Why Don’t Students Like School?

by Dan Willingham
March 23rd, 2009

I have been writing about cognitive science and education for about six years now, and teachers have thrown a lot of questions at me. Many I did not feel comfortable answering-I felt that cognitive science didn’t have much to contribute. But for othersI felt that scientists did have some relevant knowledge that might apply to the classroom. When I heard such a question, I tucked it away.

After several years of saving questions, I collected nine that I thought were really central to teaching. The result was a book, Why Don’t Students Like School? This week I will post one entry each day that describes one question posed in the book and a highly abridged version of my answer.

The title-Why Don’t Students Like School? is not the question that I have been asked most often, but it is, to me, the most important. After I gave a talk at a conference, a ninth grade teacher asked me this question, obviously disappointed and frustrated. As she noted, almost everyone says that they like to learn new things; so why don’t students like school more?

It usually surprises people – and depresses teachers — when I tell them the brain is not designed for thinking. It’s designed to keep you from having to think. In fact, the brain is actually not very good at thinking.

Your brain serves many purposes, and thinking is not the one it serves best. Your brain supports the ability to see and to move, for example, and these functions operate much more efficiently and reliably than your ability to think. It’s no accident that most of your brain’s real estate is devoted to these activities. Compared to your ability to see and move, thinking is slow, effortful, and uncertain.

 About now you’re probably asking yourself, “Well, if we’re so bad at thinking, how do we function at all? How do we find our way to work or spot a bargain at the grocery store? How does a teacher make the hundreds of decisions necessary to get through her day?” The answer is that when we can get away with it, we don’t think.  We rely on memory, which is much more reliable than thinking.  Most of the problems we face are ones we’ve solved before, so we just do what we’ve done in the past.  We think of “memory” as storing personal events and facts, but it also stores strategies to guide what we should do: where to turn when driving home, how to handle a minor dispute when monitoring recess, what to do when a pot on the stove starts to boil over.  For the vast majority of decisions we make, we don’t stop to consider what we might do, reason about it, anticipate possible consequences, and so on. We just do what we always do. 

Saying we’re not very good at thinking sounds grim for educators.  But don’t despair. 

Despite the fact that we’re not that good at it, we actually like to think. We are naturally curious, and we look for opportunities to engage in certain types of thought. But because thinking is so hard, the conditions have to be right for this curiosity to thrive, and we quit thinking rather readily.  Solving problems – which I define as cognitive work that succeeds – makes us feel good.   

 From a cognitive perspective, an important consideration for educators is whether or not a student consistently experiences the pleasurable rush of solving a problem. What can teachers do to ensure that each student gets that pleasure?  I describe several practical applications in my book, but for now, I’ll focus on just one:  view schoolwork as a series of answers.  Sometimes I think that we, as teachers, are so eager to get to the answers that we do not devote sufficient time to developing the question. But it’s the question that piques people’s interest. Being told an answer doesn’t do anything for you.  When you plan a lesson, start with the information you want students to know by its end.  As a next step, consider what the key question for that lesson might be and how you can frame that question so it will have the right level of difficulty to engage your students.  

Lastly some practical advice:  Finding the sweet spot of difficulty is not easy. Your experience in the classroom is your best guide-if it works, do it again; if it doesn’t, discard it. But don’t expect that you will really remember how well a lesson worked a year later. Whether a lesson goes brilliantly well or down in flames, it feels at the time that we’ll never forget what happened, but the ravages of memory can surprise us, so write it down.  It’s worth making a habit of recording your success in gauging the level of difficulty in the problems you pose for your students.

Tomorrow: Why understanding is remembering in disguise.

 Daniel T. Willingham is a professor of psychology at the University of Virginia and the author of Why Students Don’t Like School: A Cognitive Scientist Answers Questions About How the Mind Works and What it Means for the Classroom (Jossey-Bass, 2009) from which this post was adapted. 

32 Comments »

  1. Dan,

    Interesting piece.

    Don’t mean to change the subject but I wanted to alert CK readers that E. R. Hirsch, Jr. has a good piece in this morning’s New York Times entitled “Reading Test Dummies.” Well worth the time to read it.

    Comment by Paul Hoss — March 23, 2009 @ 7:31 am

  2. Well, I just loved reading this, here at CKB. Of course, these rich ideas about engaging kids in productive thinking align perfectly with my own experiences in 30 years’ worth of teaching, so they feel like truth to me. Even more than sweet-spot questions, every brain likes confirmation that their most cherished ideas are scientifically valid.

    A couple of thoughts: First, the questions you’re describing sound amazingly like Grant Wiggins-type “essential questions”–questions that lead to inquiry into the big ideas in content domains, stimulate deep discussion and (uh-oh) critical thinking. Essential questions also can lead to creative re-thinking of old assumptions, or generating new and creative responses or new protocols for solving problems.

    I saw that happen in my 7th grade math class, when kids (using a constructivist math curriculum) were challenged to find new ways to multiply 3-digit numbers. Talk about your sweet spots and pleasurable rushes. I had to drag them away from their diagrams and invented algorithms. Of course, they came to the activity with some knowledge: a solid conceptual understanding of “multiply” and memorization of single-digit math facts. But there are lots of folks out there who would have seen this essential question–new ways to multiply–as a giant waste of time, the “best” algorithm having already been established.

