29
votes
Should LaTeX be taught in high school?
This is not an answer to the posed question, but only an
anecdote. This semester, teaching US college students (Discrete & Computational Geometry), I prepared all my assignments in LaTeX, and ...
- 29.5k
27
votes
Rings before groups in abstract algebra?
My favorite textbook for an undergraduate course in Abstract Algebra, Ted Shifrin's Abstract Algebra: A Geometric Approach, uses a rings-first approach. The primary pro is that students are much more ...
- 2,601
18
votes
Advice on teaching abstract algebra and logic to high-school students
Here's my advice.
I have no teaching experience.
Remedy that first before you lay out plans for a 6-month course of study. Find some way where you can teach just for a single day in some way at the ...
- 24.4k
17
votes
Rings before groups in abstract algebra?
I have taught both groups first and a rings first course.
When I was a post-doc at Rutgers University, I taught their standard introduction to modern algebra course using Hungerford's undergraduate ...
- 626
17
votes
Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?
Your assumption that teaching calculus needs to be backed by the $\varepsilon$-$\delta$ definitions could be challenged, but since it is not your question I won't do that here.
My recent experience ...
- 9,079
17
votes
Accepted
Midterm in Mathematics Courses
"Cheating Lessons" by James M. Lang argues (and has many references to back up) the claim that smaller, more frequent, lower stakes assessment both improves student learning outcomes and decreases the ...
- 24.4k
16
votes
Prisoner's dilemma formulation for children
Here's a silly example:
Give students collections of the same type of thing, where each collection contains "good" objects and "bad" objects -- for example, a stack of Pokemon cards with both rare ...
- 9,184
15
votes
Accepted
Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?
Let me first say how I have taught this, and then why it was worth doing.
Here is the stripped down version I speak of. The first block of bullet points is one day.
Forget about straight edge and ...
- 5,243
15
votes
Should LaTeX be taught in high school?
I don't think it should be a base skill for students in general. Have held jobs in engineering, chemistry, military, and finance and never needed it. Nor did my colleagues.
Didn't need it for a ...
- 159
14
votes
Rings before groups in abstract algebra?
I've done it both ways, although I do rings-first now and for the foreseeable future. I think the pros and cons have a lot to do with the audience, especially if there are a lot of pre-service ...
- 1,962
14
votes
Prisoner's dilemma formulation for children
I found out about the Prisoners' Dilemma as a kid from a book about the Harry Potter phenomenon, which had a chapter about the problem, but presented as a story about Harry and Draco being accused of ...
- 241
13
votes
Teaching Calculus I to engineers
Without directly answering your question, you don't seem to have the background you need to be "improving" the undergraduate experience yet, and have some work to do. I think you're right in sensing ...
- 231
12
votes
Why do standard geometry textbooks not start with trigonometry?
If you really want to understand why the curriculum is structured the way it is, and how it got that way, you might want to read a brief history of the discourse around geometry education for the past ...
- 17.3k
11
votes
What reasons are there preventing me from using an old edition text?
Some universities (like mine) are accredited by a third party agency. One of their requirements for a university to be accredited is for it to have an "updated set of reference books" where "updated" ...
- 10.8k
11
votes
How should I deal well-known versus the obvious rubric?
Quoted from the first part of my answer on https://academia.stackexchange.com/questions/80898/should-a-student-be-penalized-for-using-a-theorem-outside-of-the-curriculum/:
... the point of an exam ...
- 24.4k
11
votes
How to teach a student algebra who misses too much previous knowledge?
My guess is that he depends on "following the rules", and there are now too many rules for him, because none of the 'rules' makes any sense to him. I believe he needs to see things differently to ...
- 20.1k
11
votes
Algorithmic thinking problems
One well-known source is Project Euler. The concept behind it is that each problem is mathematical and designed to be solved by an efficient algorithm on a "normal" computer in less than a minute. ...
- 5,609
11
votes
Should LaTeX be taught in high school?
This is clearly an opinion based question. I will answer based on my experience and opinion.
No, LaTeX should not be taught at high school. It is a skill that is costly to learn with essentially no ...
- 218
11
votes
Advice on teaching abstract algebra and logic to high-school students
Regarding "How do I recruit students:"
You should start here -- you have started with this cool thing you want to do, and are wondering how to do it. But you should instead try to find some ...
- 21.2k
10
votes
Impossibility of trisecting the angle, doubling the cube and alike, what are reasons for or against discussing them in a course on algebra?
Perhaps rather than spend time establishing that trisecting an angle is impossible via Euclidean (ruler-compass) constructions,
you could instead (a) Make that claim without proof,
and (b) ...
- 29.5k
10
votes
Accepted
"We already passed that course!" How to overcome this?
Sorry for the necromancy but I had a slant to add and too long for comment.
Viewpoint: It's not reasonable for the students to eschew previous techniques. But it's ALSO not reasonable for you to be ...
- 1,812
10
votes
Is there a class curriculum that studies the work of a mathematician?
I taught a class based on the work of Bertrand Russell. It was essentially devoted to set theory, but via his life and emerging interest in mathematics, philosophy, and ultimately logic (and its ...
- 101
10
votes
Teaching Calculus I to engineers
Given 100% control, I would have one-to-one instruction. One instructor meeting individually with each student. That instructor can change the approach, the speed, the order of topics, the method of ...
- 7,369
10
votes
Accepted
Special topics for introductory probability
A classic application of Bayes' Theorem is in medical testing, and the difference/conversion between "what is the probability I test positive, given I have the condition" vs. "what is ...
9
votes
Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?
I had the same thought this year. My suspicion was that many students get anxious about suddenly dealing with quantifiers and they also struggle with understanding how the ordering of them can affect ...
9
votes
How to teach a student algebra who misses too much previous knowledge?
It seems he has a lot of gaps. It would be good to teach him each gap separately. For example, don't expect to teach him about adding negative numbers and identifying like terms by exponents at the ...
- 7,999
9
votes
Should LaTeX be taught in high school?
I only want to give anecdotical advice since I happened to have been taught LaTeX in regular school (10th grade in the German system, iirc). However, I attended a school with a MINT focus and ...
- 449
9
votes
What mathematical topics are important for succeeding in an undergrad PDE course?
They must understand the quadratic equation and how to factor it, solve it and manipulate it formally in both the real and complex case. Also, how to solve simple trigonometric equation and knowledge ...
- 10.7k
8
votes
Why do standard geometry textbooks not start with trigonometry?
I cannot speak to curricula outside of the US, and I don't really buy your argument that geometry courses are "focused more on memorizing theorems rather than understanding where they come from." It ...
- 7,520
Only top scored, non community-wiki answers of a minimum length are eligible