I recently watched a video of a teacher helping a student master tens and ones using ten frames and unifix cubes. While the video showed some of the ways Singapore Math teaches number sense well, a few things about the teaching style struck me. These are pertinent to tutoring because it was a one-on-one situation.
 
One thing that stood out was that the teacher sometimes gave the answer to the student before the student had a chance to think. This is a mistake that is so easy to make; the tutor knows the answer, and the child doesn’t, so why not tell the student what the answer is? That will help them learn, right?

The thing is, any good teacher or tutor knows that the best learning happens when the child discovers something for him or herself. For most people, if they know the answer, it’s hard to hold themselves back from giving it to the child. But the best teachers guide or lead children to making their own discoveries. If children are moving in the wrong direction, a good tutor guides them toward successful results. This requires a knowledge of why students are making the mistake they are making.

For example, say I’m checking some pre-algebra homework. The problem the student has to solve is 3x + 4 = 73. The student’s answer is x = 25-2/3. From my experience working with students, I will know that the student performed all steps correctly except for adding 4 to 73 instead of subtracting it. Depending on the pattern that shows up with other problems, it could be a fluke, or it could point to the need to review the concept of positive and negative integers, or how to solve an equation with a variable. If it’s the latter, we may need to go back to the concrete stage of learning and work our way back up to the abstract (equation) level. Throughout the process, I will not give the child the answers, but will ask them to justify their answers each step of the way. That way, they are more likely to catch their own mistakes and correct faulty thinking.

Being a good tutor requires more than just mastery of a subject. It requires an understanding of how the subject works, how students learn, what kinds of mistakes they might make and what those mean in terms of review. Most of all, it means being able to guide students toward their own voyages of discovery and learning.