults. Also, the adults learned better if the foreign language was in the subtitles, not the soundtrack, but the children learned better if the foreign language was in the soundtrack and the subtitles were Dutch. Apparently children with previous formal instruction in the target language did not learn measurably more than children who were new to the language. (“Incidental Foreign-Language Acquisition by Children Watching Subtitled Television Programs,” by Géry d'Ydewalle and Marijke Van de Poel, Journal of Psycholinguistic Research, Volume 28, Number 3, May, 1999.)

These latest findings seem very interesting to me. It's pretty obvious that babies and adults learn languages very differently, each age leaning on its own strengths. School-age children can access some of the adult techniques to learning language, such as reading subtitles, but can generally do so, it seems, less well than can adults. On the other hand, at least some of the children maintain some of the abilities they had as babies, to a greater degree than most adults. Thus they were able to learn with subtitles but did so better when hearing, rather than reading, the foreign language. I find language learning incredibly interesting—first language, second language, by babies and children and adults, through conversation, “immersion,” TV—all of it is fascinating!

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NOTES:

*Some research findings do indicate actual harm from television to very young children. Commercial advertising and attention-jarring quick-edits may cause children to have less ability to focus and other cognitive deficits. (See this and this.) A historical study by Matthew Gentzkow and Jesse Shapiro disputes the idea that TV harms children, but when research studies are inconclusive, I would still err on the side of caution and limit babies' and toddlers' exposure to TV. These varied findings certainly indicate the need for more research.

**As I reported earlier, research shows that bilingual children find learning a third language easier than monolingual children of the same age learn a second language.

Why Baby Einstein can't teach your baby languages

2010-02-22T08:15:00.000-08:00

In my last post, I described some of the benefits of speaking two or more languages. Those of us who are monolingual parents might be tempted to buy DVDs and CDs of songs and stories in other languages and play them for our infants. After all, infancy is when kids learn languages most easily, right?

Apparently, the DVDs and CDs would be a giant waste of money. Babies learn languages, all right, but apparently only from live people. So say the research findings of Lucia French, Ph.D., from the University of Rochester; Catherine S. Tamis-LeMonda, Ph.D., from New York University; Betty Hart, Ph.D., & Todd R. Risley, Ph.D.; and others.

These scientists have found that, although some DVDs, such as the Baby Einstein brand, present pictures of objects as babies hear sentences in the target language about those objects, babies are much more interested in speech that is accompanied by a human face than in disembodied, voice-over speech.

Also, experiment after experiment confirm that the responsiveness of a parent or other human to the baby's sound-making and early speech is the most crucial factor of all in language acquisition.

Most of us know instinctively to talk to, play and interact with, and respond to our babies. These normal parental behaviors provide the environment in which our children learn their mother tongue, as one's native language is aptly called. If we wish to bring more than one language to our babies, but we cannot speak another language ourselves, our only recourse is to arrange playtime (or other interactive time) with someone who does speak that language.

These findings also disprove the rather common belief that children can get language skills in their native language from TV, that cheapest of “babysitters.” Instead of parking a baby in front of a TV while the parent makes a meal, for example, the baby would be far better off strapped into a front pack, backpack, or car seat while the parent cooks—and chats with, and responds to, the baby.

(If you want to read more about bringing rich language experiences to your baby, check out the linked article about Lucia French, above, for some clear, practical tips.)

Another point indicated by the research is that, for the first few years of life, one important criterion for judging a day care situation (day care center, nursery school, baby-sitter, whatever) is how much talk occurs between caregivers and children. This is one reason why a low caregiver-to-child ratio is important.

There can be a huge disparity in amount of speech heard by children in various homes and child care arrangements—with some kids hearing 3 million words a year and others hearing 11 million words per year. Children in language-rich homes can achieve better vocabularies by age 3 than the parents in language-depressed homes have!

To sum up:

Babies learn languages from other humans. Not TV. Not CDs or DVDs.

One important factor in babies learning language is how much those humans talk to him or her.

The most important factor in babies learning language is the humans responding to his or her babbling and early words.

By the way, there is an entire chapter on this in the 2009 book Nurture Shock: Thinking About Children, by Po Bronson and Ashley Merryman. I haven't read this book yet but would love to! Most of the reviews are glowing.

Notes from a Mono-Glot

2010-02-07T23:26:00.000-08:00

I was pretty motivated to learn Spanish when I was in school. Having traveled in Mexico with my family, and even just living in Southern California, I figured it would be useful. Helpful in getting jobs. And just all-around cool.

Europeans I met in fiction all spoke multiple languages, and being a polyglot automatically made them seem smart.

So I was motivated.

However, exposure to Spanish in elementary school, two solid academic years in junior high, four years in high school, and several more in college—and straight As in all these courses—yet all I can muster when asked if I speak Spanish is “Solo un poquito.” [Spanish – Only a little.]

Quel dommage! [French – What a pity!]

As a consequence of my own experience, I am not a big fan of “learning” a foreign language through worksheets, vocabulary tests, and conjugations on the blackboard. I've seen successes who have learned languages in school, but they generally achieved fluency through immersion programs in another country—situations in which they HAD to learn, or be hopelessly confused for months. A few success stories have been exceptions; I know a woman who supplemented her Spanish courses with Spanish-language soap operas and volunteer positions working with Spanish speaking adults.

Basically, it seems that children and adults who have real, actual reasons to learn another language do, and those who don't, don't.

Real, Actual Benefits of Bilingualism

There are several non-obvious benefits to speaking more than one language, research now tells us. (Yeah, I can't help wishing I had tried the Spanish soaps!) Here are a few highlights of recent findings:

Bilingual people find it easier to learn another new language than do those who only speak one language. In other words, it's easier to go from 2 to 3 than to go from 1 to 2.

Babies in bilingual homes retain an ability to figure out when speakers have switched languages based on visual cues only, but babies in monolingual homes lose the ability by age 8 months.

Even those who have seemingly “lost” a second language (say, someone whose exposure to a second language ended at age 4) still retain important knowledge that allows them to easily relearn the language.

Being bilingual helps slow certain aging processes of the mind.

Yeah, that last one is a doozy, isn't it?

Biligual to Polyglot
Researchers including Northwestern University's Viorica Marian found that children who learned two languages in their own home—either English and Mandarin or English and Spanish—learned more than twice as many vocabulary words in another language, unrelated to either Mandarin or Spanish, as did those who learned only English in their home. Marian believes that the bilingual advantage translates to other sorts of language learning as well.

Visual Input
Apparently all babies can tell when speakers switch to another language from watching the rhythms and shapes of the speakers' mouths—even when there is no audio to go along with these visual cues. Babies as young as four months old, whether from bilingual or monolingual homes, notice a switch. However, only the bilingual babies keep the skill. By eight months of age, babies from monolingual homes can no longer use visual cues alone to notice a shift in language. This report comes from the University of British Columbia and researcher Whitney Weikum with others.

Not Lost, After All
According to Jeffrey Bowers and other researchers from the University of Bristol, even unused languages are retained to some extent in the brain. The team studied native English speakers who had learned Hindi or Zulu as children when living abroad but no longer used the languages. The English speakers were tested to see if they still recognized vocabulary in the neglected languages. They didn't. Then they were trained to distinguish phonemes (sounds) of the neglected language—phonemes that were deliberately chosen because native English speakers find them very difficult to recognize. The English speakers with childhood exposure to the languages were able to quickly relearn and recognize the problematic phonemes.

The Doozy
Dr. Gitit Kavé and others at Tel Aviv University discovered that senior citizens who speak more languages test better for cognitive functioning. Being a polyglot isn't a surefire wonder-cure against aging minds, but multiple languages may provide a sort of exercise for the brain. Kave warns that causation has not been proven, but goes on to say that “[o]ther languages are good for you at any age. They allow for a flexibility of thought and a channel for understanding another culture better, as well as your own...”

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Well, I certainly wish my now-adult children and I had all these benefits coming, but although we have dabbled with Spanish, Italian, and ASL, we seem to be pretty solidly monolingual. However, younger parents, teachers, and homeschool teachers might consider these benefits of bilingualism. It would be nice if people in the U.S. had language learning opportunities earlier and better than those afforded me.

Wunderbare Idee! [German – Wonderful idea!]

