One of my favorite Shrek movie moments is Donkey leaping up and down behind a crowd of people who have just been questioned by Shrek, enthusiastically exclaiming, “I know the answer! Call on me! Call on me!” While used for comic effect, these few seconds of film capture the essence of a much repeated scene in childhood: children vigorously raising and waving their hands in class, desperately eager to catch their teacher’s attention: “I know! I know! Call on me!”

While such noisy, chaotic behavior can sometimes be a problem for teachers in terms of managing the group behavior of younger children, it is nevertheless a wonderful problem to have. There are too many awkward moments of silence in classrooms filled with older children, where very few of them seem interested in raising their hand at all. Younger children love to notice, discover, think, and know things—and when they have even partially mastered a new concept or skill, they love sharing their euphoria, especially with their elders.

I think of our little neighbor Veronica knocking at our front door, asking me to come out and see what she could do. “Watch this!” she called, as she jumped from our front porch all the way down to the sidewalk (a total distance of two steps). I remember her happy, expectant face looking up at me, waiting for words of admiration to cheer her fresh triumph. That scene played itself out again another day, when I was called upon to witness the fact that she could not only ride her bike from clear down the street all the way to my house—but she could do it with only one hand holding on to the handlebar!

Not just young people find the simple act of knowing a fact to be stimulating and delightful and worth sharing with others. Think of all the adult games and TV game shows where the whole point is telling what you know—and beating everyone else by telling it first. Possessing knowledge is pleasurable, whether you are young or old.

Now go back in time and imagine some of these enthusiastic hand-raisers, boys and girls who are whizzes at math in elementary school. Some people naturally find numbers to be more fascinating than others, and these kids are definitely at the top of that list. They always catch on first in math class, and are thoughtfully probing in making new discoveries. They often have their hand in the air, hoping to be called on yet again, eager to demonstrate their mastery of new knowledge. Math learning is not a miserable, thankless task for them, as it is for many other children. They are good at math, and they love it.

Now follow these boys and girls on through middle school and high school. Their enthusiasm never wanes, their mastery is ever-growing, their thirst for new knowledge is never quenched, and their appreciation of the beautiful logic of numbers continually matures and deepens. And their attitude of “I know it! Call on me!” never leaves them. Their school grades are brilliant, and their SAT and college entrance exam scores are breathtaking. They could easily have impressive careers in science, research, or industry. But their love of math is so great that they decide to become high school math teachers. What could be more exciting and satisfying?

So they do just that. Their personal and professional vision is to produce students who are as good at math and as excited about it as they are. And that does happen part of the time with some of their students—the students who are naturally gifted at math, like they are. But then there are the rest of the students. The development of their understanding seems to move at a snail’s pace, compared to what the teachers and the best students can do. But the teachers know that everyone has untapped potential, so they pull out all the stops in a concerted effort to bring out that potential in the “lesser” students. Their lectures are very focused, organized, efficient, and high-energy, they have a rich storehouse of examples and evocative stories to share, they excel at making connections between math and other subject areas, and they vigorously challenge all their students to make their best better.

After some years, though, the teachers become somewhat tired and discouraged. It is true that some of their best students go on to do great things in math. But the low-achievers are draining the fun out of their jobs. The teachers are under great pressure from parents, administrators, and the general public to improve average scores on standardized tests—which are embarrassingly low compared to many other countries. And nowadays, students can’t even get a high school diploma unless they have passed Algebra. The pressure on teachers for all their kids to produce is intense and exhausting.

But the low-achievers seldom break through their shrouds of limitation. Their natural “I know it! Call on me!” reaction is rarely seen to surface. Their curiosity seems stifled. Their mental energy and their ambition are too low. They don’t focus, don’t pay adequate attention, and don’t follow directions well. And the teachers’ sense of hope is often dampened by their perception that there are too many lazy kids who don’t care, too many with sloppy study habits, too many with unsupportive family backgrounds and inadequate proficiency in English, too many with concept and skill gaps that show inadequate preparation by previous math teachers, and too many who are so far behind that their individual needs are very difficult to address—even in typical mixed-level classes.

And perhaps most exasperating to the teachers, these low-achieving students tend not to ask questions in class! They claim not to understand the math topics and problems under consideration (which seems almost impossible, when the teachers have gone to such pains to make everything abundantly clear)—but then they don’t ask intelligent questions in class when they have a chance to. How can the teachers help these students, if they don’t know what it is that they don’t get, and if the students don’t clarify the exact nature of their need by asking good questions? If they’re not going to say “I know it! Call on me!” the least they could do is to raise their hands and say, “I don’t get it. And this is the part that I don’t get. Help me to understand it!” But that doesn’t happen nearly often enough. And yet the teachers are being held accountable for the students’ lack of initiative. For teachers and students alike, it can feel frustrating, maddening, and unfair.

It may seem like a hopeless situation. But are there changes that could be made that would significantly improve the situation? Many of the teachers feel that they do not need to make any changes; they are already performing well, doing all of the things that are expected of a good teacher—and spending more time doing it than they are being paid for. The problem is that they are doing a good job of teaching, but the students are not doing a good job of learning—or so they think. The obvious solution to many teachers is for everyone else to change. The students’ earlier math teachers must do a better job. Lagging students must get private tutoring. Students and their parents must get more serious about getting homework done. Families must place greater importance on education. Society must elevate its values. Etc.

