Questions tagged [course-design]

For questions about creating a new course or altering the format of an existing course.

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85
votes
13answers
9k views

How to assign homework when answers are freely available or attainable online?

I find that making homework meaningful is becoming increasingly challenging. Let us suppose that I am planning for next semester's first-semester or second-semester calculus course at my university. ...
43
votes
16answers
25k views

How is calculus helpful for biology majors?

It's common for majors in biology to take calculus courses, and many calculus textbooks (and calculus professors) try to cater to these students by including applications to biology. My question is, ...
15
votes
5answers
1k views

Is Peer Instruction suited to mathematics classroom?

Peer Instruction is a method developed by Eric Mazur in Harvard, designed with a student-centered approach in mind. In a nutshell, the core of the method is that when presented with a problem, ...
11
votes
3answers
477 views

How to teach a student algebra who misses too much previous knowledge?

I am now tutoring a student in Grade 9, who falls behind in math study. He lacks the basic understanding of operations and inverse operations, and have trouble dealing with negative numbers and ...
32
votes
4answers
4k views

Rings before groups in abstract algebra?

The default approach to teaching abstract algebra seems to be groups first, then rings. However, occasionally a textbook pops up (e.g. Childs' A Concrete Introduction to Higher Algebra or Hodge et al'...
17
votes
6answers
3k views

What is the ideal course sequence for an advanced student of mathematics?

Suppose that you meet a student who: has a firm grasp of algebra and trigonometry and is at least moderately intelligent has read a book such as Love and Math by Edward Frenkel so has some ...
20
votes
2answers
734 views

Emphasizing the discrete in early undergraduate education?

From time to time, I have come across course ideas emphasizing the discrete over the continuous, such as Peter Saveliev's Fantasy Math curriculum (update: see also his material on discrete calculus) ...
16
votes
3answers
683 views

How to build a class based on Project Euler?

Project Euler is a very popular self-challenge website where users complete various projects designed to test their number-theory intuition and programming skills. I've been considering various ideas ...
27
votes
9answers
4k views

Teaching by Slides, Yes or No?

Mathematicians use (Powerpoint/Beamer) slides for their lectures. My question is about using slides for teaching math. There are several positive and negative arguments about teaching by slide show. e....
24
votes
2answers
936 views

Student Poisoned Experience with Math

I’d like to start off with saying I am not a teacher so I don’t know how much of this is already trying to be addressed in math education throughout the world. In talking to and tutoring fellow ...
32
votes
3answers
3k views

What happened to the Moore method?

I always read about the Moore method with great enthusiasm. Somehow I always felt that it should be how we do it in an ideal world, but it is impossible to use because of time and other constrains. ...
15
votes
6answers
955 views

Where can I find resources for creating a mathematics “bridge course”?

I originally asked this over at MathOverflow, but it was suggested I might also find some good answers over here. My university department is in the very early stages of developing a "bridge course" ...
26
votes
4answers
2k views

How should LaTeX be taught to university students?

There are several groups of people that would benefit from learning LaTeX in college. Future teachers can use it to write exams, scientists and mathematicians can write papers, and everyone can write ...
19
votes
11answers
1k views

How can I familiarize elementary school students with infinities larger than $\aleph_0$?

Cantor's discovery of the existence of more than one infinity was a revolutionary change in human knowledge. He defined the notion of counting by bijections and showed that one can use infinities as ...
11
votes
2answers
277 views

Quotations of Great Mathematicians as a Source of Inspiration for Young Students

I like using quotations of great mathematicians as a source of inspiration for young students. I think even a short sentence could have a great influence on forming their research interests and point ...
8
votes
6answers
368 views

On the use of calculators in elementary/high school? Computer algebra systems later on?

I know this subject is inflamatory... but I also believe it is something that requires broader discussion (and hopefully some consensus). My own position (from personal experience) is that today you ...
5
votes
4answers
376 views

Would teaching nonstandard calculus in an introduction calculus course make it easier to learn?

Nonstandard calculus is a reformulation of calculus that is based on infinitesimals instead of epsilon-delta definitions. Of course, people had tried to use infinitesimals in calculus before; in fact, ...
20
votes
2answers
795 views

Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?

When I taught courses on algebra giving a first exposition to Galois theory I usually included some discussion of classical results showing the impossibility of constructing certain points with ruler ...
20
votes
3answers
2k views

What are the differences between graduate and undergraduate classes, relevant to course design and teaching?

I will be a postdoc in the fall and will be teaching my very first classes aimed at graduate students. One will be an intro class, and the other a topics class. There are of course many differences ...
19
votes
4answers
412 views

How to balance higher order thinking and drill/practice

Some place emphasis on higher order thinking skills at the cost of lower emphasis on drill/practice. Others disagree. Personally, I agree that higher order thinking skills are necessary for effective ...
12
votes
2answers
188 views

Course-based undergraduate research experiences in math

"Course-based undergraduate research experiences" (CUREs, or CBEs) are being explored in various STEM fields, especially biology, chemistry, geology. Here is one geology link that gives a flavor: "...
7
votes
4answers
1k views

How to standardize grading across several sections of a course?

Suppose you're the instructor of a large university course split into several sections, each of which has a TA. (Think of a giant lecture-style calculus course with several hundred students that meet ...
15
votes
1answer
299 views

How do you fix a broken course plan?

The most terrifying thing about teaching my own class is 'do I actually know enough to effectively teach students?' I know this is anxiety brought on by a lack of experience but finding the tools to ...
11
votes
1answer
255 views

What are some resources for “ungrading” in a math class?

Most of the stuff I'm finding online about ungrading are either general descriptions of its virtues, or personal accounts from instructors from subjects other than math. Does anyone know any resources ...
11
votes
1answer
563 views

Ideological Teaching in Logic Courses

Logic and its sub-fields are closely related to philosophy. There is an undeniable mutual interaction between one's philosophical point of view and his/her approach in teaching mathematical logic. In ...
11
votes
3answers
278 views

Teaching somebody else's class

How do you approach a class taught by somebody else? There are multiple reasons why one could find him/herself in such a situation: an instructor is sick, there is a scheduled rotation of teachers, ...
16
votes
5answers
916 views

Rigorous proofs vs. illustrative examples

No one would argue against the idea/ observation that proofs are very important in mathematics. Some people are trying to make their notations on a blackboard during a lecture as consistent as ...
9
votes
4answers
294 views

Teaching mathematics and its charms to non-mathematicians

I am teaching English in Japan and I have a student who speaks English well, and to keep up his level, in our weekly lessons would like to learn some subjects related to my degree in mathematics. I ...