Go Deep

2010-02-02T22:48:00.000-08:00

There honestly is too much to learn these days. In this “information age,” we who are lucky enough to own personal computers (about 76% of households in the U.S.) are awash in an ocean of information (and, unfortunately, misinformation). Topics as specific as steampunk clocks, Chilean holidays, and Norse runes—and even as esoteric as quarks and preons—can be easily researched in seconds in our own homes.

This enormous amount of easily-available information presents a problem for students and particularly teachers—what, specifically, should be learned and taught?

Pity the poor high school teachers with subjects such as World History or Biology: they can only hope to scratch the surface of their topics in a single school year. Many people have asked if it is best, under these circumstances, to try for breadth or depth of learning and teaching.

In other words, should Biology I teachers (for example) try to skim over all the topics of modern biology, or should they go in-depth on fewer topics?

Many school districts mandate the former. After all, educators reason, students have to pass achievement tests that cover “the entire book.”

However, last year's study by Robert Tai, Marc Schwartz, and others found that students do better in science courses in college if their high school science courses dipped deeper into fewer topics. The study involved more than 8,000 students in introductory science courses in four-year colleges and universities. With careful controls for differences in students' backgrounds (including socioeconomic group, English skills, math achievement, and so forth), the researchers found a benefit from even studying just one topic in-depth (at least a month), even if other topics were taught in a surface-skimming way.

Further, the study indicated that standardized achievement tests did not necessarily give feedback about students' mastery of particular topics, nor did these tests predict success in college science classes.

It's clear that teachers should develop courses around fewer key ideas and go more in-depth on those ideas, although an overview of the subject alongside the in-depth study is a good idea. Research confirms once again that teachers should not “teach to the test.”

Expectation and Intuition

2010-01-25T09:28:00.000-08:00

Some recent papers and articles have explored the role of the unconscious mind in learning, playing chess, and listening to music.

In regards to learning chess, and playing it, a Time magazine profile of Magnus Carlsen, the youngest chess player ever to achieve the Number 1 world ranking, reveals that he learned primarily by playing lots and lots of games of chess on his computer—competing against computer programs, and also, in online games, against other people. (Carlsen only plays chess on the computer while at home; he says, “People come over to my house and say, 'You must have a lot of chess sets.' I say, 'Well, we might have one somewhere, but I’m not sure.'") Carlsen was able to play many games at one time, on his computer. All of this play inevitably involved a chance to make many, many mistakes, and to learn from them, and in this way Carlsen built a kind of intuition for good moves.

Chess master and coach Garry Kasparov says that Carlsen senses the “potential energy” in each move even if he—or even a computer—cannot actually calculate the eventual effect of the move. (Amazingly, Carlsen can plan 15 to 20 moves ahead! But sometimes he needs to choose a move whose effect is beyond this calculable range.) Carlsen relies on his intuition in these cases. As he puts it, “Sometimes a move just feels right.”

Journalist and blogger Jonah Lehrer explains Carlsen's intuition: deliberate practice of skills embeds our experience into our unconscious so that complicated calculations can be done almost automatically. The intuition that something feels right is hard to explain, for it depends on hundreds or thousands of experiences—and from the prediction errors that practice inevitably entails. Lehrer quotes physicist Neils Bohr as defining an expert as “a person who has made all the mistakes that can be made in a very narrow field.”

Playing music is another skill that benefits from deliberate practice and building unconscious connections. However, scientists from the University of London published a paper about the act of listening to, rather than playing, music. According to the brain waves measured while students listened to hymns, music lures our brains into making predictions about what note will come next—but it is the low-probability notes, the surprises, that cause our brains to react the most. In other words, it's not the perfect patterns that cause our interest in music, but the element of uncertainty, the confounding of our expectations, and the tension we experience while waiting for the pattern to return.

Once again, I turn to Lehrer. In his book Proust was a Neuroscientist, Lehrer discusses an analysis of Beethoven's String Quartet in C-sharp minor, Op. 131, undertaken by Leonard Meyer. Lehrer writes that “Beethoven begins with the clear statement of a rhythmic and harmonic pattern and then, in an intricate tonal dance, carefully avoids repeating it. What Beethoven does instead is suggest variations of the pattern.... He wants to preserve an element of uncertainty in his music, making our brains beg for the one chord he refuses to give us. Beethoven saves that chord for the end.”

Once again, this pattern-seeking, prediction-making, and even surprise are largely unconscious. What we experience as we listen to music is emotion, including satisfaction as the tension of unmet expectations are finally released in that long-awaited final chord. According to Lehrer, “the longer we are denied the pattern we expect, the greater the emotional release when the pattern returns.” Music that doesn't play “hard to get” strikes us as a bit boring and evokes less emotion.

Intuition isn't a magical, mystical sixth sense. Instead, it is what we can develop by working hard at a particular skill, practicing often and making a whole lot of mistakes. It's the result of our subconscious churning through predictions and possible patterns, and it is what we feel as hard-to-explain hunches or emotional responses.

“First, you take the second right...”

2010-01-16T09:01:00.000-08:00

“Then, you take the first left... When you see the McDonald's, turn right again, then a quick left. And the house is the fifth one on the left.”

Could you get there?

Thanks to GPS devices (sometimes built into our cars or phones!), many of us no longer have to deal with trying to remember long lists of driving directions, but there are other situations in which people have to listen to directions and then try to follow them. With directions it is often important, not just to remember the steps, but to remember the correct ORDER of the steps!

Five experiments conducted to see how students' memory for oral directions could be improved were published (long ago) in The Journal of Educational Research (“Oral Directions: Remembering What to Do When,” John A. Glover, Vicky Timme, Dave Deyloff, Margie Rogers and Dale Dinell, Vol. 81, No. 1, Sept. - Oct., 1987, pp. 33-40). The findings are easily stated:

Students did significantly better at remembering oral directions using one of two techniques:
using a mnemonic device,
or paraphrasing the directions (restating them in their own words).
Students who used a mnemonic device did even better than those who paraphrased at remembering the correct order of directions.

However, as I read the research findings, it's a bit hard to understand how students had time to either develop mnemonic devices or paraphrase directions while listening to directions.

Let's say Mike has heard the first in a short series of steps. As he begins to restate it to himself so that he can better remember it, the teacher has, perhaps, gone on to explaining the second step. Mike either halts the paraphrasing or misses the second directive, right? By the time the teacher has reached the third step, I would expect Mike's paraphrases to be a pair of truncated phrases, nothing very helpful.

How Memory Works

Short term memory, also called working memory, has room for both verbal (auditory)/text elements and visual/spatial elements. Tests indicate that working memory is severely limited—with slots for only 4 visual/spatial objects and 7 verbal/text objects—and that overfilling either buffer can cause us to experience “cognitive overload.” Experiments also suggest that a “multisensory convergence of neurons”—hearing a word AND seeing an object at the same time, for example—can help us to remember both verbal and visual objects.

Long term memory also comes in two flavors: episodic and semantic. The first results from involuntary storage of sensory input. It degrades fairly quickly unless we think about whatever we are seeing, hearing, tasting, feeling, or smelling. Once we think about something (or, rather, bring it into our working memory), then the traces of those thoughts are stored as semantic memory.

How Memory Can Work For Us

Courses designed to help people build memory power emphasize mnemonic devices such as building memory maps or memory houses, in which we visualize each new item in its own room or branching off like roads—whatever fits the particulars of what is being memorized. We are urged to make the visualizations vivid and colorful, and maybe humorous as well.

Some mnemonic devices are more auditory than visual. Just think of all those silly sentences we learned as children (such as “A Rat In The House May Eat The Ice Cream” or “Every Good Boy Does Fine”), or entire rhymes such as “Thirty days hath September...” Some of these phrases and stories can be easily visualized, too, which strengthens the memory, but others depend more upon auditory cues such as rhythm and rhyme.

One specific mnemonic device is called the memory room or Roman room. We are instructed to think about a room we know very well. In that room are many different objects. All we have to do to remember a mass of information is to associate each bit of information with one of the objects in the room. When it is time to remember, we can just take a tour of the room and recall the fact hooked to each item. Note that this technique isn't as good for information that must remain in a particular order.

To memorize a long list that must remain in order, visualize a well known journey, such as the way from home to the grocery store. Picture associations to the list items in particular locations so that you will be able to call back the items in the correct sequence. For example, picture George Washington (familiar from his image on money) washing his shirt on the front lawn; the man who lives on the corner outside his house, waving to us, with a hugely swollen Adam's apple (for John Adams); Thomas Jefferson (thank goodness for money with pictures!) gesturing, wearing fur, and standing with his son at the stop sign; a man known to you whose name is James eating a Dolly Madison snack cake at the first stoplight; a banner with a row of moons next to James' face draped across the gas station (for James Monroe); and at the next stoplight, a man known to you who is named John eating a quince, his Adam's apple bobbing up and down each time he swallows.

