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

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64 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 (...
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2answers
92 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 ...
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3answers
208 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 ...
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2answers
98 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 ...
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3answers
109 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%...
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0answers
78 views

High school mathematics textbooks across the world [closed]

I come from India and am familiar with the textbooks used for high school mathematics. While it is clear that almost all students will be learning certain core topics like calculus, trigonometry and ...
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1answer
115 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 ...
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2answers
87 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 ...
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2answers
191 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 ...
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3answers
267 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 ...
4
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1answer
98 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-...
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6answers
521 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 $\varepsilon$-$\...
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1answer
89 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. ...
3
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1answer
227 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: ...
7
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3answers
181 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 ...
15
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1answer
141 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. ...
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4answers
612 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 ...
3
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0answers
103 views

Should college courses be run strictly sequentially instead of parallelly?

In today's mathematical teaching, and any teaching class in general, we have 4-5 courses running parallel to one another in a semester which are sequentially put together with other semester courses. ...
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7answers
521 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 ...
8
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3answers
217 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 ...
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2answers
154 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: "...
4
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0answers
72 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 ...
18
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3answers
652 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 ...
9
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4answers
236 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 ...
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0answers
136 views

Cognitively Guided Instruction (CGI) for 5th Grade

Are there any schools out there successfully using CGI with a 5th grade curriculum? Our students have poor number sense, and we'd like to remediate using CGI. I'd love to compare sequences of lessons ...
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1answer
188 views

How important is the act of writing his own script for the learning outcome?

There are several styles of delivering a lecture: The lecturer uses the blackboard and the students write their own lecture notes. The lecturer uses the blackboard and also provide a script so that ...
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4answers
2k 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'...
9
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0answers
153 views

How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
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3answers
2k views

Looking for realistic applications of the average and instantaneous rate of change

I am looking for realistic applications of the average AND instantaneous rate of change, that can serve as an entry point to calculus for students. The main-idea is to show them a (simplified) problem ...
17
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2answers
490 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 ...
9
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4answers
280 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 ...
12
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2answers
432 views

What to teach in Set Theory & Logic Course

I will be teaching a third-year introductory course on Set Theory and Logic soon and was hoping to get advice from this community. I would rate my students' proof abilities as weak and was hoping to ...
7
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2answers
207 views

Important topics for first numerical methods course

I will be teaching a one-semester course on numerical methods at a liberal arts college. The students will be primarily math, physics, and engineering majors. Note that there is no computer science ...
13
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1answer
144 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 ...
12
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3answers
292 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
3answers
803 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 ...
12
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5answers
385 views

Geometry with a view towards differential geometry textbook

I am scheduled to teach an upper-division undergraduate class on "Geometry" and I get to choose more or less what that means. Common choices seem to be non-Euclidean, hyperbolic, projective, or ...
14
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1answer
214 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 ...
9
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1answer
178 views

What courses should be a part of a Mathematics Education degree program?

I had asked the title question in an answer here, but it didn't get any recognition, so I'm posing it formally. The key word in the question is should. In my Mathematics Education degree education, I ...
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3answers
369 views

What is a good answer to the question “Which logic is better?”

In my undergraduate logic courses I introduce several types of logics to my students including propositional, first order, second order, intuitionistic and fuzzy logics and it usually happens that ...
4
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2answers
228 views

Real analysis: why usually first limits of sequences and then limits of functions?

I notice that all of the analysis books that I've studied start from dealing with limits of sequences and only then move on to limits of functions. Does this kind of approach have any particular ...
8
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6answers
381 views

What topic could I cover in an optional course at high school taking two lessons a week during a whole semester?

I'm teaching mathematics at a high school and I am offered the opportunity to get extra lessons, namely: I can provide an optional course about some topic of mathematics. The optional course will take ...
3
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2answers
173 views

How can a Q&A contest help a math teacher to improve his/her students' understanding?

Students questions and answers reflect their thoughts. It is very important to teach them how to ask nice questions and how to answer them. In order to improve these abilities I would like to commence ...
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0answers
74 views

Organization of an interview preparation course

This coming Fall semester, I will have to organize a course to prepare high school students for the maths interview they will have before entering to university. This is my first time teaching this, ...
17
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3answers
491 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 ...
4
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1answer
328 views

Abandon all hope, ye who enter my office!

The sentence in the title is inspired by a sentence on the gate of hell in Dante Alighieri's masterwork Divine Comedy (Part I: Inferno). I usually write it on my office door after exams when I think ...
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2answers
217 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
8answers
685 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 ...
13
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3answers
818 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 ...
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2answers
786 views

How can a math teacher manage a class when unprepared?

Sometimes a math teacher becomes sick or depressed like any other human and is not able to be prepared for lecture. Sometimes a math teacher spends too much time on a research project and does not ...