Teaching Math/Science to Different Thinking People

[thegreenlaser]

My friend is taking linear algebra this semester, and math is definitely not one of her passions. She was nervous about taking it, but ended up doing it because I got an A+ in the course last semester and said I would help her with anything she's having trouble with. Unfortunately I'm having a little difficulty. She'll ask me a question and things make sense in my mind, but I have trouble getting that understanding across to her. This tends to end with her feeling like she's just bad at the subject, which she isn't. I think the main problem is that we think quite differently: I love math and love going in-depth while she just wants to get a decent mark in the course and get it over with.

Does anyone have any tips about how to be a good teacher, especially in math/science? I enjoy helping people with math/science, but I'm only really good at it when I'm teaching people who have the same love of math/science that I do. Obviously, a lot of the people who ask me questions aren't like that, which makes my teaching abilities quite limited.

(I guess this should probably be in Academic Guidance. Sorry)

 

[deluks917]

Try to be as concrete as possible. I'd recommend using as many examples as you can.

 

[Unrest]

For math in general the terminology can scare a lot of people off, so I guess be careful of words that she may have heard over and over and learned to tune out to.

Another thing, which was often a problem for me as a student, was the lecturers going too fast. Once I got a little bit lost I'd never be able to get back on the wagon till I sat down and did it slowly by myself. So make sure she understands the very basics of a problem first - what the goal is (maybe show the solution there at the start so she can see where it's heading), what the symbols mean, which ones are matrices, vectors, etc.

 

[micromass]

My friend is taking linear algebra this semester, and math is definitely not one of her passions. She was nervous about taking it, but ended up doing it because I got an A+ in the course last semester and said I would help her with anything she's having trouble with. Unfortunately I'm having a little difficulty. She'll ask me a question and things make sense in my mind, but I have trouble getting that understanding across to her. This tends to end with her feeling like she's just bad at the subject, which she isn't. I think the main problem is that we think quite differently: I love math and love going in-depth while she just wants to get a decent mark in the course and get it over with.

Does anyone have any tips about how to be a good teacher, especially in math/science? I enjoy helping people with math/science, but I'm only really good at it when I'm teaching people who have the same love of math/science that I do. Obviously, a lot of the people who ask me questions aren't like that, which makes my teaching abilities quite limited.

(I guess this should probably be in Academic Guidance. Sorry)

I understand your troubles. I always enjoy helping people too, but somehow I can only help people who really love the subject. If people take the course just to get an A, then there are few things you can do for them. The motivation and the love need to come from them!

But anyways: here are some hints on how to approach such people:
1) Don't give to much background information! They'll forget it anyways, and it will confuse them.
2) Give a lot of examples and make them do a lot of exercises. (sadly, they will probably not be motivated to make a lot of exercises...)
3) If possible, relate the theory to something that does interest them. But this can be very hard and requires some creativity.

 

[Sankaku]

1) Don't give to much background information! They'll forget it anyways, and it will confuse them.

I am not sure I agree with this. Certainly, don't overwhelm someone with extra detail. However, showing the connections to things they already know is very important. Math is often taught as if each subject exists in a Vacuum. Try to connect the dots for her (as much as she can take).

The other thing that is difficult, if you find it fun and she doesn't, is slowing down. Enthusiasm is great, but make sure to let her dictate the pace. If it is a proof-based course, really take the time to show her how proofs work and help her write her own.

 

[thegreenlaser]

Thanks for all the input. It definitely gives me some things to think about.

So specifically, I was trying to teach her eigenvalues and eigenvectors, and she'd already seen the "algebraic" approach in class. Like $$A\vec{x}=\lambda\vec{x}$$ and then how to find $$\lambda$$ and $$\vec{x}$$. She was a little confused about what eigenvalues/vectors were in the first place, so I decided to try and show her a more graphical approach. I showed her in 2 dimensions using projection and then reflection matrices. It ended really badly, because she had no idea what projection was, and the whole time I was showing her reflection matrices she was just staring blankly at the page. What I tried to emphasize was how a matrix performs a specific transformation to a vector, and how an eigenvector is a specific vector for a specific matrix that ends up parallel to the original vector after you've transformed it with that matrix. Was there something bad about the way I approached it? I know she didn't absorb much of the algebraic method her teacher taught her, so I thought the graphical approach would be a good way to connect it to things she already knows.

I understand that I probably delivered it pretty badly (it definitely didn't help that my first thought was "oh hey, rotation matrices are a nice, easy first example for finding eigenvectors graphically"), and I'm going to work on using more examples and going a little slower, but I'm curious if my approach was poorly chosen to begin with.