To learn more about mnemonic devices and improving memory, go here.

Summary

Now that I've read and thought some more, my guess is that using mnemonic devices that rely on images would be possible to do “on the fly,” as we hear oral directions, because we have those two separate channels of memory (visual/spatial and verbal/text). I am sure that it is a skill that would need to be practiced, but it seems doable. I still think that paraphrasing would interfere with listening, but perhaps that's just me.

At any rate, I am very glad that we usually do not have to remember oral directions without being given a printed copy, or being able to write them down ourselves!

In which I fight back against researchers who wish to take away my nice labels...

2010-01-12T13:55:00.001-08:00

In a recent post, I reported research that shows that there aren't multiple intelligences—at least not in the way that M.I. products and workshops claim—and that there aren't different learning styles, in the way merchants of learning styles products claim, either.

The problem is, this seems to fly in the face of experience. I KNOW there are visual learners—I am one!—and auditory and kinesthetic learners—I've raised some!

The problem with anecdotal “evidence,” as opposed to scientific data made from a properly structured experiment or other study, is that our experiences are such powerful learning tools, we often cling to what we “know” from our collection of anecdotes, even against empirical data.

Sometimes, because of anecdotal evidence, we feel that a theory or proposal “just makes sense,” or intuitively feels right. It clicks in with our experiences—it helps to make sense of the experiences, and the experiences help to make sense of the theory, and the whole ball of wax helps to make sense of the world.

Here are some of my anecdotes that seem to back learning styles theory. After I relate a few (believe me, I have scads!), we can examine what's going on here.

A visual learner is defined as one who learns best by absorbing images, holds images in his or her head, has a strong sense of color, learns by watching, and notices visual details. He or she is liable to be good at the visual arts.

Since I first read about learning styles theory, I've thought of myself as a visual learner. I used to use colored pencils to diagram complex study subjects or timelines, and when taking tests, I could easily recall facts and relationships from my diagrams. I used to color-code my notes. When I'm driving somewhere new, I generally can't remember too well a list of directions (either oral or printed), but I can remember the image of the route on a map. I draw well and, as a child, was always considered the “artistic one.”

An auditory learner is defined as one who learns by hearing sounds—for example, by hearing explanations and lectures and books read aloud. He or she has strong language skills and a well-developed vocabulary, and is often good at music and foreign languages

One of my daughters seemed to me to be an auditory learner. She picked up stuff from nowhere, it seemed—until we realized that, it wasn't nowhere, she was HEARING it. As just one example, she learned our phone number at a very early age by hearing me tell it to people—but my other kids had to actually sit down and memorize it. She could recall immense amounts of facts from our read-aloud sessions. She absorbs and enjoys stories she hears while she is doing something else—even, apparently, reading, writing, or studying something else.

A kinesthetic learner is defined as one who learns best by moving his or her body. A “hands-on” learner who learns by doing, he or she often wiggles while trying to sit still—and seems to focus better that way. He or she tends to excel in athletics and dance and working with his or her hands (sculpting, mechanics, crafts).

One of my daughters seemed to be a kinesthetic learner. She focused better on her beginning-reading sessions while balancing on a ball (or doing anything else physical) than while curling up next to me on the couch (which she only did for moments at a time, anyway—she couldn't stop her wiggling!). She would erect towers of pillows to vault over while watching TV, to everyone else's consternation. She's a gifted dancer and can accurately remember all the moves of many different dance numbers, at one time. For example, even as a youngster she could perform ten to twenty dance pieces in a single show—one time, dealing with four different sets of choreography to the same music!

Even as I type these anecdotes, I am convinced all over again about our different learning styles. The theory HAS to be correct, right?

Let's Look More Closely

First, from my understanding, the scientists who have shown that M.I. and learning styles theories are not correct aren't saying that there are no such things as individual differences and abilities. As a matter of fact, a diagram in the Wikipedia article about the g-factor (general intelligence) shows a variety of tests or tasks (marked “s” for skills) that factor into performance, along with general intelligence (marked “g”).

Second, I believe that our analyses of learning styles are the results of oversimplification and confirmation bias.

To illustrate, I will look at the examples I gave with a more critical eye:

Visual

While it is true that I successfully exploit diagramming and mapping in order to remember some things, I also use rhymes and songs (auditory), mnemonic devices (verbal/textual) and physical/bodily (kinesthetic) cues for other sorts of learning and memory tasks. Here are a few examples:
Although I am very familiar with the image of the 50 United States, having loved a wooden US puzzle as a child, I used to find it impossible to list all 50 states from just “reading off” my mental image of a map. However, I finally was able to pull off the mental feat of naming all 50 states when I learned a song about the states.

I often make up mnemonic devices for short lists, license plates, gate codes, and so forth.

When I deal with cardinal directions (north/south/east/west) and relative directions (right/left) I use my physical body to help me. When I try to figure out in what direction something lies, I sometimes find myself physically turning to what I am sure is north (I'm generally correct) and from there I know the direction (south-southwest, for example). When asked to put up my right hand, say, or turn to the left, I used to (and sometimes still do) touch my thumb to the callous on my writing hand (my right) as a check for right/left directions. When I give driving directions or direct someone to a particular drawer, I sometimes physically “face” the appropriate direction and use my hands to figure out the turns or the drawer location.
In other words, I use all modalities, depending on the method that works for the particular task. In thinking about learning styles, I apparently selectively remember my visual methods and successes, perhaps because I have some ability in art and image-making that makes me turn to this method regularly (or that is important to my self-concept?).

When I read about visual learners, I tend to notice the “hits” and shrug off the “missses” so that I am able to confirm what I already “know.” Ah, good old confirmation bias!

I have to admit, I probably learn most from reading, which learning-style and M.I. theories categorize as verbal or verbal-textual. Also, I'm terrible at some visual-spatial skills, such as “turn this image around in your brain” tasks, and I often fail to notice all sorts of visual details (especially people, clothes, accessories, etc.).

Auditory

The daughter I have pegged as the so-called auditory learner is, in fact, no better than the rest of our family at foreign language and music, and she has an actual deficit in her ability to process the order of phonemes; this has led to difficulties in spelling.

Also, this daughter is AMAZING at remembering anywhere she's ever been, whether she was riding or driving, and she can find her way again using visual clues such as buildings and landscape features.

She's also super good at spatial visualization (“turn the shape in your mind”) tasks. She has an excellent sense of cardinal directions that is apparently oriented on visuals plus the physical ability to keep track of what direction she is facing, and she uses mental images of maps to orient herself, as well.

She's artistic, with distinct leanings to visual media. She's good with her hands.

Basically, I'm saying that the label “auditory learner” is, once again, an oversimplification. She has skills in all modalities, as well as relative weaknesses.

Kinesthetic

My daughter-the-dancer does have abilities in coordination, and the energy to move a lot. However, once again, let's not oversimplify.

She gets much of her dance instruction through listening and seeing. She loves music and, even compared to other dancers, she is known as having particularly good musicality. She is very artistic, able to draw and paint well, and she often explores visual arts of various kinds. When she memorizing things, she tends to use visuals such as flash cards along with oral repetition, just like most of us. I've never known her to make up some sort of body-movement cues to memory.

I wonder if lists of learning-style characteristics—headed by the question “What kind of learner are you?”—are deliberately written to be quite general. Perhaps all we need is a smidge of an idea of a skill or interest—this little boy loves to take things apart, that's mechanical, right?—to enable us to adopt an entire learning-style description as uncannily apt.

And so I must regretfully admit that my anecdotal “evidence” should be put aside, that my daughters are I (and every other person) are complex learners, that there is no silver bullet of understanding how to teach and learn.

Learning Styles, Multiple Intelligences – Debunked!??!

2010-01-08T23:24:00.000-08:00

In 1983, Howard Gardner theorized that there are eight different types of intelligence, not just one general / overall intelligence.

Thomas Armstrong loved Gardner's theory and popularized it.

A slew of others have written books and articles, created workshops and websites—so that now we are awash in tons of information and hundreds of products that have sprung up around “Multiple Intelligences” or spun off into a related idea, “Learning Styles.”

