Questions tagged [course-design]

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

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OER text for the mathematics of fair division

I'd like to design a course with a unit on fair division, and I'm looking for an OER text to use. The course will be a general education seminar, so students won't be expected to have any mathematical ...
Jared's user avatar
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11 votes
5 answers
1k views

Textbook For a Course on Classical Geometry

I have been assigned to teach a first year course in geometry the next academic year. This course has been running for quite a while in the university, but of late, has been thought of as redundant ...
Aravind Gundakaram's user avatar
10 votes
0 answers
194 views

Examples for advanced math courses based on measurable learning objectives

Background. I teach math at a German university (both undergraduate courses and courses for Master programmes), mostly for students who major in mathematics or very similar programmes. Students ...
Jochen Glueck's user avatar
7 votes
7 answers
1k views

Special topics for introductory probability

I am helping to design a low-level college course whose purpose is to teach critical thinking, logic, finance and probability. I have been tasked with developing the probability section. I am ...
dt688's user avatar
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6 votes
4 answers
648 views

What mathematical topics are important for succeeding in an undergrad PDE course?

I am a student helping to develop a remedial course for other students who have recently failed the undergraduate PDE course at our university. The topics are provided from the syllabus in the ...
brodybjones's user avatar
5 votes
1 answer
275 views

Which books on geometry and topology are best for teaching an intro graduate course?

I'm teaching a graduate (Master's) introduction to geometry and topology (e.g. some basics on manifolds, vector bundles, algebraic topology). What textbooks have you found are best for teaching a ...
David Corwin's user avatar
4 votes
1 answer
415 views

AP Calculus BC Guidance

Hello wonderful educators. I am hoping to get some help on a tough situation I am in. So first, a little bit of background facts: This is my first time teaching an AP class. I've adjuncted for Calc I ...
ruferd's user avatar
  • 2,091
-4 votes
1 answer
111 views

Help me to prepare for my first job interview presentation

My First Job Interview presentation topic for a permanent assistant lecturer position in Mathematics and Data science is below: ''You have been asked by your Head of Department to design an elective ...
Myshkin's user avatar
  • 93
7 votes
1 answer
190 views

Standards based grading design principles

I have taught some SBG courses in the past, and I am planning on converting all of my courses to SBG. I have enjoyed teaching these courses, I believe that students have learned more, and students ...
Steven Gubkin's user avatar
4 votes
2 answers
150 views

Textbooks with solutions and catering to different circumstances

Questions: Are we really taking students into account FULLY when writing textbooks for various areas? Also, are we being unintentionally elitist or dismissive when neglecting to take a more humble ...
EddieMath's user avatar
7 votes
3 answers
363 views

Rings in parallel with groups in abstract algebra

In a previous question, I asked about the pros and cons of teaching rings before groups in abstract algebra. Recently, it has come to my attention that there is a third approach - a unified approach - ...
J W's user avatar
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8 votes
7 answers
2k views

Advice on teaching abstract algebra and logic to high-school students

NOTE: This question will soon be duplicated, as I didn't make clear that I was a high school sophmore in the beginning. At first I thought it didn't matter, and somewhat arrogant to mention, but in ...
John Clever's user avatar
2 votes
1 answer
67 views

Setting up a new Ximera course with randomized values in problems

I'm working on converting a course to make it free to the students, and I'm considering using Ximera. What I haven't found online is documentation for/information on tips and best practices for ...
JMH's user avatar
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1 vote
0 answers
124 views

Number theory in an introductory course on discrete dynamical systems

Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
J W's user avatar
  • 4,635
3 votes
1 answer
446 views

How much literature research should one do when designing a course?

For each mathematical subject on the undergraduate level there are many textbooks, often with quite different approaches to the subject. Some are just concise and rigorous, some focus on examples, ...
user14543's user avatar
3 votes
1 answer
383 views

How to make maths explainer videos?

I am a maths teacher and I want to make maths explainer videos particularly like this guy is doing. In fact, in my research, I came to know that manim is the latest tool for creating maths animations ...
prashant sharma's user avatar
4 votes
0 answers
272 views

How must the "ungrading" idea be adapted to work in a math class?

After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...
Mike Pierce's user avatar
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16 votes
2 answers
1k 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 ...
Mike Pierce's user avatar
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27 votes
10 answers
9k views

Should LaTeX be taught in high school? [closed]

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 ...
FoiledIt24's user avatar
  • 1,283
8 votes
1 answer
713 views

Ideas and/or references for projects for a business calculus course

I have undertaken the teaching a business calculus course for this semester (spring II). The various assesments for the students, include quizzes/hw/midterms/final exams, adjusted with suitable ...
KonKan's user avatar
  • 185
8 votes
7 answers
2k views

Teaching Calculus I to engineers

I am in a research project where one of our jobs is improving the first-year university experience for our students. One of the topics we are looking into is changing the way we teach our introductory ...
N3buchadnezzar's user avatar
11 votes
8 answers
3k views

Algorithmic thinking problems

In Norway we will have a new national mathematics curriculum for all ages including high school beginning august 2020. A fundamental change is the new focus on so called algorithmic thinking. In ...
Jostein Trondal's user avatar
19 votes
8 answers
6k 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 ...
Kikolo's user avatar
  • 299
5 votes
2 answers
206 views

What are the benefits of an expertly curated learning pathway?

What are the benefits of an expertly curated learning pathway? Like that provided by a major publisher's textbook - CPM, a school district's mandated curriculum - IM's Open Up Resources or a ...
E_Rushton's user avatar
  • 189
6 votes
1 answer
574 views

Midterm in Mathematics Courses

Can someone point me to papers indicating whether or not a midterm is an important part of a course? I suspect I can find many 'experiential anecdotes' that midterms are good/bad/moot but I would ...
CAB's user avatar
  • 299
5 votes
6 answers
644 views

Why do standard geometry textbooks not start with trigonometry?