But here’s an important question for teachers to ask themselves. Who is the most able to initiate and sustain the changes that will improve the performance of low-achieving math students? Is it the students who have been struggling with math ever since the first grade? That is not likely. Is it the parents who never got very far in math themselves? Is it the college-educated parents, who don’t know how to help their math-challenged children, because they are so unlike themselves? Or is it the highly intelligent, highly educated teachers themselves who are the most capable of coming up with the effective innovations that will make epidemic low achievement a thing of the past? This author argues that educators have by far the greatest potential in that direction.

But what changes can teachers make? Perhaps the change that is most needed has to do with the “I know it! Call on me!” phenomenon. What do high school math teachers typically do in their classes? They explain new math concepts. They explain the mathematical processes that connect with the new concepts. They give brilliantly concise summaries. They tell the formulas, the rules, the shortcuts, the tricks, and the patterns that the students need to know. And when conscientious pupils raise their hands to ask for help with problems from last night’s homework, the teachers tell step by step exactly how to solve them. And they tell all the answers. In short, it is as if someone had said to the teachers, “How do you do these problems?” and the teachers collectively and vigorously raised their hands and said, “We know it! We know it! Call on us!” And then they proceed to do what they have been so good at from their childhood.

This is something that can be changed. It is the students (including the low-achievers), and not the teachers, who should be yelling out, “I know it! Call on me!” How can this be brought about? The first step is for teachers to decide to set aside their natural desire to demonstrate their mathematical knowledge, deferring that pleasurable excitement to their pupils. To do that, they would have to stop telling the answers, stop telling the explanations, the shortcuts, the formulas, the tricks, and the patterns. Instead, they would guide their students’ development by breaking problems down into more easily digestible component parts, and then use leading questions to stimulate their pupils to figure things out for themselves. A teacher that I admire in this regard uses phrases such as, “How would you work this problem?” “Tell me how you did it. Take me through it; give me some numbers here.” “I’m gonna play stupid. I don’t know how to solve this problem. Somebody help me out.” “What do I do next?” “Is this how you do it (showing a wrong example)?” And so on.

A major benefit of such an approach is that the teachers get to hear what their students are thinking, and get a feel for what they know, how well they know it, and how they feel about it. When the teachers are busy doing all the telling, they know what they have just said, and they know that their class was silently watching and listening. But they don’t have any tangible evidence of what the students are actually thinking. All they know is that, based on what they just did, the students should get it. But they often find out later that they didn’t get it. Asking questions opens a window into the students’ minds.

It is easy for teachers to deceive themselves into thinking that “I taught it, but they didn’t learn it,” when they have told their pupils how to do a new kind of problem. But it could be argued that “If they didn’t learn it, then you didn’t teach it,” or “You didn’t teach it in ways that they could learn it.” This may be a tough pill to swallow, but it is not without logic. We know that there are many styles of learning, and that individuals all learn differently. For teachers to rely solely on telling the rule, the explanation, etc. is a one-size-fits-all kind of solution that is really not appropriate in the arena of learning, where one size most emphatically does not fit all.

“Ask a good question, get a good answer.” But our low-achieving students tend not to ask questions in class for three main reasons: some are too shy, others are afraid to expose their ignorance, and many truly don’t know what to ask or how to ask it. Teachers’ exhortations don’t tend to change that. And teachers’ continued wordy explanations do not provide their students with a model for how to ask useful questions in an orderly manner. If teachers want their students to learn to ask better questions, then they must get better at asking their students questions; there is no possible better model. I once heard it said, in reference to the relative merits of telling vs. asking, “If you want to be a teller, go work in the bank! If you want to be an asker, go work in a school.”

To be qualified, math teachers must know their subject matter. But their actual job is not primarily to demonstrate their mastery of the subject matter; it is to lead their pupils to develop their own mastery of the subject. Nor is the teachers’ main job to disseminate information through explaining and modeling; we already have books that do that. And judging from student performance, it is clear that explaining and modeling is a teaching device that is ineffective for many pupils. Books are designed to teach math. It is the teachers’ job to teach math to kids by stimulating curiosity, creating perplexity, and engaging children’s natural power to notice. And to do that with precision, teachers must be actively aware of the students’ varying levels of readiness. What better way is there to accomplish all of these things than to ask questions?

Math teachers are clever people. When they decide to stop telling their students so much and begin asking them more questions, they will find that an intimate knowledge of exactly what their students really know (as opposed to what they are supposed to know) is not that hard to come by. That will enable them to meet their pupils exactly where they are (instead of where they should be). Task analysis of the material to be learned will then guide them in formulating a series of guided discovery tasks and related questions that will create a series of small successes, which will get the learners from where they are to where they need to be. The right series of tasks and questions will stimulate their pupils to develop and “own” their own unbreakable chain of reasoning. Then they will be the ones exclaiming, “I know it! Call on me!” And that is as it should be.

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