88 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 ...
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"...
  • 16.7k
29 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: ...
28 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 ...
21 votes

Why are triangles so prevalent in high school geometry?

TL;DR: It's not the triangles that are interesting; it's the mathematical concepts that can best be explained by using one of the most primitive geometrical shapes. The reason for intensive use ...
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 ...
  • 16.7k
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 ...
  • 8,133
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 ...
  • 10.4k
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 ...
  • 1,901
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 ...
16 votes

Why are triangles so prevalent in high school geometry?

I see one important reason: triangles are simply the simplest non-trivial configurations of points. One point configuration are boring: every two points are mapped one to the other by a translation. ...
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 ...
15 votes

Why are triangles so prevalent in high school geometry?

This is not an answer, but I share what I take to be your skepticism. I think polygons are a rich topic. For example, just understanding that every simple polygon can be triangulated would be an ...
15 votes

Why are triangles so prevalent in high school geometry?

TL;DR Triangles helped me understand both unit circle and trig functions. Super cool and super useful. Didn't really use much of my other geometry. Don't drop triangles. If you do, you should have a ...
15 votes

Thought experiment: Utopian college-level math curriculum without external constraints

Years ago, as an undergraduate student, I experienced something close to your description of a utopian mathematics undergraduate-level curriculum at Sharif University of Technology in Iran. We didn't ...
  • 4,324
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

Should we teach trigonometric substitution?

In reality, I think this is not the most important topic, and if I was designing a curriculum from scratch, I would probably omit it. We rarely have that luxury however. In my state, for example, ...
13 votes

Teaching K-8 math in the style of "A Mathematician’s Lament"

In A Mathematician's Lament, Paul Lockhart describes what is wrong with math education in schools. To get a good idea of how he would do things differently, you should read his book titled Measurement....
  • 18.3k
13 votes
Accepted

Pedagogical Purpose in Making Students Do Problems in A Less Efficient Way First

Yes. The primary reason in my mind is that you want to have multiple procedures with which you can double-check work later. Knowing only a single procedure makes for very fragile understanding; on ...
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 ...
  • 271
12 votes
Accepted

Was there an SMSG (New Math) "Algebra 2" text?

The textbooks we used for Algebra 2 at Miramonte High School, Orinda, California, in 1967 - 1968 must have been SMSG Units 17 - 18, entitled Intermediate Mathematics, Part I and II. I recognize the ...
12 votes

How early to start "abstract" math education, or, How to prevent smart kids from never getting exposed to math?

Math circles are an attempt to bring the beauty of math to young people. My book, Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers is an attempt to bring the joy of ...
  • 18.3k
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 ...
  • 10.4k
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 ...
11 votes
Accepted

Secondary Geometry Curriculum Sequencing?

While I am not sure if your mentor teacher is up for the discussion for this year, I will note that, in practice, it is important to continue to question the sequencing of topics in a particular ...
  • 356
11 votes
Accepted

Is multiplication by zero clear for and understood by K-3 students?

Turning my comment into an answer as per request: I think the graphical approach gets the idea across. You could represent $3\times 1$ by a row of three dots; likewise, $3\times 2$ is two rows of ...

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