 

[Unrest]

matrices. It ended really badly, because she had no idea what projection was, and the whole time I was showing her reflection matrices she was just staring blankly at the page. What I tried to emphasize was how a matrix performs a specific transformation to a vector, and how an eigenvector is a specific vector for a specific matrix that ends up parallel to the original vector after you've transformed it with that matrix.

Haha I've been in that situation so many times. I can see from your writing that you see it as a simple, obvious concept. The more fascinating and obvious something is, the more it seems to confuse people who aren't all excited about it :P Many people are reluctant to interrupt you when they don't understand something. Instead they just keep listening and hope it'll become clearer later - but it doesn't. I find that usually once that's happened with someone, they'll never again understand the subject because when they hear the trigger words "projection", etc. their mind shuts down. But that's people who don't really need it, I really hope your student plows through on this point just to prove to herself that she can conquor any of it.

But if she just wants an A, surely she doesn't need to know that. Just has to crank the handle. I hardly know that and I work with eigenvectors all the time!

 

[vanesch]

I enjoy helping people with math/science, but I'm only really good at it when I'm teaching people who have the same love of math/science that I do. Obviously, a lot of the people who ask me questions aren't like that, which makes my teaching abilities quite limited.

This makes me think of this (unfortunate) truth:

http://www.brainyquote.com/quotes/quotes/e/edwardgibb389013.html

But the power of instruction is seldom of much efficacy, except in those happy dispositions where it is almost superfluous.

I remember when I first read that, I didn't understand what it meant... and had to find out its truth over the years...

What's difficult, tedious and needs creativity, is to find out what is the (erroneous ?) mental construct the student already in his/her mind ; what are the available concepts in his/her mind on which to build, and to design a path from there to the desired end result (the right mental construction, or A right mental construction, together with a certain ability to use it). That path can be entirely different than the one you "obviously" and "logically" would wander if you go from YOUR concepts to the one you want to explain and "your" path entirely inadequate for that other person if concepts are missing, or worse, differently (or erroneously) represented along the way.

 

[Andy Resnick]

Does anyone have any tips about how to be a good teacher, especially in math/science? I enjoy helping people with math/science, but I'm only really good at it when I'm teaching people who have the same love of math/science that I do. Obviously, a lot of the people who ask me questions aren't like that, which makes my teaching abilities quite limited.

(I guess this should probably be in Academic Guidance. Sorry)

You have correctly identified possibly the fundamental issue in teaching- how to be an effective teacher. Learning is not the process of pouring information into some else's head, it's an active exchange between teacher and student: it requires work from *both*.

My approach (and I don't claim it's the correct/only/etc approach) is to try and bring the subject matter to the student. That is, explain the issue in terms the student is comfortable with- that requires knowing something about the student, and since I don't know about your friend, I can only offer examples. For example, when I teach Physics I, I like to put concepts in terms of driving a car, or how different parts of a car work together to produce motion. To teach eigenvectors and eigenvalues, at least to start, I toss a book in the air and show how some rotation directions remain unchanged while one does not. Again, as a teacher the onus is on you to make the subject comprehensible to the student, not bring the student to your way of understanding.

There's no magic shortcut to learning. If your friend is really only interested in getting a good grade (and in this, she is like 99% of other students), it's important that she work example after example- with your guidance- until she understands the procedures and steps needed to answer test questions.

 

[thegreenlaser]

Thanks again for all the suggestions. I taught her eigenvalues/vectors again and it went much better this time. I went slow and used a lot of examples, which I planned ahead so that they would work out nicely. She feels like she really understands it now.

 

[mathwonk]

A beginning teacher just explains the material logically and thoroughly and assumes that is all they need to do. The secret is going really slowly, and making a conscious effort to understand where her confusion lies. You should not assume you can teach it just because you understand the topic. Or rather that is not all you need to understand. You also need to know that this is hard for the other person, be patient, and set yourself the task of seeing it through her eyes.

This problem arises because the other person lacks some insight that we take for granted and do not think to mention. It is our job to see how they are thinking and approach the topic from that direction, supplying what is missing for them. I always try to make up analogies that are phrased in a language the person I am tutoring does understand.

It sounds as if you are already making progress. Congratulations.

 

[seto6]

i find linear algebra is one of those subjects, someone needs to teach you, if you try to read the book by your self, its more like a story book

 

[mathwonk]

there are 3 or 4 of free linear algebra books on my web page. but none are easy.

 

[mathwonk]

here are some cheap good books by Paul Shields:

http://www.abebooks.com/servlet/SearchResults?an=paul+shields&kn=linear+algebra&n=200000237&x=52&y=8