    I’ve actually seen YouTube videos decrying this very multiplication lesson and starter question (and, mostly, the constructivist bent of the curriculum). However, I agree with you: being told an answer doesn’t do anything for kids. Except help them get better scores on low-level standardized tests.

    I agree with your advice on keeping a collection of good questions. But a good question for one group of 7th graders may not be a good question for the next group of 7th graders. My advice is keep all questions, even the ones that don’t work. Figuring out why a question flops is a sweet spot activity to build more effective teaching.

    Comment by Nancy Flanagan — March 23, 2009 @ 12:19 pm

  3. Dan,

    That “sweet spot of difficulty” is a good phrase. I think the very same idea also goes under the name of the “just right” challenge. I think this is a very important idea in education, but one easily overlooked and easily perverted.

    But I think it is an idea that most teachers intuitively recognize and act upon. Your basic question, why don’t kids like school, is obviously very important. But when I think back to our youngest daughter’s school years, just a few years ago, I think it is fair to say that she and her circle of friends liked school, for the most part at least. Indeed I think it is very common for kids to like school. Both sides of that question, why do kids like/dislike school, are equally important. And the answers, many of them anyway, are not at all obvious. One very important reason why kids do like school is that teachers arrange the daily lessons so that many students do get that “just right challenge”, that “sweet spot of difficulty”, on a daily basis. As a result they do become actively engaged with the subject matter. And, most importantly, they get a substantial amount of satisfaction of accomplishment on a daily basis. That, I have always argued, is the real engine that drives real education.

    But this happy state of affairs is perverted in various ways. The most important way, in my humble opinion, is ideology. By ideology I am talking about the educational fads the come and go, and continuously morph into different forms. The idealistic fantasy that learning will naturally occur if we will just get out of the way, seems to have endless appeal. By this perspective the “worksheet teacher” is disparaged. But I long ago decided that I’ll be proud to think of myself as a “worksheet teacher”, on the idea that the worksheet is carefully crafted to be the “just right challenge”, to be the instrument by which students efforts are efficiently and effectively translated into the accomplishment of genuine learning, learning of lasting worth, learning that makes a solid foundation for future learning, and learning that brings genuine satisfaction.

    I had to think on it a few minutes, but I very much agree with your idea that the brain is designed to enable us to avoid thinking. Memory enables us to avoid thinking. I would also argue that ideology, of many varieties, also enables us to avoid thinking. But I think it is also true enough to say that man is the animal whose ecological niche is general problem solving. We have evolved a generalized intelligence that can be applied to a wide variety of problems. But, and here’s the kicker, that doesn’t mean we’re any good at it. True, we’re good enough to survive, to flourish in all climates, to dominate all other species, and to even become civilized, but still we’re not very good at it. Our generalized problem solving abilities do not dominate our everyday mental processes. Blindly following the crowd, blindly acting on tradition, blindly acting on prejudice, lurching from crisis to crisis, make up the bulk of our everyday thinking. Thus, when it comes to buying a house the vast majority of us are woefully lacking in understanding of what we are doing. When the real estate agent says, “sigh here”, we are happy to ignorantly do so. Yet the world keeps turning. Life goes on. Our general problem solving ability, such as it is, still has an impact. It enables us, sometimes, and as a last resort, to learn from experience, even the experience of others. We know the young should be educated, though it took us thousands of years to learn that. We know that learning to read, though an incredible drain on available memory, is worthwhile. We have learned how to make peace, not war, sometimes at least.

    I look forward to your future posts.

    Comment by Brian Rude — March 23, 2009 @ 3:20 pm

  4. Brian:

    I had to ponder a while as well on our avoidance of thinking. I think (*) it’s just a matter of efficiency–we don’t need to reinvent the wheel for everything that comes up. It’s like those manipulative voice-mail trees that try to steer you to the answer to a question that’s already been asked in the past. “Are you having trouble with your widget, or is this a billing problem?” “OK, tell me about the kind of problem you are having.” “Did this problem start today, or have you had this problem before?” “Are you able to turn the widget on?” “Have you checked to make certain that the widget is plugged in?”

    Of course, my brain must do a nicer job of it, I cannot recall ever screaming at my brain “Just let me talk to a customer service representative!!!”

