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1500 questions
15
votes
4 answers
How To Help a Quiet Class
This term I am teaching a very quiet precalculus class. I am having trouble getting students to answer questions or respond to verbal prompts, even questions I know they can answer. What I initially chalked up to first-day shyness has persisted into…
Nick C
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3 answers
What to do if all students lack prerequisites?
I am teaching a calculus class for business this summer (6 students) and all of them do not have the math background needed for the class. We are supposed to cover derivatives and integrals, but they don't even know how to evaluate functions. For…
Educator
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15
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13 answers
Mnemonics for some properties in mathematics
I am looking for various mnemonics which help students to remember some important properties or theorems. Very often students confuse signs or relations such as $\leq$ and $\geq$ in some expressions. I wonder if there are some mnemonics that can be…
YukiJ
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15
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3 answers
Does education research support the idea that answer keys are bad?
I am a physics grad student and several of my professors have stated that they are against the idea of posting answer keys (i.e., worked solutions) for homework and/or tests (after the assignment has been completed by the student, of course). Their…
WillG
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15
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When should I say "nothing is as it seems"?
"Intuition" is the best friend and worse enemy of mathematicians! Sometimes using intuitive arguments could be very helpful to understand the nature of a phenomenon. Many of the deepest true conjectures were just an intuitive argument at the…
user230
15
votes
4 answers
Why is polynomial factorization over the integers part of secondary school curricula?
By "polynomial factorization over the integers", I mean problems and solutions like the following:
Problem:
Find a factorization into irreducible polynomials for
$24x^2 +x - 10$ and
$5x^3 -2x^2-x+24$.
Solution:
Suppose a factorization…
K B Dave
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15
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3 answers
How to teach students the value of concrete counterexamples?
I teach exercise sessions for a Linear Algebra course for 1st semester students in Europe. Students have to prepare some exercises at home. In class, I call on students to present their solutions.
One big problem that I see is that in exercises of…
Haudie
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15
votes
3 answers
Cute Word Problems
I'm wondering about the use of word problems on exams which are "cute": they have a slightly funny story, or some sort of pop culture reference, or tie into a running theme of some kind. (As an example of the last category, I recall hearing about a…
Henry Towsner
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15
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5 answers
Learning operator priorities by drawing trees
As far as I know (and here I am refering to my own math education), operator priorities of $+$, $-$, $\cdot$, $\div$, power and parenthesis are taught via some simple phrases like
"pointy" operators ($\cdot,\div$) before "dashy" operators…
M. Winter
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15
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6 answers
Is it a good idea to have one or two or three classes on basic logic before teaching $\varepsilon$-$\delta$ in Calculus?
I am teaching Calculus I and will be teaching it again. To me, the $\varepsilon$-$\delta$ definition of limit is one of the key ideas of Calculus; learning calculus without learning $\varepsilon$-$\delta$ well is like building a tall building…
Zuriel
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Should the cross-product in $\mathbb{R}^3$ be discussed in Linear Algebra?
I have not yet taught Linear Algebra, but I teach Computer Graphics regularly,
which uses linear algebra at many junctures,
and uses concepts such as the cross product.
I have often been disappointed to learn that even students who took Linear…
Joseph O'Rourke
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5 answers
How does a student learn to 'dig behind the scenes' or 'feel' math like a Fields Medallist?
Source 1: Siobhan Roberts, Mathematical Beauty: A Q&A with Fields Medalist Michael Atiyah, Quanta Magazine, 2016/3/9.
Is there one big question that has always guided you?
I always want to try to understand why things work. I’m not interested in…
user155
15
votes
5 answers
What are some recent, interesting, accessible pieces of mathematics
Mathematics can come across as a sterile, dead subject - a catalogue of techniques long-ago decided, and forever relearned by each successive generation of students.
This is approximately true for elementary and secondary mathematics, and for the…
NiloCK
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Pacing your teaching for a variety of learning speeds
I am often tasked with teaching large enrollment courses, and one thing that becomes obvious quickly is that students attempt to pick up new information and solve problems at much different rates. They also succeed at their tasks with different…
Michael Joyce
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5 answers
How to get through the boring stuff?
It frequently happens that there's some material I have to cover which is, frankly, boring. The subject itself may be boring, or it may be the particular exercises, but in any case I have to get through it. When this happens I try to adopt a…
Javier
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