Questions tagged [course-design]

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

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3
votes
0answers
93 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 ...
9
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1answer
206 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 ...
27
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10answers
7k 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 ...
5
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1answer
75 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 ...
7
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7answers
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 ...
11
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8answers
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 ...
17
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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 ...
5
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2answers
194 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 ...
5
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1answer
531 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 ...
5
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4answers
359 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 ...
5
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4answers
298 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, ...
4
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1answer
168 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 ...
1
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1answer
192 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 ...
3
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2answers
173 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 ...
4
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3answers
269 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 ...
4
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2answers
119 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 ...
4
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3answers
266 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%...
2
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1answer
515 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 ...
6
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3answers
208 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 ...
8
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2answers
237 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 ...
11
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3answers
436 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
111 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-...
15
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6answers
579 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 $\varepsilon$-$\...
0
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1answer
114 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
237 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
222 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
165 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. ...
17
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4answers
639 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 ...
8
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7answers
561 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
votes
3answers
267 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 ...
12
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2answers
182 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
77 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 ...
19
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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 ...
9
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4answers
266 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 ...
2
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0answers
179 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 ...
12
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1answer
214 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 ...
32
votes
4answers
3k 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'...
10
votes
2answers
269 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 ...
6
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3answers
4k 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 ...
19
votes
2answers
710 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
votes
4answers
292 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
566 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
votes
2answers
389 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 ...
14
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1answer
205 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
votes
3answers
319 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 ...
13
votes
3answers
843 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
557 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 ...
15
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1answer
257 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
197 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 ...
6
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3answers
377 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 ...