Howard Gardner, an American developmental psychologist based at Harvard University, posited a variety of types of intelligence, including visual-spatial, bodily-kinesthetic, musical, naturalistic, interpersonal and intrapersonal. The final two types of intelligence, Gardner says, are unfairly elevated in importance by normal school curricula and practices; these privileged intelligences are verbal-linguistic and logical-mathematical.

During the 1980s and 90s, Thomas Armstrong wrote several books on this theory, bringing it to schools and parents and homeschoolers and the general public. Then and now he regularly speaks about M.I., and he sells his products in conferences and online. (I myself bought two of his books and saw him speak, back in the late 80s, as well.)

The theory of Multiple Intelligences took off and has influenced education for more than 30 years now. Granted, most schools and teachers kept doing things roughly as they had done before, but the concept that schools, parents, and teachers should assess children's intelligences in order to present materials in appropriate ways was a powerful source of reform for some and guilt for others. At the very least, Armstrong told parents and teachers, we should present materials in multiple ways to give all the kids, with all their different styles, the same chance for mastery.

The idea of “Multiple Intelligences” has to some extent morphed into a closely related idea with a slightly different vocabulary: according to this notion, we all have different “learning styles.” A Google search for this phrase brings up screens full of books and tests and videos / DVDs and other sorts of products, plus organizations and resources and events.

Learning styles are not exact equivalents of Gardner's eight intelligences; various learning styles websites and books claim that there are seven different styles, or three, or four, or...Well, they don't seem to agree on a number! According to a press release from Kevin Lyn Sisson at the Association for Psychological Science, 71 different models of learning styles have been suggested.

A lot of the learning styles have familiar Gardner-esque labels, such as “interpersonal” or “verbal-linguistic.” However, there is a LOT of variation among the learning-styles models. Most have dropped “musical” as a type of learning style (or intelligence), but many list “aural” learning for the students who learn best by hearing. One model features three of the intelligences Gardner named but jettisons the rest: according to this model, learners are either visual-spatial, aural-musical, or physical-bodily-kinesthetic. Other models proclaim entirely new categories and labels, including these two schemes: Converger / Diverger / Assimilator / Accommodator, or Concrete Sequential / Abstract Random / Abstract Sequential / Concrete Random.

What's a parent or teacher to make of all these categories, learning styles, intelligences, theories, products, and quite possibly contradictory advice?

A Dose of Reality

According to James Traub (writing for The New Republic), Gardner's theory of Multiple Intelligences has not been accepted by most cognitive scientists nor by most academics in the education field. Indeed, George Miller, one of the psychologists credited with discovering the mechanisms by which short-term memory works, wrote that Gardner's theory boiled down to “hunch and opinion.”

Many scientists and academics who have disputed Gardner's theory point out that he has simply changed the definition of the word intelligence in his writings, using the word where most would use words like ability, skill, strength, or talent.

Critics go on to point out that he has not even settled on one definition of the word intelligence. According to Wikipedia, psychologists insist that there is a lack of empirical evidence for Gardner's theory; many of his supposedly separate intelligences correlate with one another and provide support for the idea that there is one general intelligence (the g-factor).

As to the concept of different learning styles, Sisson's press release announces the finding that “there is no evidence supporting auditory and visual learning” as separate kinds of learning. The report, published in the journal Psychological Science in the Public Interest, reviews existing literature on the subject of learning styles; it states, “Nearly all of the studies that purport to provide evidence for learning styles fail to satisfy key criteria for scientific validity.”

The researchers point out that the main claim of learning styles theory is that learning styles and teaching styles should mesh (in other words, visual learners should be presented with information visually, and auditory learners should be presented with information through sound, and so forth); the survey of experiments found that the few that had an appropriate research design actually contradicted this idea!

One Size Fits All?

Research shows that multi-modal materials—those that combine images and text or images and sound—improve learning for EVERYONE. Learning by doing tends to lend a rich multi-sensory context that, once again, improves learning for everyone. Academics urge educators to choose strategies and materials that make sense for the topic being taught—but not to worry so much about the particular “learning styles” of the students.

Wanna Learn Something? Teach It!

2010-01-07T10:57:00.001-08:00

We know this, right? We've seen this at work in ourselves and in others—when we teach something, we learn and understand that thing better.

This is a case in which our anecdotal experiences as parents and teachers is backed up by research. Gwen Dewar clearly describes several interesting experiments that show that kids who are asked to explain something learn that concept better than those who study in other ways. Kids who are asked to explain something to themselves benefit, those who prepare to teach the concept to others (but don't actually teach it) benefit even more, and those who actually teach it to someone else learn it best of all.

Interestingly, one study by Rittle-Johnson and Percival Matthews showed that quality concept-driven teaching made self-explanation unnecessary. When children grades 2 through 5 were taught how to solve algebra problems and also explicitly taught the reasons for the procedure, the concepts behind the procedure, the kids who were asked to explain concepts to themselves as they studied did not perform better than those who were not.

This seems to show that self-explanation and teaching others works primarily because it causes people to wrestle with the underlying concepts of math and science. If students are taught those underlying concepts, they already have that benefit.

I believe, however, that if the study had asked students to teach to others (rather than explain to themselves), and had then compared those students to students who didn't teach, the teaching students would have performed better.

When I have taught math, including algebra, I have always explicitly taught the underlying concepts. Still, I have found that many students are able to nod their heads, answer some questions correctly, say they understand, seem to understand—and then flub a new set of problems of the same sort the next day or even 28 seconds later! In other words, I “taught” (or, rather, tried to teach) the concept behind the math algorithm, but the student did not learn it.

Students who explain things to others actually have to engage their brains in a different way: Teaching the concept takes kids (and their brains!) out of the receptor state that they all-too-often stay in, and puts them into a more active stance with the material.

The upshot of all this is that parents and teachers can help kids learn by:

presenting concept-driven curricula.
urging kids to explain concepts to themselves or to someone else as they study.
giving kids the opportunity to teach someone else.

In the old-time one-room schoolhouse, kids teaching other, younger kids was probably an every-day occurrence. This is easy to arrange in large homeschooling families as well. But everyone can share in the bounty of conceptual understanding through teaching, because kids can explain things to classmates, friends and siblings (including older kids or students who already know the material), parents, or even themselves.

Of course, kids teaching kids works with all sorts of things--not just concepts of math and science. Reading, games, songs, bad habits--kids have always been teachers, too.

Education Takes Off with Travel

2010-01-04T21:28:00.000-08:00

Parents and teachers have long known that travel is a great learning experience, with benefits that are out of proportion to the time spent doing it. Whether children travel with school, homeschool, or international exchange groups, or with their families, they can learn about geography, history, science, cultures, languages, and more.

The learning gained from travel tends to be much deeper, longer lasting, and more influential than ordinary classroom learning, largely because it is multi-sensory and multi-modal. It is first-hand experience, learning by doing.

In addition to providing educational benefits in schoolish subjects such as History and Science and so forth, travel helps children learn even more important skills and attitudes. Kids (and adults!) develop more divergent thinking as well as more confidence when they travel, since they face new challenges and must solve new kinds of problems. People learn tolerance for—even appreciation for—others when they are able to travel, and they are far more likely to care about animals and environments that they have seen for themselves.

The benefits of travel are not merely anecdotal; some research has shown the cognitive benefits of travel. It turns out that even thinking about travel can be helpful to divergent thinking!

One experiment was conducted by the psychologist Lile Jia at Indiana University. He asked groups of randomly selected undergraduate students to list as many different sorts of transportation as they could. One group of students was told that the task was developed by Indiana U. students studying abroad in Greece, and the other group was told that the task was developed by Indiana U. students studying in Indiana. Remarkably, the first group came up with significantly more transportation types. According to Jonah Lehrer, “They didn't just list buses, trains, and planes; they cited horses, triremes, spaceships, bicycles, and even Segway scooters.” Apparently, merely “knowing” that the students who asked them to make the list were far from home freed the students' minds from just the sorts of transport available there!

Another bit of evidence of the worth of travel comes from INSEAD, a business school in France, and the Kellogg School of Management in Chicago. This research team found that students who had lived abroad were 20% more likely to solve a problem known as the Duncker candle problem than those students who had never lived outside their birth country. Apparently, having to deal with cultural differences and multiple perspectives leads to more mental flexibility. The Duncker candle problem requires seeing multiple uses for an item, which is just the kind of thinking we tend to develop when we expand our horizons and explore the world.