    Comment by Margo/Mom — March 23, 2009 @ 4:08 pm

  5. Nancy I am far from an expert on Grant Wiggins ideas, but based on my superficial understanding, we have “work backwards from goal states” in common, but not much else. I need to read more to have a better informed opinion. Regarding your math example, I’m a fan of the conclusion of the Math Panel that students need 3 types of knowledge: a limited set of math facts, procedures, and conceptual knowledge, which is what it sounds like the exercise you mention was giving them. (And this strikes me as a good example of using the question “what are my students going to end up with at the end of a lesson?” as a useful guide in lesson planning.) Regarding your comment “However, I agree with you: being told an answer doesn’t do anything for kids.” I would qualify that: I would say it doesn’t do anything for their interest or motivation. But there are surely times that teachers ought to tell students things, right? In my view, one of the things that makes teaching so incredibly difficult is the demand that teachers anticipate and balance motivation, cognition, emotion, social concerns (and others I’m not thinking of right now) simultaneously in their classrooms. Lastly, I definitely agree with our suggestion that teachers keep track of everything they’ve done in the classroom and not assume (as I had) that what didn’t work one year won’t work the next year.
    Brian: I agree. By stating “Why don’t students like school?” I was, I admit, being a bit sensational. (Um. . .can I call that my poetic license?) And there are lots of reasons that students might like school . . .as I mention in the book, my wife loved school, but primarily for social reasons. I also agree with you that most teachers are sensitive to this idea of a proper level of difficulty. I agree with you—to a point—on the “worksheet teacher.” I agree that there is no reason in principle that a worksheet couldn’t be intriguing. . .but I also would argue that the human element is doubtless important, so it’s much more likely that a student will get that sense of curiosity and fun from a teacher or from interacting with her peers. And yes, I agree with your last paragraph: we don’t come close to living up to our potential as thinking beings. . .but to be fair, it’s a high standard to meet. It would be incredibly taxing.
    Margo/Mom: I agree, it’s about efficiency, absolutely. And as I describe in the book, the ability to think deeply about a wide variety of problems is, in some sense, a phantom.
    Oh, and like Paul, I encourage everyone to read Don Hirsch’s piece in the NY Times today!

    Comment by Dan Willingham — March 23, 2009 @ 8:09 pm

  6. I must adamantly disagree with Nancy Flanagan touting the virtues of a seventh grade lesson designed to get kids thinking about multiplying three digit numbers in a different way. Multiplication, and by extension, division, is a means to an end; it is the mother of all problem-solving. As a math teacher (7th grade, no less), it is my fervent hope that I can stimulate my children to engage in critical thinking and problem solving. But by the seventh grade, multiplication MUST be squared away. This actually strongly correlates to the observation that people avoid thinking. I’m sorry to say, but muliplication must be committed to memory (single digits, that is, which of course means, that if you know the algorithm, you can do everything else) otherwise every higher level problem that they encounter in the future will be too taxing.

    Multiplication is a building block for thinking about algebra and geometry, etc. If by the seventh grade, students cannot quickly and efficiently compute multiplication facts, they are doomed to become that frustrated student that just might give up. Let me drop a bombshell here. The difference between a successful seventh grade math student and an unsuccessful one is the difference between mastery of multiplication and division, and non-mastery of the two. I see it time and time again.

    But constructivist learning programs are not giving children the chance to master multiplication because of its nauseating emphasis on alternate methods, and thinking about it “another way.” It’s this kind of thinking which causes me to inherit otherwise bright students who do not know what 8 X 7 is. We are not here to teach math appreciation. We are here to teach mathematics, not to show students that there are so many ways to get an answer, but fear not, you won’t have to master these methods.

    It strikes me as alarmingly grade-inappropriate that seventh graders are working on multiplication with three digit numbers. But maybe that’s why by high school, American students are on average, two years behind their European and Japanese counterparts in mathematics. Believe it or not, critical thinking and problem solving demand the mastery of basic facts at a young age. You cannot build a house without a strong foundation.

    Comment by Rich Getzel — March 23, 2009 @ 8:37 pm

  7. There must be something particular about 8X7. I had a hard time with it, still have to verify what I think it is by adding 7 to 49 (7X7, which for some reason has always stuck), or subtracting 7 from 63 (and the nines have a cute little trick to them that my fifth grade teacher taught us). I recently learned that Linda Darling-Hammond and I experienced the same “experimental” math curriculum growing up, something that I have always credited with my facility in Algebra (multiplying by a, b, x or y never bothered me–I got the conceptual stuff). But my fifth grade teacher (the one with the nines trick) believed that we were coming up a generation of finger counters (we had elaborate introduction to units, tens and hundreds using stick men with clothes pin fingers)–and insisted on dragging out the “old books” for long division. I still remember the feeling of erasing over and over again, hair askew, fingers grimy with graphite, blouse coming untucked from my pleated skirt, and going back over and over to the teacher’s desk only to find that one more time I had a “math error” and had gotten it wrong.

    I couldn’t say to this day if that year saved me, or was just not enough to ruin me.

    But it wasn’t until I was well into adulthood and teaching GED classes that the idea of a different algorithm came up. I had an aide who had been educated in a one room school in the hills. She was reluctant to help anyone with their math, because she knew she “had her own way” of getting the answer. I believe it was borrowing that she did “backwards,” but somehow came out with the right answer. I didn’t have time to puzzle out exactly what was going on in her process that led to the right answer, but it fascinated me. Some years later I saw a young math teacher go through a handful of different algorithms for something.

    I can see where Nancy’s problem for seventh graders would excite exactly the right parts of her students’ brains to retain their interest and excitement. This is not about the process of memorizing the basic facts (and I am of the opinion that if a kid hasn’t gotten there by 7th grade, perhaps there is an organic difference and maybe it’s time to learn mechanical ways of getting the answers)–it is about truly and deeply understanding the process.

    I used to work at a camp where we allowed the teenagers to set their own bedtime. The only condition was that they had to get up and make it to breakfast on time (a mile or so away from their cabins). Year after year they would start out staying up late–until they missed breakfast one morning. The adults could just tell them them the right answer–but I guarantee the learning would have been no where near as effective as it was when they figured it out on their own.