Throughout my geometry course, I was given many theorems and postulates, which I was were expected to memorize and apply. At the time, I sorta went along with it, but I couldn’t help but wonder where ...
DonielF's user avatar
  • 159
5 votes
4 answers
1k 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, ...
Christopher King's user avatar
5 votes
1 answer
219 views

Is it feasible to expose undergraduates to a "map"-centric point of view early on?

Question: Would it be feasible to teach undergraduate math students a "map"-centric view early on? If so, how early on? Now that I'm preparing for a phd program, I'm also reflecting on my ...
Andres Mejia's user avatar
1 vote
1 answer
228 views

Evaluation and feedback using Optical Mark Recognition systems in secondary school

OMR in exit tickets I plan to use an OMR, Optical Mark Recognition systems at the end of (some of) my classes. I want to use the same OMR system for exit tickets scattered over the academic year (not ...
Morten Engelsmann's user avatar
3 votes
2 answers
270 views

Supplemental text for undergraduate real analysis

Context: I am an assistant professor at a small college in the US. Next semester I am teaching real analysis for the first time, and we are using Steven R. Lay's book. (It also happens to be the ...
AegisCruiser's user avatar
  • 1,439
4 votes
3 answers
414 views

Teaching science and engineering students the field of inverse problems

There is a Mathematics Stack Exchange question on a good book on inverse problems for engineers. Here, I would like to ask for suggestions on how to approach teaching undergraduate upper-division ...
J W's user avatar
  • 4,635
4 votes
2 answers
142 views

Exposure to Algebra 2/Calculus Under Time Constraints

As part of a free summer enrichment program for highly-motivated high school students, I need to plan eight hour-long lessons for mini-courses titled as "Algebra 2" and "Calculus" separately. Despite ...
user avatar
4 votes
3 answers
309 views

What tools are available for creating visual aids?

I would like to create some visual aids for illustrating principles in statistics, similar to the kind of graphic found here: https://en.wikipedia.org/wiki/Linear_regression#/media/File:Anscombe%...
Mark Jones Jr.'s user avatar
2 votes
1 answer
2k views

Using tensegrity structure to teach high school math?

I am exploring ideas to design a secondary-level-project-based-10-lessons-unit-learning-plan which can end with a creation from the students involving a tensegrity structure. such as or My general ...
gegu's user avatar
  • 229
8 votes
4 answers
363 views

Make a matrix algebra course (1st university year) more "project-based"

Among other courses, I'm teaching a (basic) matrix algebra course for 1st year university students (they are studying Economics, and the cursus leads them to management, finance, or econometrics in ...
Basj's user avatar
  • 273
8 votes
2 answers
382 views

What can I teach a talented student who is enthusiastic about math?

I have a very clever student in Grade 7. Due to carelessness and English (which is not his native language), he failed the placement test and can't learn Grade 8 math (algebra 1) in school. School ...
Mathis's user avatar
  • 301
12 votes
4 answers
914 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 ...
Mathis's user avatar
  • 301
4 votes
1 answer
141 views

Is there a class curriculum that studies the work of a mathematician?

Are there classes dedicated to understanding the work of a particular mathematician? I have seen courses dedicated to a theorem (I saw for example one that sought to prove and understand the Atiyah-...
Andres Mejia's user avatar
15 votes
6 answers
655 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 $\varepsilon$-$\...
Zuriel's user avatar
  • 4,265
0 votes
1 answer
213 views

Using Substitution in place of the balance model

How does substitution work as an alternative to the balance model in introducing solving equations? My biggest worry is that, lacking a concrete representation, is too abstract for middle schoolers. ...
Daniel Mourad's user avatar
3 votes
1 answer
281 views

How should I deal well-known versus the obvious rubric?

I happen to be a student in America taking AP Calculus BC, or Calculus II, and recently, I had the following problem: Determine whether the following integral converges and evaluate it if it does: $$\...
Simply Beautiful Art's user avatar
7 votes
3 answers
299 views

Design of a math exam using multiple choice or computer

I'm teaching math in first years of university (matrix algebra, differential analysis, etc.) since maybe 5 years, and I usually give written (paper) exams to the students. I'm looking for ideas to ...
user avatar
15 votes
1 answer
210 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. ...
Michael Joyce's user avatar
18 votes
4 answers
696 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 ...
AegisCruiser's user avatar
  • 1,439
8 votes
7 answers
601 views

Topics for a general education course

I'm attempting to put together a list of topics for a general education course centered around "great ideas in mathematics," and I'm looking for input. Ultimately, I would like topics to be ...
AegisCruiser's user avatar
  • 1,439
8 votes
3 answers
355 views

Is proof-based exercise-oriented math course without solution an effective way to teach pure math?

In recent years I have seen several courses in pure math in the undergrad level (year 2, 3, 4) such as real analysis and topology where the entire course consists of: notes written during the lecture ...
Fraïssé's user avatar
  • 737
12 votes
2 answers
253 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: "...
Joseph O'Rourke's user avatar
4 votes
0 answers
94 views

Split differential equations into two video courses; theory and calculation?

I'm creating a course on differential equations, and I'm painfully aware that there is a LOT to teach. As of right now, I'm considering splitting the course into two, in the following manner: theory ...
Alec's user avatar
  • 828
20 votes
3 answers
2k 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 ...
user338102's user avatar
10 votes
4 answers
299 views

Ideas for teaching a bit of linear optimization to advanced undergraduates?

I am interested in ideas what to teach when the task is to teach a bit of (linear) optimization to third year undergraduate mathematics students. More specifically: Assume 'a bit' means I'd have ...
quid's user avatar
  • 7,672