Teaching Weblog - David Krebes
19/1/2022
Why am I a teacher?
I like to help people. It always makes me feel good to hear that a student did well on an exam. I enjoy being a small part of a student's success story. It means I have done a good job of explaining things, which is fun for me.
19/1/2022
How do I determine what my student needs and what is my teaching style?
If the student brings me problems to work on then I am happy to oblige. I like working on topics and skills that the student identifies as problem areas.
As we work through a problem, I frequently pause to ask the student for the next step. This can be hard for the student but I am forgiving. When we do this I can almost see my student learning.
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. We try to work at a steady pace. The student needs to know how to solve not just individual exercises but entire clusters of exercises. This is my aim. The complaint “we never covered that” of exam questions seldom arises with my students.
I have a holistic approach to teaching. What is the best time of day for the student to study? How can they make time for study? Are they getting enough sleep?
My students feel comfortable working with me, though I do challenge them and give them responsibility.
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 varianceanalysis 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.
Why am I a teacher?
I like to help people. It always makes me feel good to hear that a student did well on an exam. I enjoy being a small part of a student's success story. It means I have done a good job of explaining things, which is fun for me.
19/1/2022
How do I determine what my student needs and what is my teaching style?
If the student brings me problems to work on then I am happy to oblige. I like working on topics and skills that the student identifies as problem areas.
As we work through a problem, I frequently pause to ask the student for the next step. This can be hard for the student but I am forgiving. When we do this I can almost see my student learning.
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. We try to work at a steady pace. The student needs to know how to solve not just individual exercises but entire clusters of exercises. This is my aim. The complaint “we never covered that” of exam questions seldom arises with my students.
I have a holistic approach to teaching. What is the best time of day for the student to study? How can they make time for study? Are they getting enough sleep?
My students feel comfortable working with me, though I do challenge them and give them responsibility.
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 varianceanalysis 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.
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