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1500 questions
12
votes
3 answers
Challenge questions for extremely bright kids
I suppose this is the place for my questions as much as any place is:
I'm a math student coming on my 3rd year of undergrad, and I am working as a counselor at a Summer math camp. The camp is for 12-15 year old kids. About 40 are taken from across…
AJY
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12
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2 answers
What to teach in Set Theory & Logic Course
I will be teaching a third-year introductory course on Set Theory and Logic soon and was hoping to get advice from this community.
I would rate my students' proof abilities as weak and was hoping to impart on them a more concrete notion of…
vrbatim
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12
votes
2 answers
Is there a correlation between academic qualifications and teaching effectiveness?
In 2010-11, 56% of US public school teachers had a master’s or higher degree, while only 43% of US private school teachers had a master’s or higher degree (43 percent) (source).
In 2014, only 13% of Singapore school teachers had a master's or higher…
user378
12
votes
1 answer
Probability textbooks repository
(This question was posted more than two years ago on math.stackexchange.com and, although there were some worthwhile answers, none actually answered the question as phrased.)
Has anyone compiled a moderately comprehensive list on the web or…
Michael Hardy
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12
votes
8 answers
How best to explain the logarithm to the mathematically naive?
Suppose you need to explain "What is a logarithm?" to an intelligent
but math-phobic adult (or a student well-prior to her introduction to logarithms).1
I have used base-$10$, saying that, essentially, the logarithm (base-$10$) of a number
is the…
Joseph O'Rourke
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12
votes
6 answers
Algebraic Solving and Uniqueness Proofs
The following issue came up in my Intro to Proofs course and I wasn't sure how to explain my distaste of the student proof.
Prove that the solution for $x$ in $ax+b=c$ is unique ($a \neq 0$).
Student Proof: Solving gives \begin{align*}
ax+b &=…
Aeryk
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12
votes
6 answers
Graphing functions from a finite field to itself
I have been teaching a ring theory course this semester, focusing on modular arithmetic and quotient rings of polynomials over fields.
Several students have asked me how one could graph functions from a finite field (or any $Z_n$) to itself. I've…
Brian Rushton
- 11,680
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12
votes
1 answer
elementary level assessment tools
I'm looking for an assessment tool to ability group 4th and 5th grade students, in particular setting a "top" group. This group would receive more enrichment, less practice on concepts and a faster pace of instruction. Our goal is to figure out by…
Marjorie
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12
votes
2 answers
Why don't we teach codomains of functions in high school?
When I was a university student, I learnt that a function is the data of three informations:
the rule that tells how to associate an object $x$ to its image $f(x)$,
A domain $E$ where live the values of $x$ that are transformed by $f$,
and a…
Taladris
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12
votes
1 answer
Is there any footage of Let's Make a Deal illustrating the Monty Hall problem?
The Monty Hall problem is a classic probability riddle and I will be gleefully explaining it to my class of discrete math students.
It is apparently based on his classic game show Let's Make a Deal. But I couldn't find any relevant footage despite…
Frank Thorne
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12
votes
0 answers
Books on meta-cognition that would be relevant for those involved in mathematics?
In 1992 Schoenfeld wrote an excellent "review" of (among other things) metacognition as it applies to mathematics: whether from the perspective of a student, or a teacher.
Metacognition, as quoted by Schoenfeld from Flavell, is:
Metacognition…
bzm3r
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12
votes
3 answers
Can I call $(ab)^n=a^nb^n$ "Distribution"?
My grade 8 students generally know how to use the distributive property: $a(b+c)=ab+bc$
However, we're now learning exponent laws, and one of them is $(ab)^n=a^nb^n$. In order to help my students remember to raise $a$ to the $n$ and not just $b$, I…
David Ebert
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12
votes
3 answers
Fighting math phobia with history
After years of experience in some area of expertise, you can easily forget how difficult it can be for the uninitiated to grasp some fundamental concepts, and, indeed, people often edit out of their own personal history memories of their initial…
Tom Copeland
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12
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4 answers
How do I get them to appreciate learning a new way of doing that thing?
A typical student mistake
You see this:
$$\frac{15}{4\sqrt{15}}=\frac{15}{4\sqrt{15}}\cdot\frac{\sqrt{15}}{\sqrt{15}}=\frac{15\sqrt{15}}{4\cdot15}=\frac{15\sqrt{15}}{120}.$$
You can see that the student tried to rationalize the denominator. They…
ymar
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12
votes
1 answer
Has someone written an essay on the role of axioms in mathematics (suitable for undergrads)?
I'm just starting up the academic year (yes, it starts in February here in the Southern Hemisphere) teaching a 2nd-year Introduction to Pure Mathematics class.
For general background, I would like to explain the general concept of axioms and the…
Gordon Royle
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