32 votes
Accepted

Whether to tell students how difficult (you think) a problem is

In a setting where students aren't working from a book with these labels on questions, is it worthwhile for the instructor to indicate to students where the work they are asking them to do falls on a ...
Justin Skycak's user avatar
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 ...
Nick C's user avatar
  • 9,406
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, ...
Andrew Sansom's user avatar
21 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 ...
Chris Cunningham's user avatar
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 ...
Steven Gubkin's user avatar
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 ...
Misha Lavrov's user avatar
16 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 ...
Timothy Chow's user avatar
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 ...
Schwern's user avatar
  • 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 "...
Joseph O'Rourke's user avatar
11 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 ...
zipirovich's user avatar
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 ...
Xander Henderson's user avatar
  • 7,697
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,...
Lawnmower Man's user avatar
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 ...
usr0192's user avatar
  • 493
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 ...
Daniel R. Collins's user avatar
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 ...
Nate Bade's user avatar
  • 1,941
8 votes

Whether to tell students how difficult (you think) a problem is

A Frame Challenge I think that the premise of the question is slightly flawed: I do not think that the distinction between "exercises" and "problems" is one of difficulty—an ...
Xander Henderson's user avatar
  • 7,697
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 (...
Daniel R. Collins's user avatar
7 votes

Whether to tell students how difficult (you think) a problem is

Donald Knuth certainly thought so: he graded the exercises in his monumental work The Art Of Computer Programming from 00 ‘An extremely easy exercise that can be answered immediately if the material ...
gidds's user avatar
  • 385
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-...
DavidButlerUofA's user avatar
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 ...
Dan Fox's user avatar
  • 5,843
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 ...
paul garrett's user avatar
  • 14.3k
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 ...
Peter LeFanu Lumsdaine's user avatar
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 ...
Pedro's user avatar
  • 1,132
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 ...
ncr's user avatar
  • 2,986
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 ...
Daniel R. Collins's user avatar
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 ...
Nick C's user avatar
  • 9,406
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 ...
dbmag9's user avatar
  • 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. ...
Alexei Levenkov's user avatar
5 votes

If I take Modern Analysis next year, will I be prepared to teach multivariable/vector calculus?

I'm going to throw in a frame challenge: you stated your goal is to be prepared to teach at a collegiate level. All the other answers talk about whether you have the correct material, whether various ...
obscurans's user avatar
  • 167
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....
guest's user avatar
  • 636

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