    Comment by Margo/Mom — March 23, 2009 @ 9:52 pm

  8. I agree completely with Rich Getzel’s post. And on a related topic how could Nancy Flanagan, a K-12 music teacher, wind up as a seventh grade math teacher? I’m confused. Nacy, having read many of your past entries I was under the impression you were a music teacher – not that there’s anything wrong with that.

    You stated, “I saw that happen in my 7th grade math class, when kids (using a constructivist math curriculum) were challenged to find new ways to multiply 3-digit numbers. Talk about your sweet spots and pleasurable rushes. I had to drag them away from their diagrams and invented algorithms.”

    How does a music teacher wind up teaching 7th grade math? I’m sure there’s a reasonable explanation for this apparent misunderstanding. I apologize for my confusion.

    Comment by Paul Hoss — March 24, 2009 @ 7:41 am

  9. The comments above by Nancy, Rich, and Margo about learning math, and multiplication in particular, are very interesting. I find much to agree with all of them, even when they are disagreeing. I share Rich’s negativity about a seventh grade math class looking for new ways to multiply whole numbers. But context is very important. Nancy describes her class as having “a solid conceptual understanding of “multiply” and memorization of single-digit math facts.” That sounds like a smart class. Classes vary considerably. My experience teaching in junior school was over forty years ago, and it was a total of only two years, but I can well remember the seventh grade in that first year. That was not a smart class. I can well imagine that if Nancy tried with that class the same thing she describes in her post, she would modify it considerably. This class, as I recall, could not at all be described as having “a solid conceptual understanding of “multiply” and memorization of single-digit math facts.”

    Of course I was a first year teacher at that time, and about as naive as you can get. I don’t know just what Nancy would do with that class. I can well imagine that she would have methods and ideas that would bring out the best in them, ideas and methods that I could only guess at. But I cannot imagine that the activity she described in her comment would work well.

    Context is everything. To really get a picture of what Nancy describes would take a lot more than can be fit into a paragraph or two. We would have to have some idea of the culture of the students. We would have to know something about their abilities and past education. And we would have to know just how this one topic, alternative methods of whole number multiplication, fits into the seventh grade math curriculum.

    Rich mentions that it is “alarmingly grade-inappropriate that seventh graders are working on multiplication with three digit numbers”. I had to think on that a minute, but again context is very important. Yes, it does seem to me that whole number multiplication is probably introduced at least by fourth grade. Why are they doing it now? If Nancy indeed has a smart class, then those students probably learned the mechanics of whole number multiplication several years in the past. They used that knowledge in learning about fractions, decimals, percents, and applications of all of the above. If that is the situation then what Nancy describes must be enrichment. One reason teachers like to have a smart class is that there is time for enrichment. There is time for a lot of things. That is a luxury that many teachers do not have. Is it appropriate enrichment? Is it good use of the student’s time? I have no way of knowing. All I have to go on is the idea that most teachers, especially those that have a lot of experience, use their intuition and common sense. I can’t know much about Nancy or her class, but if I were a betting man I’d put my money on a positive, optimistic outcome. That doesn’t mean that every good teacher would choose to do exactly what Nancy did on that particular day with that particular class. But I don’t see cause for alarm.

    I do see cause to carp a little about how teachers use words. I have long complained that there is a woeful lack of simple description in the field of education. I have mentioned above that to put Nancy’s scenario in a meaningful context would take a lot of description. I realize that is not an easy thing to do. I don’t mean to criticize Nancy for not doing so in her comment. I presume, like me, she has to grab a few minutes whenever she can just to get off a paragraph or two now and then to blogs like these. But in the big picture I would argue that until educators get accustomed to expecting a lot more description we’re not going to advance much in educational theory.

    I am especially irked by how the word “constructivism” is thrown around. I presume Rich responds negatively to the word. I certainly do. However I also call myself a constructivist. When I say, as I do, that I am “worksheet teacher” (a term attractive mostly because some disparage it), it is because constructivism, when carefully thought out, leads to the practices that I use and believe in. A well constructed assignment is the epitome of constructivism. Learners construct their own meaning. They have to. So a good teacher gives them the materials and tools needed to do that. That includes some presentation of a topic – a good explanation. It also includes an opportunity to apply and practice that topic – a well constructed assignment. Then the student is in a good position to construct meaning. This is not to say that students can construct meaning only when given a well laid out assignment. We all have brains, and we use them in many ways. Students construct a lot of meaning out of a lot of things, some of which we definitely don’t like. But school learning should be efficient. Learning is most efficient when students have well laid out materials and tools to work toward a defined goal. Lazy teachers, like me, try to find that well constructed assignment among the problems in the book at the end of the section. Conscientious teachers, like me, take the trouble to make a handout (worksheet), of the problems in the book won’t do the job. I make a lot of handouts.

    The idea that the principle of constructivism leads to things like group projects or making posters is very strange to me. It is the result, in my humble opinion, of very shallow thinking about what “constructivism” can or should mean. (I have an article on my website expanding on these ideas about constructivism.)

