What are tutoring strategies for students struggling in math?

Question

I am a tutor for a student and I work with him 7 days a week, for about 2-3 hours a day. The student severely struggles with math, although I am a tutor for every subject (he is in high school). His first chemistry exam he got a 77, and I brought it up to a 96. I studied with him for history and he received 100 on that test. However, his first math test was a 73. I spoke with the parents and told them that the homework he is receiving is very different (in terms of difficulty than the exam). The homework is much easier. So I decided that despite how easy his homework is, I will come up with challenging problems that are similar to his exam problems.

He had the test today and said he really messed up on it. I spent 4 hours yesterday and 4 hours the day before preparing with him. I gave him a mock exam, I came up with questions that are similar to his review sheet. I did everything I thought I could to help him. What should I do?

I noticed that during the mock exam, he could barely answer any questions without turning to me to ask for clarification and then he would stop midway and though his logic was sometimes correct, he would make silly errors.

Is there anything I can do in order to fix this situation? I feel responsible for his bad grade. What more can I offer to help him, or what more can I do in order to make him succeed?

I feel like I failed him, and that it's my fault. During the sessions I am very attentive and any small thing he doesn't understand, I make sure he gets it. So I don't know what to do. I've never experienced this before.

Answer 1

This is very hard to answer without details such as:

• Is this student generally a sense-making student or one who just seeks answers? How do you know?
• Is the student lacking prior knowledge? Many students get high grades for years in math because they rote memorize procedures while understand ~nothing. For example, they can do long division to calculate $249\div15.3$ but cannot estimate an answer nor can they generate a word problem that might go with it or distinguish it from $15.3\div249$. What have you done or are you planning to do to assess for this? Weak prior knowledge is almost always the biggest problems with students who struggle with math but succeed in all other courses.
• You said "... any small thing he doesn't understand, I make sure he gets it." How are you making sure of this? How do you know he is only appearing to understand? Inferring understanding of mathematical concepts from typical school math is not like push ups. If you do 10 push ups, you can obviously do 10 push ups. If you do 10 division calculations correctly, you might have zero understanding of division.

I can give this advice, though. Generally, it is not a good idea to help students part way through a problem. Make them try their hardest first, then share all their thoughts, and then you both have a clear idea of where they're at. Now, you have the information you need to provide appropriate feedback and hints. After they succeed, then they should try a mix of different types of problems, at least one of which is like the on you just helped them with. [If it isn't a mix, they might just robotically apply the same algorithm without thinking.]

Assistance before their best effort means that anything that makes it to the page is a joint effort. Furthermore, students typically ask for help with the hardest part of the question, e.g. deciding if it's permutations, combinations, or neither. If you say "It's permutations", they might then spend 5 minutes hand-calculating an answer, getting it right, then thinking they've mastered it... when really they had no conceptual idea of what was happening at all and would have gotten a zero on the test.

Answer 2

A raw score on an exam doesn't mean anything in and of themselves, so we have no context for evaluating what a 73% means. If this is a class where the grading scale is 90%=A, 80%=B, 70%=C, then this student passed his math exam, which doesn't seem like a bad outcome for someone who really struggles in math. Grade inflation notwithstanding, not everyone is going to get an A in every subject.

I spent 4 hours yesterday and 4 hours the day before preparing with him.

You don't say whether this is college or high school. If it's college, then the typical expectation would be that for a 4-unit math class, the student would spend about 8 hours a week outside of class on the work. So 8 hours of work (ordinarily independent work) would be a typical week. And 8 hours a week isn't a maximum, it's more like a minimum. For a student who is particularly bad at a certain subject, and who wants to get a good grade like a B, probably more like 10, 15, or 20 hours a week will be needed.

Math is a subject that requires constant, steady practice. Mastering most skills (violin, chess, ...) requires about 10 years of steady, intense work. What has this student's work been like for the last 10 years?