Arrange field trips, day outings, weekends away, longer trips. Travel locally or, if you can, globally. Consider house-swapping with another family for a low-cost way to experience life away from home. Look into camps and exchange programs and scholarships for both. Remember, adults learn a ton from traveling, too. Get out there—way out there, if you can—and gain some of those benefits for your family!

Update on Dyslexia: Reading ability “uncoupled” from IQ

2010-01-03T23:49:00.000-08:00

The January 1, 2010, issue of Psychological Science details more findings on dyslexia. According to Sally E. Shaywitz, M.D., professor and researcher from Yale University, most children's scores on reading and IQ track together. But the Connecticut Longitudinal Study, an ongoing 12-year study of cognitive and behavioral development in schoolchildren, has shown that IQ and reading are not linked together in dyslexic children. Some very bright children struggle to read, and, Shaywitz explains, the problem can be lifelong, with adults continuing to struggle with reading all of their lives.

Shaywitz points out that people with dyslexia take a long time to retrieve words, and this may affect their spoken language as well as reading, causing them to speak less fluidly than others.

However, she points out that bright dyslexic people also tend to be creative, out-of-the-box thinkers. Many accomplished professionals have dyslexia, including people who read and write a lot such as attorneys and writers.

One of the practical tips coming out of the research by Shaywitz and other researchers at Yale and University of California Davis is that dyslexics should be given more time on timed tests so that they can reach their full potential—and so that our society can benefit from these creative problem solvers.

(Source: Eureka Alert.
Earlier findings on dyslexia are described here.)

Thinking about Teaching Thinking

2009-12-28T22:26:00.000-08:00

Many of us parents and teachers agree with the saying that one shouldn't teach kids what to think so much as how to think. Especially in a fast-paced world and a diverse society, it's hard to prepare kids for every situation—so we are better off teaching them how to cope with change, how to think on their feet, how to deal with floods of incoming “information” (some of which is misinformation!).

The question is, what is the best way to help our kids learn how to think? Should we model critical thinking? Should we cheer them on whenever they problem solve or brainstorm solutions or test hypotheses? Or should we explicitly teach them about logical fallacies and skills of analysis and deduction?

Yes.

Yes to everything.

Certainly we all know that kids pick up a lot from the behaviors that they see modeled by others, especially parents. Of course positive reinforcement is an important tool for encouraging attitudes and behaviors. But, according to Gwen Dewar, studies have shown that making critical-thinking skills explicit, that specifically teaching them, is even more important. In two separate research studies of seventh-grade students, Richard Herrnstein and Anat Zohar found that teaching critical thinking boosts, not just logical thinking, but language skills, IQ, and even real-world problem-solving skills.

What is critical thinking, exactly?

According to Michael Scriven & Richard Paul, critical thinking entails “actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information.”

Whether the information is gathered from one's own experiences and senses, from reading or hearing others' experiences, from careful observation and measurement in a scientific setting, or from reflection, critical thinkers consider the source of the information; the evidence, consistency, and relevance of the information; and the soundness of the logical reasoning.

Dewar's list of the skills of critical thinking is:

• analyzing analogies
• creating categories and classifying items
• identifying relevant information
• constructing and recognizing valid deductive arguments
• testing hypotheses
• recognizing common reasoning fallacies
• distinguishing between evidence and interpretations of evidence

Don't just teach this stuff, live it.
BUT also, don't just live this stuff, specifically and explicitly teach it, as well.

We can specifically teach our kids how to analyze an argument, test a hypothesis, and judge a source. We can explain fallacies such as arguments from authority, incredulity, or popularity, and we can show them the difference between fact and opinion, between evidence and conclusion. We can show examples of correlation that is NOT causation, and we can help kids ask important questions when people unthinkingly mix up the two.

Here are some resources to help teach critical thinking:
Critical Thinking in Education
Foundation for Critical Thinking
Fallacy Files – to teach about logical fallacies

Math – The Old, The New, and the Algebra

2009-12-18T21:07:00.001-08:00

I went to elementary school in the U.S. during the 1960s. Therefore, I was taught “new math.”

I know what you're thinking: “Oh, the horrors!” New math has a very bad rep. It's counted as a gigantic failure, figured to be a national disgrace, and (to sum up) described as an ill-planned experiment on poor, hapless children.

Indeed, in my own case, I entered junior high school (7th grade) with the feeling that I hated math and math hated me.

A brief definition of “new” math

In the late 50s and early 60s, American schools (and to some extent European schools) adopted new curricular requirements and standards for math, mostly in a sort of national panic that the West had fallen behind the Russians in math and science, as witnessed by the Russians' lead in space exploration. In other words, Sputnik made us very, very nervous.

The new math standards emphasized set theory, number systems other than base ten, and other topics such as modular arithmetic, algebraic inequalities, symbolic logic, and Boolean algebra. It emphasized understanding over rote learning (drill) – and (gasp!) even understanding over “getting the right answer.”

(Source: Wikipedia)

Was new math really so bad? Was it even “new”?

None of these topics were actually new to mathematics. What was new was addressing these topics at an early age and lessening the memorization / one-correct-answer / arithmetic orientation that had held sway over elementary-age instruction for most children throughout most of the history of formal education.

There are at least two huge problems in assessing the success or failure of the 1960s new math “movement.” First, we must ask how well it was taught. In other words, did teachers love it or hate it, or even understand it? Did parents support it? The overwhelming verdict of anecdotal evidence (I know of no rigorous studies) is that, generally speaking, neither teachers nor parents understood the so-called new math, and that (probably because of this lack of understanding) they either consciously or unconsciously undermined it. Some teachers actively feared the new math, and some parents complained about it loudly and steadily. With all of that going on, of course students learned new math rather poorly. Students did learn, of course (humans are learning machines!), but what they learned, in many cases, was: “New math” is bad and confusing and not based on the real world.

The second question we must ask is how much new math was taught. Presumably the adoption of new math standards and textbooks meant that teachers, however unwillingly and poorly, taught new math, but what I remember from my childhood was a smattering of set theory and base two, but a HUGE amount of drill, testing, and public exhibition of good, old-fashioned base-ten arithmetic operations. I endured timed multiplication tests, pages and pages of addition and subtraction problems, long hours over long division of increasingly longer numbers, and the “fun” of public humiliation through arithmetic “games.” The latter included hearing titters behind my back as I tried to “race” another student to solve a multi-digit multiplication problem at the chalkboard. My response wasn't to get ever-faster and more accurate in an attempt to win, but to get ever more brain-fuzzed, ever more unable to even try to solve problems publicly. I often had the distinct feeling that my brain was dissolving and dribbling out of my ears.

I'm pretty sure that every one of my teachers mostly stuck with “old math,” no matter what the standards and textbooks said. They produced homemade worksheets in grubby purple ditto paper, probably thinking that it was important that my classmates and I develop strong computational skills. They probably thought that the old math had been good enough for them and would be good enough for us, too, and perhaps they thought, “if it isn't broke, don't fix it.”

Of course, my memory of my elementary math instruction is necessarily hazy and super-subjective, not to mention the epitome of anecdotal not-evidence. Without any hard data on how much and how well new math was taught, this is just a guess, but I suspect that a huge reason for new math's failure was that it wasn't taught very much, and what was taught wasn't taught very well.

What about old math? How well did (and does) that work?

As I've already said, “old” math can be characterized by memorizing algorithms and number “facts.” In a previous post, I discussed why early arithmetic instruction can be utterly confusing to children who don't understand what it is they are supposed to be memorizing. I have seen repeatedly in my tutoring that many, many children successfully memorize algorithms but later cannot correctly remember or apply them.

For example, children learn how to add unlike fractions by changing one or more of the fractions so that both have the same denominator.

Here's the “trick” for that procedure: to change two-sixths to twelfths, the child says to herself, “Six goes into twelve two times, and two times two is four...So the answer is four-twelfths.”

A week or so later, children learn how to “reduce” fractions to their “lowest terms.” Here's the trick: to reduce four-twelfths, the child says, “Four goes into four one time, and four goes into twelve three times...So the answer is one-third.”

A while after that, children learn how to multiply fractions. There's not much of a trick to that—they just multiply “straight across”: to multiply one-half and one-third, the child says, “One times one is one, and two times three is six...So the answer is one-sixth.”