    And as usual we tend to forget all about discipline. In conjecturing about Nancy’s smart class, I passively imagined a well behaved class. It probably is. But why is it? Because Nancy is a good teacher, and knows what it takes to get good behavior from her students? Sure. That’s easy to imagine. But what works for her in the culture of her students may be quite different than what works, or doesn’t work, for Rich in (I’m guessing) a different culture. But we don’t like to think about discipline. The ed school mentality, for about a hundred years now, has actually put down those who think we should think about it. Well, I think we should think about it, a lot. It’s incredibly important. Students will not construct much of anything in a chaotic classroom environment. The “materials and tools” to construct any academic learning must start out with an orderly environment.

    Margo pretty well describes it all. “I still remember the feeling of erasing over and over again . . . . .”. What I get from this picture is a student given the materials and tools needed to construct meaning, and applying the effort required to turn those materials and tools into real learning. That’s constructivism, real constructivism.

    Comment by Brian Rude — March 24, 2009 @ 12:20 pm

  10. “Rich mentions that it is ‘alarmingly grade-inappropriate that seventh graders are working on multiplication with three digit numbers’. I had to think on that a minute, but again context is very important. Yes, it does seem to me that whole number multiplication is probably introduced at least by fourth grade. Why are they doing it now?”

    My local district just voted to switch to the notorious “Every Day Mathematics” curriculum. After watching a 2nd grader in a neighboring town that uses EM struggle to figure out the correct change from $20 for a $16 Girl Scout cookie purchase, I did a little investigation.

    I found a scope & sequence for EM Grade 2, and their goal is for students to do 2 digit subtraction “using manipulatives, number grids, tally marks, and calculators.” It isn’t until 4th grade (!) that students are expected to do subtraction with “automaticity”.

    Compare this with the “Right Start Mathematics” Level C that I’m using in my homeschool (designed for 2nd graders). It has students mentally subtracting a 2 digit number from a 3 digit number with regrouping (e.g. 103 – 58) in lesson 86. The table of contents for “Saxon Math” Grade 2 lists subtracting 2 digit numbers in lesson 109. “Singapore Primary Math” 2A also lists subtracting two and three digit numbers with regrouping. So 3 of the math programs popular with homeschoolers all expect 2nd grade students to solve even harder subtraction problems than 20 – 16 = 4.

    If students using EM don’t master subtraction until 4th grade, then absolutely I can see them not having mastered multiplication by 7th grade.

    Comment by Crimson Wife — March 24, 2009 @ 1:31 pm

  11. Step away for a few hours, and all heck breaks loose. I am, of course, enormously relieved to know that Paul thinks there’s nothing wrong with being a music teacher. (laughing)

    Here’s the story of how I ended up teaching math, three times in my 30-year career: math sections were full, per contract limits, and the contract put no limits on the size of instrumental music classes. So three different principals moved kids in my band classes around to free up one hour, so I could take the overload in math. The first time it happened, in the early 80s, there were no major/minor content preparation requirements for a teacher teaching any subject in the 7th and 8th grade. The junior high was the dumping ground, the last resort for teachers bumped out of other jobs (for which they were qualified). It happened again in the 90s (causing my first hour band class to swell to 93 kids)–and again in 2004. In 2004, there was Highly Qualified Teacher language out there, but I was grandfathered in, under my state’s HOUSSE regs because I taught math previously.

    But what you want to know is what my academic background in math is, so you can use that to suggest that I don’t know anything about math pedagogy, right? OK–I have a major and two minors in music. I took 12 hours of math in college, just because I like math. I am not a highly qualified math teacher. But I am curious and observant, and–unlike many people now making policy–have had extensive experience in teaching, across grades K-12.

    I taught from three different math curricula. In the 80s and the 90s, the books were high-level arithmetic review. Demonstrate the skill or algorithm, do a few practice problems at the board, and assign 30 problems as homework. Quizzes worth 25 points, tests worth 100 points, blah, blah. And absolutely no calculators (confiscate if seen).

    In 2004, it was a whole new ball game. The curriculum was new the previous year, and of the four “real” math teachers, two hated it (both former HS math teachers, moved down to middle school to avoid multiple preps), and two absolutely loved it. All four were math majors, BTW. The two teachers who liked the curriculum were younger– in the 5-10 years experience range, and the two who loathed it were 20+ veterans. I thought the lessons were fascinating, and well-constructed, and I have to say that the kids were vastly more engaged with the work than the kids I had in the 80s and 90s, if for no other reason than it was variable. And–they were asked to solve problems, using skills and knowledge they already had. When they floundered, I helped them put the concepts and skills together–but the curriculum offered lots of opportunities to problem-solve, and they got better at applying their skills in context.

    The class was created in mid-September by allowing the other four teachers to bump kids out of overloaded sections into mine. So it was hardly a group of math superstars. They bonded quickly however (a few were glad to get away from their original teachers) and turned into a wonderful group, a pleasure to teach. Which was good, because I was seldom more than a week or two ahead of them. The mathematics in the new curriculum was more intellectually complex than the old advanced-arithmetic stuff. By the end of the year, the 7th graders were doing work with linear equations, using graphing calculators, and solving one-variable equations. I learned a number of new ways of conceptualizing math concepts myself, including strategies for working with positive and negative numbers, and new ways to teach probability.

