Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
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3 answers

How can creativity be incorporated into elementary school mathematics?

Creativity is the core of research mathematics. However, most introductory math consists of learning fixed rules to perform basic, essential mathematics. Thus, for many elementary school students, math is perceived as a rote and routine subject.…
Brian Rushton
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Factoring quadratics where the coefficient on the $x^2$ term does not equal 1

so we are working through various methods of factoring quadratic equations and the students seem comfortable factoring basic quadratics such as: $$x^2 - 7x + 12 = 0$$ by finding the factors of $12$ that add up to $-7$. I feel like this is intuitive…
celeriko
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What to do when students are not keeping their eyes on their own test?

At my university, exams take place in a lecture hall, but it is usually pretty packed. Along with alternating versions of tests, it is pretty easy for a student to look to the next row or their neighbor for inspiration. How do you confront a student…
Felix Y.
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1 answer

Textbook for multivariable calculus with interesting modern applications

A colleague of mine in a math department at another university is looking for a textbook on multivariable calculus that discusses applications of higher-dimensional integrals that feel contemporary rather than solidly traditional. In particular, he…
KCd
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5 answers

How can I retain the mathematics that I've supposedly learnt?

First off sorry if this question isn't suited to matheducators.stackexchange I just thought here would be a good place to ask seeing as you would probably have experience with students. Anyway here is my question and other related information: So my…
Jack Woolford
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14 answers

How to teach binary numbers to 5th graders?

I already tried the direct approach, starting with "this is how it works". That turned out ok but took too long and was boring for all of us. My second attempt was using the twofingered alien. This worked better but needs improvement. The problem…
Esmaya
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3 answers

What deficiencies are present in Precalculus curricula that causes so many students to fail Calculus I?

At our university we now require one semester of Pre-calculus instead of one semester of Algebra and one semester of Trigonometry before you take Calculus I (for those who do not test into Cal I). Since we have implemented this, it seems that…
Todd Thomas
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Are teaching about finding the missing member(s) of the sequences really appropriate?

I notice that in current mathematics education they always have sections teaching about finding the missing member(s) of the sequences e.g. in this way: $1,2,4,8,16$ , the next term is what? Someone would argue that the next term is $32$ since they…
doraemonpaul
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11 answers

Topological fun facts for high school students

I'm going to give a class to highschoolers about topology. I've prepared the beginning of the class where I introduce what is topology and give them different ways we use to describe spaces, but everything is described very intuitively since they…
bml64
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Do any middle-school texts indicate that irrationality requires proof?

I believe that most middle-school math curricula have at least a brief section about irrational numbers, in which students are taught (among other things) that $\sqrt{2}$ is irrational and $\pi$ is irrational. What I'm wondering is if students are…
Timothy Chow
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8 answers

What is the right feedback for incorrect cancellation?

Here are three "cancellations" seen during algebra simplification, two of which are invalid. (1) $\frac{x + 6}{6} = \frac{x+6\hspace-1.2ex\diagup}{6\hspace-1.2ex\diagup} = x$ (2) $\frac{6x + 1}{6} = \frac{6\hspace-1.2ex\diagup x +…
Chris Cunningham
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Why is there a disconnect in the usage of "domain" between high school and higher mathematics, and where does it come from?

In high school (in the US, at least), it is common to define the domain of a function as the set of real numbers for which the function is well-defined and returns a real result. Then students are asked questions like, "What is the domain of $f(x) =…
Reed Oei
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7 answers

How to deal with fast students without neglecting weaker ones

In my class, what often happens is that some smart students do problems faster than other students. And they are actually going well ahead of my course plan. While I am teaching to other students a certain chapter, they are doing the next chapter to…
Four Seasons
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Flipping (or not) a large graduate class

I teach a graduate class in algorithms. Students take this class primarily as a breadth requirement in grad school, and they are a mix of MS and Ph.D students in computer science. Most students taking the class have a CS background, but a few don't:…
Suresh Venkat
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4 answers

Requiring students to know all the proofs on an oral exam

I'm asking this question as a student, wondering what various pros/cons to the given formula for oral exams could be. Let me give some context first. I am a first year mathematics student at a university. The are two approaches available to students…
Ormi
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