29
votes
What mathematics activities get students physically moving?
To start things off, some moments my students move around during class:
I have given students tape measures and had them determine how much they would spend at the paint store if they wanted to paint ...
- 8,586
27
votes
Accepted
What's the point of learning equivalence relations?
Perhaps emphasize to students the spirit of equivalence relations. They partitions sets into equivalence classes--cutting down the amount of cases necessary to prove something.
To illustrate this, ...
- 495
20
votes
Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?
When a student writes incorrect notation, ask them to read it out loud. I would say something like:
Something here doesn't look right, but we can fix it. Could you read this work out loud? I think ...
- 20.4k
18
votes
Accepted
If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
It is impossible to say whether you will be ready to teach multivariable calculus after taking this course. Certainly many of the topics you list will employ some multivariable calculus, but using ...
- 23k
16
votes
What's the point of learning equivalence relations?
In general, all applications are going to be more of the "here is what we have to check to make sure that our algorithm/theory/definitions work". We don't usually encounter practical ...
- 671
15
votes
If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?
Assuming you already have a good understanding of the material in a standard course in multivariable calculus and vector calculus, I would recommend that you take a class in electricity and magnetism ...
- 473
13
votes
What mathematics activities get students physically moving?
The Hungarian Quicksort Dance demonstrates a computer science algorithm with dance. It's pretty advanced, but the idea is to have your students physically act out algorithms.
Perhaps something ...
- 231
12
votes
How To Help a Quiet Class
I've had a remarkable (remarkable to me) success in a different environment on a different topic, so I am not sure this will translate. But I'll mention in anyway.
With one change, the same quiet "...
- 28.8k
11
votes
Making solutions to all problems freely available
This is an opinion, but perhaps worth sharing:
When I assign that I expect students (particularly lower division students, such as those in calculus or precalculus classes) to do on their own time, I ...
- 7,137
11
votes
What's the point of learning equivalence relations?
Equality vs. Identity
Alexei touched on this topic by mentioning hash tables, but I would like to spell it out more explicitly, because this is a critical and fundamental topic in software engineering,...
- 633
10
votes
Multiple students writing $y\frac{d}{dx}$ rather than $\frac{d}{dx}y$ -- why?
I see the same mistake in my Calculus students' work a lot. And from my observations, I think there's a very simple reason for that — for typical students (here in the U.S.) this is ...
- 844
9
votes
How To Help a Quiet Class
Start calling on students individually without waiting for any one to raise their hand. For a long time I never did this since I am conflict avoidant and since I didn’t want to put students on the ...
- 503
9
votes
Accepted
Why is distribution prioritized over combining?
This grew a bit long for a comment.
(My first note is similar to Alexander Woo's remark about factoring polynomials; perhaps he intended "polynomials" to subsume the case here, in which we add ...
- 18.3k
9
votes
How to design multiple choice questions
Personally in my own math courses, I have found that the gold-standard is to have an advance cycle of short-answer responses, document the most common student responses, and then turn those into the ...
- 22.8k
8
votes
How to design multiple choice questions
Use them for what they're best at testing, like conceptual understanding questions.
One way to do this is by having students evaluate statements they would never be expected to come up with on their ...
- 1,921
7
votes
What is accelerated developmental math education, and is it a good idea?
Accelerated developmental education includes a variety of mechanisms to shorten time students spend in remediation. It can include: Batching together multiple courses of remediation in one semester (...
- 22.8k
6
votes
Formats for Calculus instruction at different colleges and universities
I teach in the Universidad Politécnica de Madrid, which is a fairly large public engineering school with research objectives. The students are comparable to those I have taught in engineering degrees ...
- 5,679
6
votes
How To Help a Quiet Class
Here are some ideas:
Try using shared vertical surfaces for doing problems. For example use whiteboards/windows. According to Peter Liljedahl http://www.peterliljedahl.com/publications/building-...
- 8,883
6
votes
Accepted
Is it appropriate to assign an extra credit homework question on the "next" session?
In general, I'd think that anything that helps students to break out of a tendency to passivity is good. Initiative should be rewarded, looking ahead is good, and so on.
Sure, if there is a pervasive ...
- 13.8k
6
votes
What's the point of learning equivalence relations?
If you have looked at modular arithmetic, then one possibility is: Give/recall some example of an algebraic argument in modular arithmetic; then point out that the argument is implicitly relying on ...
6
votes
What's the point of learning equivalence relations?
The notion of equivalence relation is one of the basic building blocks out of which all mathematical thought is constructed. (Paul Halmos)
What's the point of learning equivalence relations?
The ...
- 992
5
votes
Making solutions to all problems freely available
I teach a highly selective Liberal Arts College. If you don't assign a component of the final grade to the homework, the majority students in a typical introductory class just won't do it or, if they ...
- 2,976
5
votes
Teaching limits and asymptotics at the same time
If I understand you, I do often think this way when solving a problem. For example, see this answer of mine at Mathematics Stack Exchange.
However, limits involving infinity (as the independent or ...
- 2,522
5
votes
How To Help a Quiet Class
Am I just asking or expecting too much from this group?
I empathize with your goals completely, and they are honorable. Bear in mind that sometimes, due to a conflation of factors, a particular class ...
- 22.8k
5
votes
Advice on Full Time Community College Math Instructor Position
Please take 12-15 minutes to introduce your lesson
Your intuition is correct that this is far too much for a 12-15 minute lesson. The committee knows that there is no way you could deliver a whole ...
- 8,586
5
votes
What mathematics activities get students physically moving?
To build intuition for the Cartesian plane, assign axes to the room (or to students, depending on how many you have and how they're arranged in the room). Then you can do things like:
Stand up if ...
- 670
5
votes
What's the point of learning equivalence relations?
Dictionary/hash table relies on equivalence to bucketize items.
So knowing that one would never try to build a hashtable by a distance between cities (objects on a plane): distance is not transitive.
...
- 151
4
votes
Advice on Full Time Community College Math Instructor Position
Caveat: I'm just a random Internet poster, not an instructor, so take this with a grain of salt. And get some advice from blooded veterans.
A. It's too much. 1 and 2 are plenty for 12 minutes.
B....
- 636
4
votes
Formats for Calculus instruction at different colleges and universities
I'm studying physics at Eötvös Loránd University, Hungary, so my answer will not be complete, but I will try my best.
In the first semester, we can choose between "advanced" and "normal" level ...
- 151
4
votes
Formats for Calculus instruction at different colleges and universities
At the University of Michigan, all instruction at the level of Precalculus, Calculus 1, and Calculus 2 is conducted in small "Recitation" sections -- no lectures!. Traditionally (since the mid-1990s),...
- 17.1k
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