    The three-digit multiplication exercise was a two-day exploratory lesson on place value in decimals, in a larger unit on decimals and fractions. It would not have worked, as Brian pointed out, if the kids did not bring mastery of single-digit math facts and an understanding of what multiplication was. It was not, in any sense, a low-expectations lesson on multiplication review. They already knew how to multiply three digit numbers. But what suddenly clicked for many of them was place value–how/why the traditional algorithm aligns numbers to get the right answer, for example, or different ways of combining what they had previously seen as two separate processes–addition and multiplication. They could have parroted back which place each digit was in, as well–but inventing their own algorithms put lots of pieces together for them. The lesson was enormously useful when we began working with decimals.

    I used the word constructivist deliberately in my original post, because it’s a red flag for some people. (Mostly people who thrived under direct instruction, and feel anxious when they have to bump around looking for solutions or interpretations, I think.) **You cannot construct knowledge of out nothing.** As Dan notes, some knowledge and skills have to be transmitted through explanation and practice. When you remove the opportunity for students to try their hand at putting content pieces together, making mistakes along the way, you lose something important. If believe that classrooms are a place for students memorize the one right answer, you’re missing that sweet spot, the place where kids engage and take risks.

    Comment by Nancy Flanagan — March 24, 2009 @ 2:37 pm

  12. One more thing: my math students’ statewide assessment scores were indistinguishable from the other teachers’ math students. No students were harmed by my math teaching. And a couple of them told me they never understood math until they were in my class. I am not dumb enough to think that had anything to do with my math skills–and I know that 7th graders aren’t particularly skilled at identifying excellent pedagogy. But I do know they “liked” math, for one year–and that’s not all bad.

    Comment by Anonymous — March 24, 2009 @ 2:43 pm

  13. To remember 7×8, what I told my son to remember was this: 5-6-7-8. Multiply the last two (7×8) and you get the number 56.

    On the subject of Dan Willingham’s post, I was very much reminded of the book by Chip and Dan Heath, “Made to Stick.” They contend that one of the key things you can do to stimulate attention and memory in your audience is pose a mystery. Why are things this way? Why did this bad thing happen? How was this thing invented? Get the audience wondering, because everyone likes a mystery of some sort. Then deliver the answer. But if you deliver the answer right off the bat, people think, “Why should I care?”

    The book isn’t online, but you can see a small sample of this reasoning here and in the last few paragraphs here.

    Comment by Stuart Buck — March 24, 2009 @ 3:03 pm

  14. Nancy, the math program that you are describing sounds interesting. Could you let us know the name of the program?

    Comment by Judy — March 24, 2009 @ 3:17 pm

  15. Connected Math Project (CMP). The unit (on fractions and decimals) was called (if I remember correctly) “Bits and Pieces.” Some of the progenitors of CMP are at Michigan State University, and the series is popular in Michigan.

    Comment by Nancy Flanagan — March 24, 2009 @ 4:22 pm

  16. Nancy,

    Mine was an innocent comment/question. No ill intended. I’ve read and participated in this blog now for about six months and remembered your citing yourself as a music teacher. I was confused when you started talking about “your” math class.

    No, there is nothing wrong with being a music teacher. The arts are clearly a very important component to a well rounded education for all our students.

    Comment by Paul Hoss — March 24, 2009 @ 5:42 pm

  17. No offense taken, Paul. I actually thought you were riffing off a classic Seinfeld line, and decided to respond similarly (hence, the laughter). I *am* a music teacher–and as my story must make clear, I was thrust unceremoniously into teaching math three times.

    I did sincerely try to do right by the kids, however. It was never their fault that contract grievances on class size stuck them with a music teacher in their math class. I was also following the Math Wars as a policy issue at the time (the Palo Alto standoff, and the angst over the original NCTM standards, etc). Although I didn’t appreciate an additional prep, an additional 25 students, and having my 8th grade choir swell to 75 kids, it was a great opportunity to teach an integrated math curriculum and see what all the shoutin’ was about for myself.

    Comment by Nancy Flanagan — March 24, 2009 @ 10:43 pm

  18. Well, Nancy, I am relieved to see that the multiplication exploration was part of a bigger unit on decimals and fractions, because that is extremely important in the grand scheme of things.

    Out of curiosity, what state do you work in?

    I work in New York, and I am quite agitated that decimals and fractions are almost completely removed from the curriculum in the seventh and eighth grade. It pops up here and there, but I can’t tell you how many kids have trouble with the oh-so loathsome, adding fractions with unlike denominators. The curriculum in New York was changed in 2005. I went to NYC public schools from ’91 – ’04.

    I am 23, but I was the recipient of a mathematics education that was heavily skewed towards direct instruction. Incidentally, my district was the highest performing district in New York City. I now teach in an area where 95% of students receive free lunch. I inherited a program called Impact Mathematics. I have a CTT class with general education and special education students, but the vast majority of them are not on grade level, regardless of any diagnosed special needs.

    The kids routinely complain that the textbook is confusing. At NO point does it explain, even in a roundabout way, how to go about solving a problem. Since their toolkits are already lacking, they cannot induce their own imaginative ways to solve problems. There is of course a pervasive motivation problem from which many students suffer. I once met a developer of the Impact Program, and he said that it is really only appropriate for high-performing students.

