104
votes
How to assign homework when answers are freely available or attainable online?
My suggestion is that you stop thinking of homework as an assessment tool, and instead find the true meaning of homework, which is a method for students to gain proficiency with the ideas on their own....
- 3,986
48
votes
Accepted
What should be included in a freshman 'Mathematics for computer programmers' course?
TL;DR 2-semester course is not enough.
Disclaimer: I write this as a computer-scientist that uses math a lot in his work (I'm a research assistant at a university).
Introduction:
There are three (...
- 8,729
47
votes
How to assign homework when answers are freely available or attainable online?
The underlying issue is something that is hinted at in JDH's answer, but not explicitly stated. So I'd like to state it.
The key is to decide what your homework is for. The big words are Formative ...
- 3,558
42
votes
Accepted
Teaching by Slides, Yes or No?
First, a little background. I switched to slides a few years ago when teaching a 3rd year course at my university. Because of how teaching works at my university, this course is one of the first ...
- 3,558
42
votes
Accepted
How is calculus helpful for biology majors?
I'm an old-school biologist (animal physiology) who works with mostly cell biologists. I sent out an email to a bunch of grad students and postdocs I work with. Here is the data so far:
Senior ...
- 1,494
28
votes
Should LaTeX be taught in high school?
This is not an answer to the posed question, but only an
anecdote. This semester, teaching US college students (Discrete & Computational Geometry), I prepared all my assignments in LaTeX, and ...
- 28k
27
votes
How can I familiarize elementary school students with infinities larger than $\aleph_0$?
I think that actually trying to get students at this age to contemplate infinities in a rigorous way is probably ill advised.
I do think that exploring counting from both an "ordinal" and a "cardinal"...
- 19.4k
26
votes
Accepted
What happened to the Moore method?
The Moore Method is alive and well, and so are a great many variants. These days the community is more likely to use the term Inquiry-Based Learning (IBL), because the Moore Method can be seen as a ...
- 864
26
votes
Rings before groups in abstract algebra?
My favorite textbook for an undergraduate course in Abstract Algebra, Ted Shifrin's Abstract Algebra: A Geometric Approach, uses a rings-first approach. The primary pro is that students are much more ...
- 2,513
24
votes
Accepted
How should LaTeX be taught to university students?
In my experience, students in sophomore or junior level math courses usually have very little trouble picking up LaTeX on their own. They typically require the following assistance:
Some guidance in ...
- 7,930
22
votes
What happened to the Moore method?
The Moore method is used at the University of Chicago in some sections of "Honors Calculus", which is really an introductory real analysis course for top incoming freshmen. I assisted with it a ...
- 6,210
21
votes
Accepted
Are there any benefits to having an entire course's homework problems available from day one?
I always organize my courses with the totality of the course set from the outset whenever I can. I see this as being closely tied to your question concerning homeworks assigned.
The benefits I see:
...
- 10k
20
votes
How is calculus helpful for biology majors?
I happen to have revised our calculus syllabus for first year biology majors about one year ago (in a French university, for that matter). I benefited a lot from my wife's experience as a math-...
- 8,713
19
votes
Accepted
How do you go about writing your own lecture notes for a new course?
What are the most important considerations when writing your own lecture notes for a course?
I would say that the single most important consideration is to make life easy for yourself. It is easy to ...
- 3,558
18
votes
Are teaching about finding the missing member(s) of the sequences really appropriate?
Theoretically, there's no way to determine the next term in the sequence
$$
1,\quad 2,\quad 4,\quad 8,\quad 16,\quad\ldots
$$
It literally could be anything.
At the same time, it is a vitally ...
- 7,930
17
votes
Accepted
What are the differences between graduate and undergraduate classes, relevant to course design and teaching?
Of course there are many differences between undergraduates and graduates, including:
Mathematical independence. In a graduate class, one may generally presume a much greater level of mathematical ...
- 3,986
17
votes
What should be included in a freshman 'Mathematics for computer programmers' course?
After reading the previous answers, I'd add logic and proofs. To reason about a program's (in)correctness is proofs, even if you don't go to the length of proving correctness formally.
Many students ...
- 12k
17
votes
Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?
Your assumption that teaching calculus needs to be backed by the $\varepsilon$-$\delta$ definitions could be challenged, but since it is not your question I won't do that here.
My recent experience ...
- 8,713
16
votes
Alternatives to University Lectures: Non-lecture Mathematics Classes
There are a few ways to do this. I recently did it in Carnegie Mellon's introductory proofs course. I'll try to outline here a few different solutions that various places have tried.
Carnegie Mellon ...
- 1,950
16
votes
How to assign homework when answers are freely available or attainable online?
I agree that this is a problem in teaching calculus and other classes where solutions manuals and online forums are readily available and I don't know that there exists any one thing that you can do. ...
- 1,754
16
votes
What happened to the Moore method?
I took a number theory class at University of Cincinnati that was taught using a modified Moore method. The class size was pretty small, and credit-wise it was an "upper level mathematics elective" (...
- 1,665
16
votes
Hand out lecture notes or not?
I hand out notes in most of my courses. These notes parallel my lectures, sometimes precisely, sometimes just roughly. Some of them are typed, some of them are pdf-scans of my handwritten work. I ...
- 10k
16
votes
Computational topology for engineers
I'm just finishing up a graduate course in computational topology which could be adapted very effectively for this purpose. We're focusing on topological data analysis and computational homology. All ...
- 1,665
16
votes
Rings before groups in abstract algebra?
I have taught both groups first and a rings first course.
When I was a post-doc at Rutgers University, I taught their standard introduction to modern algebra course using Hungerford's undergraduate ...
- 607
16
votes
Accepted
Midterm in Mathematics Courses
"Cheating Lessons" by James M. Lang argues (and has many references to back up) the claim that smaller, more frequent, lower stakes assessment both improves student learning outcomes and decreases the ...
- 19.4k
16
votes
Prisoner's dilemma formulation for children
Here's a silly example:
Give students collections of the same type of thing, where each collection contains "good" objects and "bad" objects -- for example, a stack of Pokemon cards with both rare ...
- 7,686
16
votes
Advice on teaching abstract algebra and logic to high-school students
Here's my advice.
I have no teaching experience.
Remedy that first before you lay out plans for a 6-month course of study. Find some way where you can teach just for a single day in some way at the ...
- 20.6k
15
votes
How to assign homework when answers are freely available or attainable online?
Here's another idea: Give a completely different type of homework assignment.
For example, this year, collect all of your homework as usual. Look through the homework for examples of solutions that ...
- 1,113
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