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1500 questions
31
votes
8 answers
What was the problem with New Math? Why did it end?
During the 60s, people in the US (and also in Europe), school curricula introduces New Math where students began with set theory in the first grade before learning to perform addition or multiplication.
Somehow, this has ended. Can you explain why?…
Markus Klein
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31
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11 answers
What are the arguments for and against learning the multiplication table by heart?
I think, a lot of students are bothered by learning multiplication tables by heart, in particular when it comes to numbers greater than 10.
Why should one learn (or not learn) these things by heart?
Markus Klein
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31
votes
7 answers
Mathematical education by country
Depending on the university, there are always slight differences in the syllabus and the structure of the standard material undergraduate students learn.
But I also noticed that undergraduate mathematics differs more greatly if one compares for…
k.stm
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31
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9 answers
What to do with students who think they "already know it," but actually don't?
Many students take calculus or algebra courses in high school, then later take college courses of the same name. There are various reasons for this, but in most cases the students in a college calculus class are not already experts in calculus.…
Chris Cunningham
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31
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1 answer
Which product of single digits do children usually get wrong?
(I was inspired by the comments in this answer to ask this question.)
I have some multiplication table cards from Kumon that have a list of commonly mistaken multiplications: $7\times 8, 4\times 8, 11\times 12, 7\times 9, 6\times 7, 12\times 8,…
JRN
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31
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4 answers
What websites allow students to purchase solutions to problems?
I am a college instructor who's just had an outbreak of academic dishonesty connected to students posting take-home exam problems on a platform called Chegg. Chegg collects a membership fee from students and uses it to pay contractors to answer…
Kevin Carlson
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31
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6 answers
Alternatives to University Lectures: Non-lecture Mathematics Classes
I am looking for resources for designing undergraduate mathematics classes that are not lecture-based. (Bonus points if the design is for an introduction to proof course).
For example, Robert Talbert blogs about flipped classes (calculus, and…
David Steinberg
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31
votes
8 answers
How to react to students saying that they are allergic to applied mathematics?
I'm working in the field of applied mathematics (optimization and numerics) and I meet a lot of students saying that they are allergic to applied mathematics or that they hate it or some quotes like "I'm here to learn how to think and become a…
Markus Klein
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31
votes
10 answers
Why do we teach even and odd functions?
I've been either a student or an instructor in Precalculus or Calculus 1 at about 6 institutions now, and teaching the definition of even functions (where $f(-x) = f(x)$) and odd functions (where $f(-x) = -f(x)$) has been universal.
But why? I don't…
Nick Matteo
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31
votes
10 answers
Is this homework problem on counting triangles within a 4x4 grid too vague?
My six-year old daughter was given this maths problem for her homework:
Given a regular square grid of 4 × 4 dots, how many different triangles with one dot in the middle can you draw?
We were given no additional information other than that stated…
Bob Tway
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30
votes
7 answers
When $-x$ is positive
This recent question reminded me of a question: this year several students expressed concern about the expression $\sqrt{-x}$, on the grounds that it must be undefined because $-x$ is a negative number, and negative numbers don't have square roots. …
Henry Towsner
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30
votes
9 answers
Teaching by Slides, Yes or No?
Mathematicians use (Powerpoint/Beamer) slides for their lectures. My question is about using slides for teaching math. There are several positive and negative arguments about teaching by slide show. e.g.
Positive: One can show many mathematical…
user230
30
votes
5 answers
Should word problems be reasonable?
I've recently run across a series of problems that didn't reflect reality.
For example -
An algebra problem with two teens on bicycles. The resulting times showed the bike was moving at 120MPH.
A quadratic equation, "The football follows a path…
JTP - Apologise to Monica
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30
votes
6 answers
f(x+h) in the difference quotient
When teaching students how to compute the difference quotient in a precalculus or calculus class, we need them to evaluate the expression
$$\frac{f(x+h) - f(x)}{h}$$
for various simple functions, like linear and quadratic functions. Let's say we are…
Chris Cunningham
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30
votes
20 answers
‘Lies to children’ in mathematics and statistics education
In teaching, we sometimes necessarily oversimplify concepts. Terry Pratchett famously referred to this as Lies to children:
A lie-to-children is a statement that is false, but which nevertheless leads the child’s mind towards a more accurate…
Joel Ottar
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