Practicing Math in the Classroom page 2

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Still wondering why he hasn’t responded.

But I second the thought of you being too condescending. I don’t go to uni however so I can’t comment, but I know I dislike teachers who think that they are so infinitely superior to me.

 
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Originally posted by DarkBaron:

As many of you know, I instruct courses in mathematics. I recognize that

1) most of you hate math here, so you are the perfect audience to ask

Note: I don’t hate all math (love algebra); given enough time and practice, I normally like it.

What is something you would like to see from an instructor (in a problem solving session) that will help you to solve it? Do you prefer it if the instructor solves everything out mechanistically and then asks you to help him solve the next similar problem? Or do you prefer he start from scratch on the first one, and encourage participation on each step of the process?

Probably the best thing to do would be to solve a sample question on the board, and give the students some same questions (similar to that) to work on themselves.

I can’t emphasize this enough (at least for me): Examples/templates are golden. I find that this applies to most left-brain topics. Right now I’m soldiering my way through an accounting course. What is the only way I’m still hanging on? Looking at numerous examples of balance sheets, income statements, etc. to see what goes where. It really helps to bridge the gap between theory and actually putting it into practice.

So if you can, provide your students with some solid examples or handouts they can refer back to.

2) You’re too shy to ask a question you’re struggling with. As someone who doesn’t read minds, we cannot anticipate your difficulties. How would you like your instructor to approach the problem, assuming he did anticipate your difficulties?

And I can’t emphasize this one enough—never treat your students like they are stupid or suffer a knowledge deficit because they ask questions. Be even glad they are curious enough to seek out the knowledge. I was in a course once where students got in some sort of trouble for asking the instructor any type of questions, and instead had to guess or look up the information on the internet and just hope they had it right. Some students were failed for seeking answers (one, a male friend of mine who really just loved the subject and wanted to learn).

Right now I’m asking an instructor numerous small questions about accounting, because among other things, he seems like a hard grader, and he invited us to ask early. So, just invite/encourage your students to come to you early with any questions they have. And mean it.

<3) Do you prefer seeing alternative ways to solving a problem, or would you rather see one method used universally to every problem you see (I strongly advise against the latter).

Alternate ways. Everyone learns differently. Some get it out of reading, some by examples, some by practice, etc. There’s not a one size fits all to learning, so offering different options is great.

If you can provide insight for calculus that would be lovely.

I can’t provide insight on calculus—thank God—but as my husband is an engineering student and is still struggling to pass Calculus II, I’ll ask him to pop in here and give feedback.

 
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1) You exist as you are. You find yourself in a math course, and you struggle to solve problems. What is something you would like to see from an instructor (in a problem solving session) that will help you to solve it? Do you prefer it if the instructor solves everything out mechanistically and then asks you to help him solve the next similar problem? Or do you prefer he start from scratch on the first one, and encourage participation on each step of the process?

1) Give students background information via simpler problems (that they know how to solve) that illustrate the same concept. Give them time to work these out, and attempt to relate the concept to the available challenging problem.
2) Present the challenging problem and give them a bit of time to ponder.
3) Have them help you throughout each step of the process, making suggestions and such to boost them forward. After a bit of time — not too much — move forward automatically, explaining conceptually and mechanistically.



2) You’re too shy to ask a question you’re struggling with. As someone who doesn’t read minds, we cannot anticipate your difficulties. How would you like your instructor to approach the problem, assuming he did anticipate your difficulties?

Ask the student personally.


3) Do you prefer seeing alternative ways to solving a problem, or would you rather see one method used universally to every problem you see (I strongly advise against the latter).

The Former.

 
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By the time someone gets to college…the damage is, essentially, done. It will be VERY difficult to get them to like math. It is an extrodinarily rare student who grumbles his or her way into a calculus 1 classroom and dances joyfully into differential equations. It is more common to have someone skip a math class and get all A’s despite. Odds are they’re only in your course because their major sticks it in as a “requirement” rather than a requirement. (the first is one they’ll never actually need. )

Now, I must admit, I recently ran into a wall called Bra-Ket notation, also called dirac notation. |y>. And no, that is NOT a crow smiley. My best efforts thus far have resulted in an extra integral on this one homework problem; I am still not sure which step was supposed to absorb said integral. Bracket vectors and matrices are annoying-you can’t just divide them away from both sides of the equation, you first have to maneuver them into position with transposes and inverses. And not always.

I like math. Quantum mechanics is the first math class to make me cringe since algebra 2. I never did enjoy conic sections, and their approach to matrices was ALL wrong. And yes, I consider quantum mechanics to be a math class, not a physics class. It’s a class that would be categorized as “applied math” but for the little detail that “applied math” is a codename for “watered down math”.

But I repeat: 99% of the time, if they’re in college, you won’t be able to change their minds about whether they like math or not. Is the remaining 1% worth it? I cannot say. That particular problem is very nearly equivalent to the halting problem. there is no way to say in advance.