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1500 questions
47
votes
12 answers
What should be included in a freshman 'Mathematics for computer programmers' course?
Many universities are changing up the way that they teach math service courses. 1-3 semesters of calculus and maybe a course in linear algebra are often included in majors (such as computer science) that will not use the majority of the…
Brian Rushton
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46
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18 answers
How to explain the flipping of division by a fraction?
This question is inspired by @DavidButlerUofA's discussion of
"$\div \frac{2}{3}$ as $\times \frac{3}{2}$" in
"Are fractions hard because they are like algebra?"
Q. How can one best convey to beginners—without algebra—the flipping of denominator
…
Joseph O'Rourke
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46
votes
16 answers
How is calculus helpful for biology majors?
It's common for majors in biology to take calculus courses, and many calculus textbooks (and calculus professors) try to cater to these students by including applications to biology.
My question is, in what specific ways is a calculus course…
Jim Belk
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46
votes
9 answers
Knowing mathematics does not translate to knowing to teach mathematics. Why?
Many brilliant mathematicians seem to make average or even poor classroom teachers. Is this an accurate assessment? Has there been any research to explain the phenomena?
What is the difference between knowing mathematics and knowing to teach…
Mara
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46
votes
4 answers
How to respond to “solve this equation” in a basic algebra class
I asked this question once on math.se, but don't follow the link unless you want to risk biasing your own response: https://math.stackexchange.com/questions/444696/how-to-respond-to-solve-this-equation-in-a-basic-algebra-class
It is really a…
alex.jordan
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45
votes
18 answers
How to teach logical implication?
One of the challenges of undergraduate teaching is logical implication. The case by case definition, in particular, is quite disturbing for most students, that have trouble accepting "false implies false" and "false implies true" as true sentences.…
Benoît Kloeckner
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45
votes
21 answers
How to help new students accept function notation
I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation.
Their main complaint: "Why do we need $f$ when we can just…
Nick C
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44
votes
4 answers
Teaching undergraduates who expect a high-school-like learning environment
tl;dr: Some students expect to be told "what's on the test", to memorize and then move on. What can be done to change how they learn while teaching them what to learn?
Context: Introductory, foundational course for undergraduates, like College…
Brendan W. Sullivan
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43
votes
28 answers
Good, simple examples of induction?
Many examples of induction are silly, in that there are more natural methods available. Could you please post examples of induction, where it is required, and which are simple enough as examples in a course on proofs (or which includes proofs, e.g.…
vonbrand
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43
votes
24 answers
Response to Students Who Say "This Is Not Important"
Lately, my students keep telling me why what we are learning is not important. They ask me when will we use this in the real world?
I explain how math is important in gambling, cooking, finance, engineering, programming, electronics, philosophy, and…
W. G.
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42
votes
12 answers
Is it advisable to avoid teaching "multiplication as repeated addition"?
I've had this discussion with a couple of friends. I argued that teaching multiplication as repeated addition isn't a good idea because it doesn't help children differentiate between the two operations and see them as independent. My friends argued…
Mark Fantini
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42
votes
11 answers
Formula sheets and books during tests and exams
Some teachers make memorizing formulas, definitions and others things obligatory, and forbid "aids" in any form during tests and exams. Other allow for writing down more complicated expressions, sometimes anything on paper (books, tables, solutions…
dtldarek
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42
votes
5 answers
How can I help a student who has a "wrong" kind of enthusiasm?
Alice (not real name) is a student in one of my Math 100 (calculus) classes. It's a course offered by my college as a dual credit course at a high school, so the whole class is about 17/18 years old, and I'm aware that there's sometimes a maturity…
Torsten Schoeneberg
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41
votes
8 answers
How to teach math to someone who is neither [really] willing nor able to understand it?
I'm not a teacher, I am a student. But in math, I am one of the best ones in my class so sometimes other people will ask me to explain stuff to them. And usually it works quite well: If I understood the topic, I am able to explain it quite well…
IchBins
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41
votes
2 answers
What does math education research know about difficulty vs. effectiveness?
I've asked basically the same question previously on on math.SE, then
cogsci.SE without much response, surely here is the place to ask this.
As anecdotal evidence is plentiful, but unfortunately for whatever conclusion you wish to draw, I'm hoping…
user370