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 ...
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48 votes
Accepted

What should be included in a freshman 'Mathematics for computer programmers' course?

TL;DR 2-semester course is not enough. Disclaimer: I write this as a computer-scientist that uses math a lot in his work (I'm a research assistant at a university). Introduction: There are three (...
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  • 8,729
38 votes

Common Core, threat or menace? Or maybe ok after all?

I'm really wondering if this is the end of the world or the beginning of an improvement in the way we teach math. I'll answer this first, and then talk a little bit about the rest of the question. ...
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  • 7,385
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"...
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  • 16.3k
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: ...
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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 ...
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23 votes
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A Lexicon of Math Mistakes

Edit 9/5/14: It has recently come to my attention that another helpful paper is: Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review ...
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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 ...
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  • 16.3k
20 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 ...
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20 votes
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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 ...
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19 votes

A Lexicon of Math Mistakes

As a first guess, I'd give the following categories: Overgeneralization of known theorems or techniques. Application of these theorems or techniques in unsuited situations. Overconfidence in intuition ...
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  • 3,362
19 votes
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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 ...
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  • 1,881
18 votes
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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 ...
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  • 7,575
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 ...
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17 votes

What should be included in a freshman 'Mathematics for computer programmers' course?

After reading the previous answers, I'd add logic and proofs. To reason about a program's (in)correctness is proofs, even if you don't go to the length of proving correctness formally. Many students ...
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  • 12k
16 votes

A Lexicon of Math Mistakes

Through the repetitive drilling of pointless, boring, exercises many people develop a disconnect between the mathematical formalism and semantics. Many people have lost the ability to reason logically ...
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  • 2,951
16 votes
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Why aren't logarithms introduced earlier?

The appendix A in the Common Core State Standards for Mathematics seems to agree that traditional curricula put logarithms somewhere after Algebra I. CCSSM isn't a curriculum, and it doesn't suggest ...
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  • 7,385
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 ...
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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 ...
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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 ...
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15 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. ...
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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 ...
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  • 4,316
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 ...
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  • 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, ...
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13 votes

Why aren't logarithms introduced earlier?

Historical comments. Early on, the study of logarithms and logarithmic tables was incorporated into trigonometry. For more on this background from the perspective of the history of trigonometry ...
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13 votes

Mathematical education by country

If this is of any interest here is the case of Romania -Bourbaki's heaven (or hell): A year-long course of Analysis: starting with the Peano axioms, construction of Integer, Rational and Real Numbers ...
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