All of this seems easy enough; the kids often do very well on the tests, and then the class moves on to a completely different topic. But the next time they need to add or multiply or reduce fractions, many children misremember the algorithms, can't remember which procedure works for what kind of problem, or even draw complete blanks.

They have no basic understanding of why each algorithm works, what they are actually doing, or why, and so they cannot recover what they confused or forgot.

As I have said, I have seen this over and over (and over!) in my tutoring. When kids are taught only through rote memorization, many never achieve understanding and then don't have anything to draw on later when their memory fades.

The “new new math”

Some schools and teachers are embracing a new new math, which again emphasizes concepts over memorization and estimation over one correct answer. From my brief exploration of the movement, it seems to stick to traditional arithmetic-based curriculum rather than set theory and all the other topics of the old new math (gee, this is confusing!).

This seems to me to be a great compromise, likely to provoke less resistance among parents and teachers. However, from the articles I found (one example here), there might be almost as many detractors of this new hybrid of new and old approaches.

Perhaps the detractors should pay attention to recent research that shows that private schools are losing ground in standardized math tests to the much-maligned public schools. The researchers concluded that public schools are more likely to hire teachers certified in the subjects they teach (in middle school on up) and are more likely to update curriculum and teaching methods. Private school students often learn back-to-basics math curricula that prepare them to take the sorts of tests given 40 years ago rather than the tests of today.

And now, algebra

For many years, algebra was routinely taught in the U.S. beginning in grade 9. Recently, partly in response to comparative studies about math instruction in the U.S., Japan, and Germany, there has been a push to move algebra down to 8th grade.

Right now many districts allow the best math students (as measured by class grades, test scores, or teacher recommendation) to take algebra in grade 8. Some critics complain that this policy further handicaps the lower students; they insist that all students in the U.S. should be taught algebra in 8th grade. They go on to point out that, with this practice, all students can take geometry in 9th, Algebra 2 in 10th, Pre-calc in 11th, and Calculus in 12th.

Once again, I go to anecdotal evidence, since I haven't found research studies with firm data. My anecdotal experience very strongly suggests that moving algebra to younger students, across the board, is a bad idea. Some districts are mandating Algebra-for-all at age13 already, and I've been struggling to help some of the kids who are struggling with it.

Obviously my tutoring tends to deal with students who aren't doing well in math rather that kids who are just fine. But there are an awful lot of kids who aren't at all fine. Thirteen-year-old students who don't actually understand ratio, percentage, or even multiplication, not surprisingly, don't do well with algebra. Instead, they become even more frustrated and confused.

The teachers become frustrated, too. Algebra teachers often have to put a lot of their time into remedial arithmetic, and I've seen quite a few eighth graders getting credit and C or even B grades for Algebra 1, even though they and their classmates learned or even attempted to learn precious little algebra.

I can get behind the idea of exposing everyone to algebra, but I think there should be sensitivity to individual student's readiness. There should be better, more concept-oriented arithmetic offered before, during and after this exposure to algebra. Both arithmetic and algebra should be taught by people who enjoy the subject. Finally, it seems to me that exposure to higher math is quite different than requiring mastery of the subject. Perhaps not every child has to master every algebra technique and formula and concept. I can guarantee that not every child will use or even remember every bit of Algebra 1 in her adult life!

It's Smart to Get Fit

2009-12-11T15:45:00.000-08:00

A new study published by lead author Maria Aberg of the University of Gotherburg, Sweden, Nancy Pederson of USC, and others has demonstrated that aerobic fitness correlates to intelligence tests.

The results do not prove that cardiovascular health actually causes people to be smarter, but they do indicate that the relationship might be causal. Other contributing factors such as family and genetics were looked at, but siblings, twins, and even identical twins in the study still demonstrated the correlation between good fitness and good scores.

A wide range of intelligence tests were used to assess verbal ability, use of logic, geometric perception, and mechanical skills.

Also, the study looked at the relationship between muscular strength and performance on intelligence test, and there seemed to be no correlation. It is, instead, heart health and aerobic exercise that matters here.

Most important, perhaps, are the findings that it is important to get healthier while the brain is still changing. Boys who improved their cardiovascular health between ages 15 and 18 had higher scores—and were more likely to go to college—than boys who became less healthy in that age range.

Thanks to Kathy Orlinsky for sending me a link about this!

Creating Creativity

2009-11-25T11:28:00.000-08:00

Some adults just seem more creative than others. It's not wholly a matter of comparing people in the “creative” professions – visual artists and musicians and fiction writers – to those in supposedly less-creative jobs. When we actually consider the latter, we realize that engineers have to be creative to solve problems, physicists have to use divergent thinking to pose previously unasked questions, detectives have to “think outside the box” about where to look for evidence—in other words, that every profession benefits from creativity. And some adults just seem to have more of it. However, we often say that all young children are creative. The famed artist Pablo Picasso said, "Every child is an artist. The problem is how to remain an artist once we grow up." Albert Einstein advised adults to become more like children: “To stimulate creativity, one must develop the childlike inclination for play and the childlike desire for recognition.” Studies of brains and brain function are beginning to tell us a few things about creativity. There are definitely some surprises in the data, but the findings seem to back the intuitive practices of many parents and teachers and education reformers.

Yes, we all have the capacity to be creative.
Tom Stafford describes adults who have had frontal lobe damage; they often tell very inventive and elaborate lies—in other words, very creative lies—but without meaning to be dishonest, indeed, without the ability to see the difference between confabulation and truth. He points out that the fact that these brain-injured patients demonstrate so much creativity tells us that we all have the ability to be inventive, creative storytellers. Those of us lucky enough to have undamaged brains have something in our frontal cortex that helps us to know the difference between fiction and truth; Stafford asks if this something also, to some extent, inhibits our creativity. Source: Jonah Lehrer's November 23, 2009, post called “Lying and Creativity,” on the blog Frontal Cortex.

Let little kids BE little kids.
Kenneth M. Heilman, MD, suggested in his lecture at the 17th Annual Meeting of the American Neuropsychiatric Association that Albert Einstein’s “developmental dyslexia”—the fact that he still was not talking by the age of three—could have caused a greater development in his right-brain spatial intelligence. In Heilman's words: “Could Einstein’s dyslexia and lack of development of his left hemisphere have allowed his right hemisphere to grow and be well connected and to have excellent modules?” Source: NeuroPsychiatry Review, May, 2006. “Exploring the Brain's Role in Creativity,” by Fred Balzac.

Dr. Heilman's musings on Einstein's brain reminds us that delay isn't always bad. Other research findings indicate that pushing children into early reading, formal school practices at pre-school ages, and paper-and-pencil math in early grades all have deleterious results, at least for the majority of children. Heilman's work adds weight to the Better-Late-Than-Early idea by suggesting that pushing formal academics into earlier and earlier grades may unintentionally squelch creativity.

Education is not just readin', writin', and 'rithmetic.
Dr. Heilman cites work by Miller and colleagues at the University of California, San Francisco, on patients with frontotemporal dementia. Many of these patients had never had artistic hobbies before but, as their left anterior temporal lobes deteriorate, they suddenly take up one or more of the arts. Heilman writes, "They actually became creative—perhaps because the deterioration on the left side ‘disinhibited’ their right side, and the right side got creative doing artistic things." Of course, we have no intention of deliberately injuring anybody's brains, but the indication that the site of an inhibitory force is in the left side of the brain gives us a clue as to how to encourage creativity in healthy, whole brains: work on developing the right side of the brain.

Betty Edward's book Drawing on the Right Side of the Brain has been a big seller, and it gives some very practical ideas for unleashing the power of our spatial intelligence. The book 's advice definitely works to improve drawing ability, which is really more about truly seeing forms and shades and colors than about how to move a pencil across the paper. A quick search on Amazon turns up several other books, too, that promise to develop our right-brain abilities.

(SIDE NOTE: Perusing the titles and authors' credentials of these other books makes me nervous that some of them dive into woo-waters. They seem to promise just a bit too much, for one thing. Authors Harary and Weintraub, who have gathered exercises to promote Right Brain Learning in 30 Days, have an entire “higher-consciousness” series that also shows people how to have Out-of-Body Experiences. I gather that OBEs are a legitimate brain phenomenon comparable to lucid dreaming, but categorizing them as “higher” consciousness gives me pause, and people reviewing the book on Amazon seem to think that their “astral travels” actually / metaphysically happened. Hmm.)

