## Teaching Weblog - David Krebes

31/12/17

How do I determine what my student needs?

Well first and foremost I can simply ask. I think it is better to work with what the student needs than with what the student wants. The student may want to stop thinking about math. They may want to think only about material they understand. But typically I think students are good at finding problems they don’t know how to solve for us to work on together.

Students don’t need to know more than one way to solve a problem. They do need effective teaching and covering as much material as possible. That means they need to know how to solve not just individual exercises but entire clusters of exercises. The complaint “we never covered that” of exam questions should very seldom arise.

There may be certain things the student needs which I cannot provide. I do not know the best time of day for them to study. I don’t know how to make time for them to study. I do not know if they are getting enough sleep, although I can ask.

The student needs to feel comfortable working with me, though I may need to push this a bit, to challenge the student, to give them responsibility.

1/1/18

How can I transfer some of my math skills to my student?

I can do some thinking out loud. By listening to what I say the student can perhaps emulate my thought patterns.

I can break problems up into simple, easy-to-understand steps that are transparent. This is analysis. If the student knows how to proceed in small increments they will be able to solve shorter as well as longer problems.

I can try to share my conviction that everyone has mathematical potential. If the student has conviction that they can succeed they will try harder and persevere longer.

I can show the student how to solve some problems and get them to work independently on others. I can make sure they are doing enough homework. With

I can try to make mathematics interesting for the student. Having fun with math is key to my own mathematical competence. If I can get the student to have fun then their stamina and persistence will improve. They may also be a little less afraid of making mistakes.

I think I need to start with the premise that my mathematical skills

2/1/18

What is gap analysis and how can I make it work for my student?

Gap analysis is the detailed investigation of the “gap” between where the student is now and where the student wants/needs to be, as well as an attempt to figure out how to bridge that gap. It is similar to the concept of

Do we really need gap analysis? Can’t we just do the math? I have certainly had some success with the latter. Just by thinking about math my experience is that the student is sure to improve. But I do think that the kind of math which students work on in grade school is tailored to a goal-setting type approach. It is measurable in a way that research-type math is not. Why not make use of that measurability? Why not acknowledge it?

Therefore we are interested in the gap between present math scores and desired math scores. But more interesting and perhaps more illuminating is the gap between how the student works now and how the student might work to get higher grades. For instance I have a student who is too slow. The gap is the differential between his present speed and a speed at which he can finish the exam and have a little time to check back over his work.

3/1/18

What is variance analysis and how can I use it to my student’s advantage?

Variance analysis addresses the question “What went wrong?” It is easier to correct problems which have already been identified than to speculate on possible problems that might arise in the future. To make variance analysis work the student must be candid about what has not worked for them in the past.

Roughly speaking, there are two kinds of things that can go wrong: mathematical and para-mathematical. “Para-mathematical” includes like running out of time on an exam, mis-reading a question on an exam, or not having good study habits. “Mathematical” includes things like calculation errors, or being stumped on a problem.

There are also two steps in variance analysis: figuring out what went wrong and figuring out how to fix it. Sometimes there is no distinction, for instance in noticing a calculation error.

I should probably be in the habit of requesting the student to bring in past exams so we can look at what went wrong.

Is variance analysis too late? Not if the student has a cumulative exam coming up. Nor is variance analysis of para-mathematical factors, which persist from one exam to the nest.

How do I determine what my student needs?

Well first and foremost I can simply ask. I think it is better to work with what the student needs than with what the student wants. The student may want to stop thinking about math. They may want to think only about material they understand. But typically I think students are good at finding problems they don’t know how to solve for us to work on together.

Students don’t need to know more than one way to solve a problem. They do need effective teaching and covering as much material as possible. That means they need to know how to solve not just individual exercises but entire clusters of exercises. The complaint “we never covered that” of exam questions should very seldom arise.

There may be certain things the student needs which I cannot provide. I do not know the best time of day for them to study. I don’t know how to make time for them to study. I do not know if they are getting enough sleep, although I can ask.

The student needs to feel comfortable working with me, though I may need to push this a bit, to challenge the student, to give them responsibility.

1/1/18

How can I transfer some of my math skills to my student?

I can do some thinking out loud. By listening to what I say the student can perhaps emulate my thought patterns.

I can break problems up into simple, easy-to-understand steps that are transparent. This is analysis. If the student knows how to proceed in small increments they will be able to solve shorter as well as longer problems.

I can try to share my conviction that everyone has mathematical potential. If the student has conviction that they can succeed they will try harder and persevere longer.

I can show the student how to solve some problems and get them to work independently on others. I can make sure they are doing enough homework. With

*practice*and*exercise*the student develops skill and confidence.I can try to make mathematics interesting for the student. Having fun with math is key to my own mathematical competence. If I can get the student to have fun then their stamina and persistence will improve. They may also be a little less afraid of making mistakes.

I think I need to start with the premise that my mathematical skills

*can indeed*be transferred.2/1/18

What is gap analysis and how can I make it work for my student?

Gap analysis is the detailed investigation of the “gap” between where the student is now and where the student wants/needs to be, as well as an attempt to figure out how to bridge that gap. It is similar to the concept of

*variance*analysis which is looking back rather than forward.Do we really need gap analysis? Can’t we just do the math? I have certainly had some success with the latter. Just by thinking about math my experience is that the student is sure to improve. But I do think that the kind of math which students work on in grade school is tailored to a goal-setting type approach. It is measurable in a way that research-type math is not. Why not make use of that measurability? Why not acknowledge it?

Therefore we are interested in the gap between present math scores and desired math scores. But more interesting and perhaps more illuminating is the gap between how the student works now and how the student might work to get higher grades. For instance I have a student who is too slow. The gap is the differential between his present speed and a speed at which he can finish the exam and have a little time to check back over his work.

3/1/18

What is variance analysis and how can I use it to my student’s advantage?

Variance analysis addresses the question “What went wrong?” It is easier to correct problems which have already been identified than to speculate on possible problems that might arise in the future. To make variance analysis work the student must be candid about what has not worked for them in the past.

Roughly speaking, there are two kinds of things that can go wrong: mathematical and para-mathematical. “Para-mathematical” includes like running out of time on an exam, mis-reading a question on an exam, or not having good study habits. “Mathematical” includes things like calculation errors, or being stumped on a problem.

There are also two steps in variance analysis: figuring out what went wrong and figuring out how to fix it. Sometimes there is no distinction, for instance in noticing a calculation error.

I should probably be in the habit of requesting the student to bring in past exams so we can look at what went wrong.

Is variance analysis too late? Not if the student has a cumulative exam coming up. Nor is variance analysis of para-mathematical factors, which persist from one exam to the nest.