What Should a Math Tutor Know and Do?

Hulu shows a TV ad for online tutoring that I have seen many times. It features a girl who looks like she is about 10 years old and her online tutor who is working from home. The ad is effective because many people can relate to it. The math assistance depicted in the ad, however, is not effective in the real world.

Here’s how the ad goes: A girl contacts her online tutor and asks her how to find the area of a triangle. The tutor gives the girl the formula (“Area=one-half x base x height”) and tells her to “multiply the base times the height and divide by two.” Both the tutor and the girl seem very satisfied with this solution.

While the intention of the organization that is behind this ad is admirable, the quality of the instruction in the ad is problematic. There is no math in plugging numbers directly into formulas, and there is no meaningful way for the girl to recall the formula if she forgets it. It would not have been difficult to show where the triangle area formula comes from using first grade geometry concepts, and the girl would have  become  empowered to come up with the formula on her own if she could not recall it.

Another issue is that, for a girl that age, it may not be obvious that “one-half times base times height” gives the same result as “multiply the base times the height and divide by two.” Conceptually, they are different.

This ad is an accurate representation of most math tutoring. Tutors tend to be college students who know math, but not math pedagogy, or school teachers who know very little math beyond the grade levels they are teaching. Such tutoring gives short-term satisfaction, but does not advance mathematical understanding, and leads to misconceptions that need to be repaired later on. In short, this process breaks down as students progress through school math.

In order to tutor effectively, a math tutor should guide students toward solutions and mathematical understanding based on what they already know or almost know, rather than simply tell students how to do the type of math problem that they are working on, step by step, piece by piece. A piecemeal approach keeps a tutor employed for a long time, but doesn’t empower students to eventually learn math on their own.

In order to tutor effectively, a math tutor should be mathematically proficient at a level that is far ahead of the math content level of the student. The reason for this is that the math tutor is helping to lay a foundation for more advanced math learning, and should thus know how the concepts and procedures evolve.

A math tutor should also know the following: 

• What is typically difficult for students;
• How to represent procedures and ideas;
• How the use of specific language can help or hinder understanding;
• How to adapt material to student abilities and prior knowledge;
• Common misunderstandings; and
• How to make math accessible to students.