Even without special training in right-brain learning, we can encourage children's right-brain abilities by allowing lots of block play, lots of mucking around with sticks and sand, lots of make believe, lots of big crayon scribbles and drippy tempera dabblings and finger painting and play dough...Sounds an awful lot like old-fashioned preschool and kindergarten, doesn't it? But all these activities help develop spatial, kinesthetic, and interpersonal intelligences—in other words, right-brain stuff.

Brainstorming encourages divergent thinking.
Stafford writes that actors who do improvisation tap into the same creative powers that confabulators with brain damage tap into, but “in a controlled way. They learn to cultivate a 'dual mind,' part of which doesn't plan or discriminate and thus unleashes its inventive powers, while the other part maintains a higher level monitoring of the situation, looking out for opportunities to develop the narrative.”

It seems to me that improvisers do a quick, spur-of-the-moment version of the familiar two-step problem-solving process: first, brainstorm ideas, not judging yet, accepting any and all comers; then make choices among all the ideas generated, using one's best judgment. It is so important to have that first, uninhibited part!

To be creative, we must be free to make mistakes.
We all have an intuition that one reason young children are more creative than many adults is because they are freer with their imaginations, their words, and their behavior. They are very aware that there is a lot they can't do yet, a lot that they don't know—and so they are much less worried about making mistakes or looking foolish. Author Mary Lou Cook writes, “Creativity is inventing, experimenting, growing, taking risks, breaking rules, making mistakes, and having fun.”
Source: Quote Daddy.

Perhaps the best “creativity training” we can do for our children is to encourage this experimentation and play. Help them shrug off mistakes, when possible, and allow them to take risks, within reason. Model questioning authority, rationally and responsibly. Make a lot of room for fun.

If reading is a struggle...

2009-11-19T21:41:00.000-08:00

The word dyslexia has been so overused the past twenty years, it's difficult to know exactly what syndrome it refers to, or precisely what to do to help its victims. Scientists who have studied dyslexia have determined that there are several different types of difficulties—different causes, different symptoms, and therefore certainly different solutions. Functional MRIs have given researchers the clearest evidence for the fundamental differences among the various learning disabilities.

Dyslexia is not necessarily about seeing letters backwards or in a mixed-up order. Instead, researchers say, many children suffer from reading problems because they struggle with processing quick-changing sounds. When these children are shown and taught written letters and syllables, such as ga, they may be trying to map them onto confused sounds that normal kids can distinguish as ca, da, ga and ya.

Sound training can help these children, and the earlier, the better, says Nadine Gaab, from the Laboratory of Cognitive Neuroscience at Children's Hospital Boston. Two possible ways to train children's ears are through musical training and through a computer program called “Fast ForWord Language,” which was created by Scientific Learning in Oakland, California.

As reported in June of 2009, Cyril Pernet of the University of Edinburgh, in Scotland, has used MRIs to establish a direct link between brain structure and severity of reading difficulties.

More dyslexic news was published in October, 2009: Wai Ting Siok of the University of Hong Kong reports that Chinese children who have dyslexia seem to combine visuospatial difficulties as well as sound processing difficulties. Siok points out that Chinese characters stand for meanings, not sounds, and have “a number of intricate strokes packed into a square configuration.” The meanings of each Chinese character must be memorized by rote, she says, whereas children learning to read in most cultures only have to learn a much smaller number of letter-to-sound rules. Further study is certainly warranted as researchers try to sort out the various types of learning differences and the underlying brain-structure and wiring differences that cause dyslexia.

Remember when...? Smell and Memory

2009-11-14T23:56:00.000-08:00

Studies have shown that “smell has its own memory.”

In fact, the sensations of smell directly connect with the hippocampus (which plays an important role in long-term memory); whereas other senses—sight, hearing and touch—are all processed by the thalamus before going to the memory center. This direct neuronic pathway is probably why smells can unlock seemingly long-lost memories quickly and vividly.

Emotions are also closely tied to smell. So the instantaneous, vivid memories triggered by smells are apt to impart strong feelings, either positive or negative. Research has further shown that negative associations are the most memorable and most powerful.

Most of our “smell memories” are gained in childhood. Apparently, our odor associations are created when we first experience a new odor. This is why vanilla or cinnamon or yeast are more likely to trigger memories of Grandma's house when we were five years old than our first apartment when we were in our twenties—even if we baked a lot in that apartment.

So, how does all this knowledge about smell and memory help us? I have read the following advice to students studying for a test: hold a scrap of cloth with a pleasant scent so that the odor becomes associated with the material being learned. Later, when taking a test on that subject, students should hold the scrap again (possibly doused with a fresh dose of the same scent). This aroma-study-habit is presented as a way of helping students to feel positive about the subject and to boost memory of the material.

It seems to me that the success of this technique would be doubtful. Assuming that the student is a teen or young adult, I would guess (from research findings) that the smell would more likely trigger early memories rather than the correct definitions of terms or dates of historic events. Still, the aroma-study-habit probably can't hurt. It certainly would be interesting to see this idea tested.

Sources:
http://www.sirc.org/publik/smell_human.html
http://scienceblogs.com/cortex/2009/11/smell_and_memory.php
http://health.howstuffworks.com/smell3.htm

Mindset

2009-11-09T10:33:00.000-08:00

The book Mindset, by Carol Dweck, has an important message for parents and teachers:

Praise effort, not talent and intelligence.

Dweck, a professor of psychology at Stanford University, has discovered through research that people have either a fixed mindset or a growth mindset: they either "know" that they have a certain fixed amount of brains, brawn and talent, and that's that; or they think that whatever intelligence and talents they have—that is, whatever hand of cards they are dealt--is only the starting point, and that they can improve through learning, practice, and plain old hard work. Those with a fixed mindset give up on tasks much more quickly than those with a growth mindset, and many people with a fixed mindset end up under performing. People with a growth mindset can actually improve their talents and their intelligence, and can therefore achieve success in life. Obviously, modern Western society teaches kids that "practice makes perfect" and that effort counts. However, Dweck and others have shown that the idea that each individual has a fixed quantity of intelligence that can be measured on an IQ test runs deep in the Western psyche and can be hard to overcome. One way that the fixed mindset gets taught and reinforced in children is through parental praise; we say, "Oh, aren't you smart?" and "Look how strong you are!" and "You're so talented!" and on and on. These sorts of praises spring to our lips even when we are with very young children, toddlers and babies.

Apparently, these praises tend to have the effect of convincing children that there are personality traits and mental and physical abilities that they either have or don't have. This mindset makes it more likely that kids will give up on tasks that are difficult. “I tried; I'm just not good at _________ (fill in the blank).” This mindset also causes many to feel the constant need to prove themselves, always hoping for more praise, more reassurance that they are holding a straight-flush rather than a pair of fives. Alfie Kohn (author of Punished By Rewards: The Trouble with Gold Stars, Incentive Plans, A's, Praise, and Other Bribes) has tried to wean parents away from trying to manipulate children or even to build self-esteem through praise; Dweck's findings point us in a slightly different direction. When a child succeeds and you feel praise bubbling up, praise the effort that has gone into the success.

"Wow! I like this painting--it's so colorful! I can see you worked really hard on it." "That dance was beautiful. All your dedication and rehearsal sure paid off." "Great hitting today. I can see that you've been practicing a lot."

I agree that empty, general praise is more harmful than helpful, especially when there is a hidden agenda behind it, and I think insincere praise is rarely believed, anyway. I suspect that children who get a lot of it feel manipulated or perhaps unworthy of any real commendation. However, I find it almost irresistible to praise something truly deserving. I have always tried to make my sincere praises as specific as possible, to be helpful feedback. But giving props for effort, perseverance, and practice is not something I have had in the forefront of my mind. Perhaps I did a lot of it—or perhaps I failed in this regard—I just don't know. All I know is two things:

1. I will certainly keep Dweck's findings in mind in the future.
2. I wish Dweck had written her book a couple of decades ago!

Why Art?

2009-11-04T19:58:00.000-08:00

Many parents and teachers intuitively feel that art education is important. A recent article by Michael Posner, Ph.D., and Brenda Patoine backs that intuition with a neurological reason for the importance of the arts in education: it improves general cognition. The reason for this benefit, according to Posner and Patoine, is that anything that trains the attention system—in other words, that activates the neural pathways devoted to attention—can improve our learning of everything else as well.

