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89 votes

Why is learning mathematics compulsory?

Questions like this, or variants (from students, the notorious "when will I use this in real life") seem to be pretty common, and I'm always a little surprised, because the unstated premise - that ...
Henry Towsner's user avatar
36 votes

In what curricula are "rectangles" defined so as to exclude squares?

I cannot answer the OP's question about cross-cultural/international perspectives, but here is a historical perspective that may be helpful. The issue here (whether the category "rectangles"...
mweiss's user avatar
  • 17.4k
30 votes

Why is learning mathematics compulsory?

The OP may be interested in the controversial 2012 article by Andrew Hacker in the NYTimes: Is Algebra Necessary? Here is one reply, by Peter Flom: A reply to Andrew Hacker. His closing remarks: ...
Joseph O'Rourke's user avatar
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 ...
Joseph O'Rourke's user avatar
21 votes

Are kindergartners supposed to be steered from squares being rectangles?

Kindergartners are generally at an early stage of geometric development, in which shapes are recognized by how well they resemble prototypical images, rather than by whether or not they conform to a ...
mweiss's user avatar
  • 17.4k
20 votes
Accepted

Is there a more telling name for "Calculus 2"?

In my job, I evaluate university math courses for transfer equivalency on a regular basis. In the US, "Calculus 1" typically refers to single variable differential calculus up to the fundamental ...
user52817's user avatar
  • 11k
20 votes
Accepted

Content for a 40-minute lecture on graph theory for high schoolers

I suggest you discuss the Seven bridges of Königsberg problem (the problem that essentially started the field of graph theory), then discuss the Three utilities problem. For each, discuss the problem ...
JRN's user avatar
  • 10.8k
19 votes
Accepted

Co-curricular lessons between geometry and chemistry?

One angle you could look at is molecular geometry. Not really my subject area but a couple of examples: Organic molecules can have different chiralities. That means that while one is the mirror image ...
Nate Bade's user avatar
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18 votes

Why is learning mathematics compulsory?

Many people think that the clientele of our public school system is the students. Others act as if the clientele were the parents of the students. Those people are wrong. The client is the citizenry ...
A. I. Breveleri's user avatar
16 votes

Why is learning mathematics compulsory?

I'll make some observations from a Western perspective (which may or may resonate with a Chinese student, say). Consider: Mathematics has been at the forefront of all education forever -- since long ...
Daniel R. Collins's user avatar
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 ...
guest's user avatar
  • 159
13 votes

Why is set theory not taught at the outset of math education?

Not a complete answer (could there be one?), but too long for a comment. why is it [Set Theory] not being taught at the very outset of math education? It has been tried, most likely still is in ...
dxiv's user avatar
  • 271
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 ...
mweiss's user avatar
  • 17.4k
12 votes

Why is learning mathematics compulsory?

Underwood Dudley answers the question "What is mathematics education for?" in this article from 2010 (Notices of the American Mathematical Society, vol. 57, no. 5, pp. 608-613) (even though ...
JRN's user avatar
  • 10.8k
12 votes

Content for a 40-minute lecture on graph theory for high schoolers

I study pursuit-evasion games on graphs, so I will recommend using the cops & robbers game as a way to introduce graph theoretic terminology, concepts, and examples. It should also keep the tone ...
Brendan W. Sullivan's user avatar
11 votes

Is there a more telling name for "Calculus 2"?

The course titles "Calculus 1", "Calculus 2", etc. are not meaningful terms outside of the specific institutions where there are courses with these titles. These are names of classes, and not some ...
Xander Henderson's user avatar
  • 8,225
11 votes

How should I introduce the Chain Rule

What is difficult about the chain rule is the function concept, more specifically the composition of functions. Notation that hides or leaves implicit the composition of functions causes a great deal ...
Dan Fox's user avatar
  • 5,869
11 votes

Why is learning mathematics compulsory?

Because many high school students, especially those who are keen on pursuing the humanities, they do not see any point in studying Mathematics for the rest of their schooling life, or how any ...
WGroleau's user avatar
  • 219
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 ...
user2705196's user avatar
10 votes

Is Calculus Necessary?

Society always benefits when new mathematical tools are developed to get insights into the world around us. There is little doubt that Calculus has helped change the quality of the lives we can lead ...
Joseph Malkevitch's user avatar
10 votes

How should I introduce the Chain Rule

The intuition here is basically that of Ben Crowell's answer, and that kind of intuitive explanation might be worth going through first. What I want to show is the kind of activity you can explore ...
Silverfish's user avatar
10 votes

Dominance of connectives: Why do we teach this?

When I see exercises like this, I often find that it teaches students to make assumptions about symbolic statements that may not be there - in a real world situation, if a statement is ambiguous, I ...
Leo Ell's user avatar
  • 101
9 votes
Accepted

Why is polynomial factorization over the integers part of secondary school curricula?

"any references pointing in the right direction would be greatly appreciated" Reference [1] below is probably where you want to look. A few years ago I tried to obtain a copy of [1], but I was not ...
Dave L Renfro's user avatar
9 votes

In what curricula are "rectangles" defined so as to exclude squares?

There is a model of how people progress towards abstract reasoning through the subject of geometry called the Van Hiele model. The model describes five levels: visualization, analysis, abstraction, ...
user52817's user avatar
  • 11k
9 votes

At what point in the curriculum should the tensor product be introduced?

(This pertains to U.S. universities.) Times may have changed, but when I was in graduate school (several places, and yes I know this is unusual, but I mention it because I'm talking about more than ...
Dave L Renfro's user avatar

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