    One thing is clear, they want me to teach them how to do the math. I also have eighth graders, and last year, their teacher followed the Impact Program to the last dot. While it is a challenge to get students to work consistently, I can’t tell you how many snide remarks I’ve heard, sometimes in the presence of the other teacher, that “at least somebody teaches us.”

    Although it may not be well documented, the effectiveness of direct instruction and constructivism might vary across the socio-economic spectrum, dare I say.

    Comment by Rich Getzel — March 24, 2009 @ 10:47 pm

  19. I checked Connected Math out on the What Works Clearinghouse, and the results were troubling. It appears that Connected Math actually has a negative impact on student achievement. As for the “notorious” Every Day Mathematics, the research shows that it’s one of a handful of truly effective math programs.

    what concerns me is this tendency to praise or denounce a program without consulting the evidence. The “Math Wars” mentality tends to separate people into opposing camps that rely on ideology rather than evidence. Direct instruction and constructivism do not have to be an either/or proposition. In Japan the approaches are combined with about one out of four math lessons taking a constructivist approach. Math instruction in the United States would benefit from calling a truce in the “Math Wars” and replacing it with an open-minded appreciation of how students can benefit from a careful combination of both approaches.

    Comment by Judy — March 25, 2009 @ 11:23 am

  20. Judy–You’re assuming that the What Works Clearinghouse is an unbiased source of data. The Clearinghouse was established to give highest marks and priorities to what was construed as “scientifically based” research– quantitative, random-assignment, large data-set studies that look more like gold-standard medical research. And, of course, their data source is the notoriously un-standardized state assessment tests.

    What the data might actually be measuring is alignment of the CMP curriculum to individual state tests. If a state test is mainly composed of arithmetic calculation items, some other math series may well do a better job of preparing kids. If the test includes constructed items (which are more expensive to score, but generate different kinds of data), or problem-solving, a program like CMP is likely to do a better job. The “evidence” that WWC has provided on any number of strategies or materials is skewed toward a particular conception of what kinds of research can be trusted, but in the social sciences there is never true randomization.

    I would never adopt a curriculum solely on the basis of standardized state test data–and if you’ve been following the National Standards discussion, you’ll know that any number of state tests have recently been skewered for being constructed around low-level skills.

    I also think that Rich brings up another factor: socio-economic factors, including earlier education experiences in a subject, strongly impact the value of a particular kind of teaching. Although I teach in an area considered rural, we are on the outskirts of the wealthy suburbs. About 90% of the kids in my district go on to college. Last year, about 85% of MS parents in my district showed up for PT conferences. And they all care about rigorous math instruction. In fact, on Parent Open House night, I shared the CMP books with parents. Lots of automotive engineers sitting in the room–and they liked it. A few confessed that helping with homework was a new challenge–they actually had to think about how to set up problems.

    Comment by Nancy Flanagan — March 25, 2009 @ 3:34 pm

  21. Nancy:

    I think that you are misinformed with regard to What Works. I have been following their publications for a while, and while it is true that they are looking for quantitative randomized experimental or quasi-experimental studies, the data is based on sources other than state tests. Certainly one of the overall impressions from what works is that there is not so much available that meets their criteria. Certainly the alignment of a curriculum to state standards would be a worthy consideration when selecting a curriculum, particularly as so many teachers are heavily reliant on what is included in the text. Certainly there would be other criteria as well.

    I know that there are lots of lofty discussion regarding how research is most appropriately done and the absolute value of knowing and all that, and whether anything can truly be randomized (or known). But, I remain skeptical of studies that do not have some basis (such as randomization or a quasi-experimental design) for claiming an effect. There is certainly also room for study to demonstrate an effect for a particular group (low SES, girls, hearing impaired, whatever) that may not generalize, but may still be useful.

    I haven’t seen too many WWC reports that found more than a few studies focused on what they were looking at. Says a whole lot more to me about the need to support educational research than about any WWC bias or about the fallibility of things being done in the classroom.

    Comment by Margo/Mom — March 25, 2009 @ 5:06 pm

  22. Nancy,

    Thanks for the note. I am a huge Seinfeld fan and watch the reruns religiously – not that there’s anything wrong with that. Tonight it’s Darren the intern working at Kramerica Industry. A scream.

    That must have been a challenging experience jumping into a math class like you described.

    Comment by Paul Hoss — March 25, 2009 @ 7:18 pm

  23. The only bias that the What Works Clearinghouse has is toward rigorous scientific standards. Research that does not not adhere to basic scientific standards such as randomization is little better than anecdotal evidence. It is nice that the parents at Open House liked the Connected Math books, but it doesn’t really prove anything.

    What I find intriguing is the WWC’s lack of ideological bias. Both Every Day Mathematics and Connected Math are constructivist in outlook, but the WWC found one to be effective while the other was ineffective.

    It may be that CMP is effective in other ways such as improving problem solving abilities or increasing algebra readiness, but the burden of proof lies with CMP. Surely, someone at the University of Michigan could create a randomized experimental or quasi-experimental test that would demonstrate whether or not CMP is actually effective in these ways.

