Gifted Math Education: Teaching to Learn

You do not really understand something unless you can explain it to your grandmother.

– Albert Einstein

Should Gifted Math Students Tutor Others?

So let’s start the new year with a little controversy. 😉

Many schools ask gifted kids to “tutor” some of the other kids in class at some time or other in their school careers (particularly during the K-8 years). Most parents of gifted kids are wholeheartedly opposed to it, for a number of good reasons. However, I propose that, properly handled, this can be beneficial for kids. Let me say right up front that tutoring should never be the only thing an advanced child gets to do in class. But gifted students have time to go beyond the basic curriculum, and in my opinion, it is quite reasonable for them to spend some of that extra time doing some tutoring, in addition to other types of enrichment such as investigating topics outside the normal curriculum, doing non-routine problem solving, etc.

Typical objections to this practice include:

• I think my child deserves a full-year’s growth in the math every year.
• My child doesn’t like tutoring.
• My child isn’t good at explaining how to do things that are so easy for him.
• If learning to explain math to others is so important, why isn’t it on the curriculum for everyone?
• It’s not fair to the child being tutored to be taught by a child instead of a qualified teacher.

I’ll address each of these in turn.

I think my child deserves a full-year’s growth in the math every year.

I agree that every child deserves to have the opportunity to obtain a full-year’s growth in every subject, and this is certainly an area where gifted kids are often let down. However, I think it’s important to examine what a math education is intended to provide, and what counts as “growth”. Is the point of a good math education only to learn a pre-defined bag of tricks listed in the math curriculum for a certain grade (and to cover as many grades worth of material as a student can handle as quickly as possible)? Or is it to become a better mathematician (which may include topics and skills beyond the basic curriculum)? In my opinion, it is very narrow-minded to view advancing by at least one grade level on the basic curriculum as the only worthwhile type of growth for a gifted math student.

If a child’s mathematical thinking and mathematical communication skills improve as a result of tutoring another child, that may well be worth a lot more, in the long run, than mastering another year’s worth of arithmetic or algebra topics. A mathematician who proves an important theorem is nowhere if she can’t communicate the essence of her proof to her community. (I realize, of course that the type of explanation that is required in the latter case is much different than that of a student helping classmates, but the skills are related and I firmly believe that the ability to do the mathematical communication required to tutor math concepts one already understands is truly a crucial skill.) A year’s worth of growth does not necessarily have to be linear along curricular lines, and there are many reasons why it is often better if it isn’t.

Even if the student doesn’t go on to become a mathematician, there are times in almost any career where a person is called upon to explain and/or defend his ideas or plans to others who are less familiar with the subject matter. This very skill of explaining something to others who don’t understand it is an important life skill in almost every discipline.

My child doesn’t like tutoring.

So, I’m not so sympathetic to this one. Some kids don’t like fractions either. They still have to learn them. School isn’t about only getting to do what you like.

There is a reasonable argument that a young gifted child who loves math and hates tutoring shouldn’t have to spend all his math time tutoring. But as I said above, tutoring should never be the only thing a gifted kid gets to do. And having to do something one doesn’t like so much part of the time is not, in my opinion, unreasonable.

My child isn’t good at explaining how to do things that are so easy for him.

Isn’t school about learning to do things you aren’t already good at? It is reasonable, in my opinion, for one of a child’s goals in math class to be learning to explain the things he knows clearly, in ways that others can understand. Referring back to the Einstein quote at the top of my post, clearly I’m not the only one who sees value in learning this skill.

But… here’s where one of my caveats comes in. Too many teachers assume that because a child is good at math, he is necessarily good at teaching math. If a child isn’t naturally good at explaining the things they know, someone has to teach him how to do this. It’s not appropriate to expect a child to learn how to explain what he knows without giving him any help or guidance in achieving this goal.

If learning to explain math to others is so important, why isn’t it on the curriculum for everyone?

This may also be worded as, “why is my child required to learn to do something she doesn’t enjoy, when no one else is?” My answer to this is that the standard curriculum is pared down to a bare minimum, since students of all levels of ability have to complete it. For a child who can complete the basic curriculum in considerably less time, there is time to expand and include other valuable skills and topics. And one of those skills is the ability to communicate what you know to someone with a lower level of understanding. The fact that not everyone gets the opportunity to learn and practice this skill is a necessary effect of the fact that most students take the full time allotted to learn the more basic items in the curriculum. For those who complete the basics quickly, learning new skills and exploring topics outside the basic curriculum is a wonderful opportunity that is wasted when people insist on just moving the student as quickly as possible through the basic curriculum.

It’s not fair to the child being tutored to be taught by a child instead of a qualified teacher.

Indeed, this is an important consideration. It is of course always the teacher’s responsibility to ensure that each child has the material presented to him in a way that is understandable. It is not acceptable to put this responsibility on another student. If a teacher asks another student to spend some time explaining the material, the teacher must always monitor to see whether the student being tutored is indeed getting what he needs. This is closely related to the point about students not necessarily knowing how to explain things — the teacher must monitor and see that the “tutor” is getting the support she needs in learning how to explain things, and the “tutee” is getting the support he needs in terms of improving his understanding of the subject matter.

Theory versus Reality

“Well, that all sounds very nice, but that’s not the way it is in my child’s school!”

Indeed, in too many cases what really happens is that the teacher assigns the top kids to tutor the bottom kids, so that the teacher can teach to the middle, and not have to deal with the kids at the extremes. The advanced kids aren’t getting any advice or instruction as to how to help the struggling kids, so unless the advanced kids happen to have a natural knack for it, everyone gets frustrated.

So, as much as this post supports the notion of having gifted kids doing some tutoring, it does not give the green light for teachers to do it lightly, or as a convenience for themselves. There are several important things that I feel must be addressed in order to do this “right”, which do make more work for the teacher who wishes to employ this strategy:

1. The student being asked to tutor is taught how to do so;
2. The teacher takes full responsibility for the learning of the student being tutored, and checks in regularly to ensure that the tutoring relationship is a fruitful one; and
3. The gifted student is not expected to do this all the time — much of the time he must be given other appropriate enrichment activities.

Finally, I’ll add one additional caveat, which is social. There can be social consequences of placing a student in the role of “teacher”. It is important for the teacher to handle this well. In many cases this can work out fine with the right attitude and guidance from the teacher, but it is one more thing that a teacher needs to be aware of and keep an eye on.

Related post:
Gifted Math Education: acceleration, enrichment, and the Calculus Trap