An art form that truly engages a child—whether it is music, drama, dance, writing, or one of the visual arts—does the job of training the attention system, if the child practices the art frequently and sticks with it. One goal, therefore, of arts education might be an enjoyable exposure to many different art forms. With such exposure, each student has a chance to find something that ignites his or her imagination and passion.

Posner and Patoine describe some experiments to back up their assertion, but it is hard for me to see how these controlled experiments relate to self-chosen art practice.

The researchers describe three networks that make up the attention system: the alerting network, which enables the brain to become alert; the orienting network, which keeps the brain attuned to external stimuli; and the executive attention network, which helps the brain control emotions and choose actions. It is this latter network, apparently, that most benefits from focused art practice and instruction.

In making a plea for education in the arts, Posner and Patoine write that children engaged in an art form that they love “may get so involved in learning the art that they lose track of time or even 'lose themselves' while practicing it.” The researchers go on to say that “few other school subjects can produce such strong and sustained attention that is at once rewarding and motivating. That is why arts training is particularly appealing as a potential means for improving cognition. Other engaging subjects might be useful as well, but the arts may be unique in that so many children have a strong interest in them.” Jonah Lehrer describes the “losing oneself” state as flow. This concept, first proposed by Mihály Csíkszentmihályi, is total immersion in what one is doing. Lehrer points out that people who are engaged in flow activities, “be it composing a poem or constructing a Legos set,” tend to be very happy.

In Other Words: Researcher Kenneth A. Wesson published a study in the American School Board Journal in which he states that the arts develop brain function, special reasoning, visualization, and, often, fine motor skills.

According to the National Art Education Association, art is a kind of work: “work done to the best of one's ability, for its own sake, for the satisfaction of a job well done.” Of course, it is a way to communicate, to express oneself, to be creative, and to play. But art has always been work, as well, and art can lead to financial remuneration and social recognition as well as personal fulfillment.

Art is also a way to transcend language barriers—in fact, all sorts of barriers of time and space. It can help us to communicate with, and understand, people all over the world. Because of this, art can be a force for peace. Art can cross the chasm of centuries and generations—even thousa nds of generations!

Ideas Can Be a Treat

2009-11-02T09:00:00.000-08:00

Have you heard about dopamine? Most people think of dopamine as a chemical reward in the brain that is released when we do pleasurable things like eat something yummy. In fact, it is a neurotransmitter (that is, a chemical produced in the brain that relays and amplifies signals between brain cells) that is released when we see or think about something that will be pleasurable. It is more about motivation than reward.

According to Wikipedia, a research team deprived rats of 99% of their dopamine. The rats lost all desire to eat. When the rats were force-fed, scientists determined that they liked the food as much as ever—that is, getting the food was as pleasurable to the rats as if they had chosen to eat it themselves. However, without dopamine, they had no motivation to eat (or do anything else)!

(By the way, if you're like me, you are probably wondering just how scientists “determined” that the rats liked the food they were being force-fed. The rats' facial expressions were recorded and compared to facial expressions of rats choosing to eat food.)

http://en.wikipedia.org/wiki/Dopamine

Jonah Lehrer, author of the Science Blog “Frontal Cortex,” says in his October 27th post that scientists call dopamine the currency of the brain, the “price tag of sensory information.” Dopamine allows us to quickly assign value to a wide variety of things in our environment, and of course that helps us to decide what to do, eat, pick up, strive for.

http://scienceblogs.com/cortex/

Interestingly, dopamine “price tags” get assigned to ideas as well as things. Read Montague, a leading dopamine researcher at Baylor College of Medicine, says that intellectual concepts are tied to the same motivation-and-reward system as are food and other animal appetites. That's why people can choose to fast for a religious, political, or health idea.
As Montague puts it, “[T]he human brain is able to choose the abstract thought over the visceral reward, as long as the abstraction excites our cells more than apple juice.”

http://seedmagazine.com/content/article/a_new_state_of_mind/

Are There Numbers in our Nature?

2009-11-01T01:48:00.000-07:00

Radio Lab (WNYC) is a great podcast that has many interesting episodes on tons of different topics, from laughter to lying, from parasites to placebos. A recent episode explores numbers. Studies with babies and toddlers show that we come into this world hard-wired with instincts about numbers and math.

http://www.wnyc.org/shows/radiolab/

Stanislaus Dehaene showed very young (2-3 m.o.) babies pictures of things such as ducks or trucks. The babies were outfitted with sponges with teeny-tiny electrodes, so brain activity could be monitored as they looked at pictures with either interest or boredom. Dehaene found that even very young babies have an internal sense of number, an intuition about quantity that shows up in startled interest when the number of ducks or trucks suddenly changes dramatically.

Strangely, Dehaene's work indicates that babies' internal sense of number is logarithmic rather than integral, more about ratio than counting. In other words, to a baby, the difference between 1 and 2 is enormous compared to the difference between 8 and 9. This is because 2 is twice as large as 1, but 9 is only a small fraction larger than 8. I haven't seen all the details of the research backing up Dehaene's assertion, but I hope to track down his book, The Number Sense: How the Mind Creates Mathematics, to find out more.

A long time ago, I read Young Children Reinvent Arithmetic, by Constance Kazuko Kamii. This fascinating book describes experiments with youngsters, but without brain-imaging technology, Kamii and others naturally had to work with children who can talk rather than babies. One important message from the book is that it is a bit ham-handed of adults to insist that children work with paper-and-pencil math processes before the children have a conceptual idea of that process. Even if kids can manage to remember a particular operation or procedure, if they don't understand what they are doing, they are likely to mess it up, forget it, or at the very least decide that school arithmetic is unrelated to real life.

An example, loosely taken from Kamii's book (the details of the interaction, such as the actual numbers used, may be different):

A girl who had “learned” to carry when adding explained to a researcher how to do it.
She wrote “18 + 5” on the board in vertical form. She drew a line under the problem and then explained, “Eight plus five equals 13, so you write that here”--and she wrote the number 13 below the line. “And one plus nothing equals one, so you write that here”--and she wrote the number 1 next to the 13.
The answer now looked like 113. The researcher asked, “Can you read the answer for me?”
The little girl labored over the task a bit but finally said, “One hundred and thirteen.”
“So,” the researcher went on, “18 plus 5 equals 113?”
“Yes. Because it's called 'carrying.'”
“So, if you had 18 pieces of candy, and I gave you 5 more, you would then have 113 pieces of candy?”
The little girl laughed. “No,” she explained. “It doesn't work with candy!”

Let's please, none of us, teach math in such a way that kids think that something that doesn't work for candy or apples or other countable items DOES WORK with chalk marks on a board or numbers scribbled onto a piece of paper!

In a world where most high school and college math classes--and even the SAT test, which often lies between—accept the use of calculators, in a world in which calculators are inexpensive and ubiquitous (especially as every cell phone has one!) perhaps children don't have to practice calculating so very early and so very often. Perhaps it's time to move formal arithmetic instruction back to higher grades so that young children can use and capitalize on their innate number sense without getting confused by the imposition of procedures for which they haven't yet developed a conceptual foundation.

In other words, perhaps with math as well as reading, “Better late than early.”

Ms. Frizzle was right!

2009-10-28T21:26:00.000-07:00

In the Magic Schoolbus books and TV show, Ms. Frizzle would always tell her students, “Take chances, make mistakes, get messy!”

According to research, she was absolutely right to tell her students to make mistakes. According to an experiment run by Nate Kornell and colleagues, and reviewed in Mind Matters by psychologists Henry L. Roediger and Bridgid Finn, kids DO learn better when they make mistakes.

In the experiment, kids were asked to guess answers to questions about some reading material before they had read the piece. Of course, most of the guesses were wrong. But after those kids went on to read the material, they tested 10% higher than other kids who hadn't had the chance to make mistakes—even those kids who had had their attention drawn to the important points that were going to be on the test, even those kids who were given more time as well as more direction on how to study for the test!

What does that mean for teachers and parents?

Let kids make mistakes. Encourage guessing (or hypothesizing). Sometimes, at least, let kids struggle to figure out the correct answers. All of this is called “active learning”—even if the learner is sitting the entire time it goes on—because the brain is active.

The researchers suggest encouraging older kids to pre-test themselves before they read something, using questions at the end of the chapter, perhaps.

And of course, Ms. Frizzle says simply:

TAKE CHANCES! MAKE MISTAKES! GET MESSY!