    Comment by Judy — March 26, 2009 @ 1:44 pm

  24. Would that be the “notorious” Every Day Mathematics?

    Margo may be correct in noting that WWC does not use state assessment data–but all of WWC’s vetted program assessments are linked to standardized testing data, either the NAEP or another nationally normed test. And standardized tests thus measure how well the curriculum is aligned to test items. Tests should be aligned to curricular goals if they’re measuring instructional effectiveness (or, especially, the value of a particular curriculum).

    Lots of people who don’t understand that–or have an axe to grind– believe that WWC has cut through the fog and can reliably tell us which programs a school “should” adopt. The premise behind WWC is elevating randomized experimental trials as the best way to do social science research, and using standardized test data as the one best measure of student learning. And that–is a bias.

    The recent IES study on the four math programs, with its “puzzling” results of two very diverse math programs leveraging the highest scores was not so puzzling when the items being tested were compared with curricular goals embedded in each program. And when the researchers casually noted that the Saxon program students received approximately an extra hour of instruction per week, per program recommendations– well, so much for pure, bias-free science.

    Exclusively using standardized tests to measure learning is a bias against human judgment (which is used in the workplace and the real world as often or more often than measured outputs). Anyone who’s ever sat around a table trying to understand why a child with off-the-charts IQ numbers did poorly on a standardized test, while a kid whose daily work is mediocre scores at the top of the scale will tell you that standardized tests tell us some things, but not everything. And those huge data sets, while seductive to psychometricians and economists, are not impacting learning as much as one-to-one relationships and other soft, “anecdotal” practices. You can measure learning through student work products, too. It just takes a great deal more time and skill.

    I agree that the econometric model of measuring student learning is ascendant, and controlling the discourse at the moment, with the attendant narrative of equating test scores to accountability. But more rigorously controlled research models haven’t gotten us where we want to go in improving student learning, have they? They’ve just given us more data. And more data doesn’t always lead to better choices.

    I don’t pretend to be a research expert. I’m not. I’m a lifelong teacher, who had the opportunity use a very engaging curriculum model. The only scientific evidence I have was my observation that the content was challenging, and often hit the spot between what kids had mastered, and problems that pushed their mathematical thinking. And I repeat–I would never choose a curricular program based on standardized test data–I would choose one based on the learning goals embedded in the program, not the items selected by the test developer.

    Comment by Nancy Flanagan — March 26, 2009 @ 10:29 pm

  25. Totally, exactly.

    There may also another reason. When you apply phrases such as uniforms, no touching, no talking, no mandatory attendance, lockdowns, zero tolerance, police monitors, security cameras, barbwire, body searches, property searches and forced “community service” surrounding what you do in a “room” all day; where is the difference between school and the state penitentiary.

    Comment by Dee — April 3, 2009 @ 2:12 pm

  26. Wow, an entire book on why students hate school, and there’s not a single mention in this blog entry about how schools are designed to destroy original thought, to place the locus of control outside the self, and ultimately to produce mindless drones who buy what they’re told to buy, work where they’re told to work, and seek approval from equally mindless managers at work and in politics.

    Something’s amiss.

    Students hate school until it functionally lobotomizes them, and then they graduate. They survive thereafter as barely-literate automatons who do as they’re told by the folks whom they mistakenly attempt to please. Then they experience an externally-imprinted version of success, have their own children, and then nostalgically subject those children to the same machine that ground up their brains for 12-16 years. Rinse, repeat, at infinitum, since 1895.

    See John Taylor Gatto’s work for more on this (www.johntaylorgatto.com).

    Comment by Paul — May 4, 2009 @ 11:50 am

  27. Um, how does telling the story of Cortez’ ruthless attack on Tenochtitlan or teaching algebra or having kids write a persuasive essay “produce mindless drones who buy what they’re told to buy” or “lobotomize” kids? All of these nefarious crimes were committed at my middle school today.

    Comment by Ben F — May 4, 2009 @ 10:11 pm

  28. Ben, All I can say is, you’ll have to read the book. Then make your own choice. Maybe I’m full of mularkey, maybe Gatto is. It’s called _An Underground History of American Education_, and you can read it for free online at the website I linked.

    Gatto’s thesis is that forcing children to write about Cortez when they’d rather write about something else has an effect that is the opposite of education. I don’t want to get too lengthy here. I’d rather let you enjoy the book for yourself–it’s very well written and full of facts that require one to ruminate deeply. In the end, Gatto will blow your mind, even if he doesn’t change it.

    My point is not that learning, or even schooling, of any kind is bad. I was saying that the formula by which schools achieve their version of education is fatally flawed, and more often results in lobotomization than in education. Schools hijack curiosity and enslave it to the clock, the bell, and to the mindless formulaic repetition of figures that are unimportant to the free mind. They force children to seek the approval of a teacher (in most cases, a complete stranger) in the form of grades or verbal praise, rather than to be proud of their own work for their own reasons.

    For a less destructive alternative to the current model, take a look at the Sudbury Valley schools (http://www.sudval.org/)

    Comment by Anonymous — May 5, 2009 @ 8:02 am

  29. Mr Willingham, you’ve got faithful readers even in France ! We plan to write a review of your book on our blog, once we’ve finished it. SOS Éducation’s Team.

    Comment by SOS Éducation — July 17, 2009 @ 12:04 pm

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