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. ...
46
votes
12answers
30k views

What should be included in a freshman 'Mathematics for computer programmers' course?

Many universities are changing up the way that they teach math service courses. 1-3 semesters of calculus and maybe a course in linear algebra are often included in majors (such as computer science) ...
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, ...
33
votes
4answers
1k views

Are there any benefits to having an entire course's homework problems available from day one?

I am designing a course for the upcoming fall semester, and I am tossing around an idea in my head. While planning which topics to cover each week and how to set the pacing of the course, I figured I ...
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. ...
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'...
27
votes
10answers
8k views

Should LaTeX be taught in high school?

This semester, I was forced to learn LaTeX for my Real Analysis class. The professor wanted all homework assignments to be typed in LaTeX in order to produce "high-quality" work. At first I was ...
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....
26
votes
6answers
3k views

How do you go about writing your own lecture notes for a new course?

In advanced graduate courses, there are often no textbooks on the material being covered, and sometimes no good introductory material at all. Even when there are textbooks, many professors prefer to ...
26
votes
4answers
531 views

Alternatives to University Lectures: Non-lecture Mathematics Classes

I am looking for resources for designing undergraduate mathematics classes that are not lecture-based. (Bonus points if the design is for an introduction to proof course). For example, Robert ...
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 ...
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 ...
23
votes
8answers
2k views

“We already passed that course!” How to overcome this?

I've heard the phrase "we passed that course already!" too many times when asking for e.g. the derivative of a simple rational function or a simple integral, getting blank stares, and digging deeper. ...
22
votes
5answers
1k views

Hand out lecture notes or not?

It lectured a stochastics course for pre-service teachers last semester and had a teXed manuscript for myself which grew as the course was running. After some debate with the students, I made a ...
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 ...
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
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) ...
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 ...
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 ...
19
votes
3answers
525 views

Requiring basic skills to pass a course without increasing their grading weight

As I grade my final exams, I sometimes find calculus 1 students who will pass with a C but lack critical skills like the chain rule. This can be for a number of reasons, for instance: They understand ...
19
votes
3answers
1k views

Group theory for high schoolers, want the opinion of other educators

So I am going to be teaching the basics of group theory to high schoolers in a few weeks, and I want to hear what the Stack Exchange network has to say on the matter. What are the applications and ...
18
votes
5answers
496 views

Making standards for “showing work” explicitly clear to students

I do not mean for this thread to be a discussion of whether or not students should show work on an exam, whether they should be docked points for just "seeing" an answer and writing it down, whether ...
17
votes
8answers
5k views

Prisoner's dilemma formulation for children

I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's ...
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 ...
17
votes
4answers
365 views

Are teaching about finding the missing member(s) of the sequences really appropriate?

I notice that in current mathematics education they always have sections teaching about finding the missing member(s) of the sequences e.g. in this way: $1,2,4,8,16$ , the next term is what? Someone ...
17
votes
3answers
1k views

Computational topology for engineers

Increasingly, I see computational topology being applied to problems involving sensor networks, robotics, data analysis, signal processing and various other areas. The topics I mention are interesting ...
17
votes
4answers
647 views

What reasons are there preventing me from using an old edition text?

Background: I'm a final-year math student applying for faculty jobs at small schools in the US. I'm currently designing a few courses, and this questions has been bothering me for some time now: Why ...
17
votes
3answers
286 views

Teaching a class you never took

How can you design an adequate course for a subject you never formally had classes? This is similar to teaching somebody else's class. As an example, suppose you are an algebraic geometer and you ...
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 ...
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 ...
15
votes
6answers
589 views

Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?

I am teaching Calculus I and will be teaching it again. To me, the $\varepsilon$-$\delta$ definition of limit is one of the key ideas of Calculus; learning calculus without learning $\varepsilon$-$\...
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" ...
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, ...
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 ...
15
votes
1answer
169 views

Pacing your teaching for a variety of learning speeds

I am often tasked with teaching large enrollment courses, and one thing that becomes obvious quickly is that students attempt to pick up new information and solve problems at much different rates. ...
15
votes
1answer
265 views

Order of Topics in Introductory Proofs Class

Beginning next semester I am teaching a course in proofs and mathematical problem solving at my local university. For some background, the university is primarily a commuter university and the ...
14
votes
8answers
822 views

Teaching advanced math using books with cartoons

Could an effective and 'comprehensive' course on advanced math be taught through a series of fun comic books, say a fun and adventurous series of stories each exploring advanced math principles ...
14
votes
2answers
670 views

How is calculus possible in a small number of very long class periods?

This summer, I am teaching 8-week calculus courses that meet a total of 16 times in 210 minute class periods. This sounds insane to me since Return of the King is only 201 minutes long, but it is the ...
14
votes
2answers
281 views

Physics-based mathematical courses

I've seen many courses labelled as 'mathematical physics', but I'm interested in knowing about the opposite: 'physical mathematics'. I've noticed that some areas of mathematics which I found ...
14
votes
1answer
225 views

Advantages of learning different topics simultaneously

The context In high school here in Australia, students have one mathematics class which runs all year. The students do maths class most days, and the course passes from one topic to the next, one ...
13
votes
7answers
700 views

Non-Mathematical Examples of Orders

Different properties of different types of orders including partial, total, scattered and well-orders are a part of any graduate/undergraduate set theory course. I am looking for interesting "non-...
13
votes
3answers
1k views

Mathematical Knowledge for Teaching

Does anyone know of any course called Mathematical Knowledge for Teaching? Where is this course taught? If it's not a course, is there any workshop about this? Or possible a book? It's not knowing ...
13
votes
3answers
847 views

How would introductory classes change if they didn't need to be taken by non-mathematicians?

I read an article the other day about how physics professors have to teach their introductory classes in a somewhat old-fashioned manner. This is due to pressure from the other departments (other ...
13
votes
4answers
1k views

What are effective alternatives to a written math exam to evaluate knowledge?

Some students do not do well under pressure or testing situations and cannot demonstrate their knowledge of a math subject with a written exam. On the other hand, I think that students that do not ...
13
votes
3answers
271 views

Using Several Textbooks in a Course

Sometimes a teacher prefers to use several textbooks in his/her courses because he/she thinks the arguments of each book is better in a part of course material or there is no comprehensive textbook in ...
13
votes
2answers
338 views

What prerequisites would college students need for a course based primarily on Euclid's elements?

I love Euclid's elements, and would like to base a course around them. Before I can pitch it to my supervisors, I need to know where it would fit in the curriculum. While it begins from elementary ...
12
votes
3answers
2k views

Conceptual Mathematics by Lawvere & Schanuel as text for bridging course?

I have recently come across Conceptual Mathematics: A First Introduction to Categories by Lawvere & Schanuel. It is a gentle introduction to Category Theory and strikes me as a potential ...
12
votes
2answers
415 views

How to divide up readings in a flipped classroom?

Next semester I plan to experiment with "flipping" a classroom, by assigning required readings from the textbook (perhaps with supplementary notes) so that lecture doesn't have to "cover all the ...
12
votes
3answers
323 views

Resources on interdisciplinary curricula

As I try to incorporate more history, science, language, computing, and art into my math class I keep finding the lessons to be very successful and my students always seem to enjoy them. While I know ...
12
votes
2answers
218 views

How do I adapt a MWF class into a TuTh class?

Both universities I have taught at have tightly-stuctured calculus courses that follow a pattern of 3 sections of Stewart Calculus every week, with some sections afforded two days. I find it ...