Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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What are some of the qualities that inviting textbooks share?

Many, perhaps most, math textbooks are very hard for most people to dive into. A few textbooks are delightful, and encourage people to learn math by their engaging tone. What textbooks have helped draw you into the subject, and what was it about…
Sue VanHattum
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Difference in meaning of 'algebra'

The other day, in a conversation with colleagues, I realised that the word 'algebra' means different things to us. To me, it brings to mind the study of algebraic structures: vector spaces, groups, rings, fields, algebras, modules... On the other…
Jessica B
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Critiquing Proof Style During Class

I would like to spend a day with my students analyzing mathematical writing. One way I might accomplish this is to offer multiple proofs (some good, some poor) of the same simple statement and ask them to critique the writing. Is there a good…
Austin Mohr
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How to balance higher order thinking and drill/practice

Some place emphasis on higher order thinking skills at the cost of lower emphasis on drill/practice. Others disagree. Personally, I agree that higher order thinking skills are necessary for effective application of mathematics to problems, but I do…
e-sushi
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What basic algebra skills and techniques are most important for calculus students to know?

In my experience, algebra is one of the biggest stumbling blocks to calculus students. For instance, sign errors are common, and exponent laws (and log laws!) cause a lot of headaches. Many courses have algebra pre-tests to let students know if they…
Brian Rushton
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Fourier Animation

Are there any resources which show Fourier series approximating a given waveform? I am looking for examples which have a real impact on students and provides motivation. I am trying to find something visual but it could be just audio based.…
matqkks
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A parabolic arc is not semicircular. But students think so

I'm teaching a Calc 2 class now (integration and applications) and I'm surprised that more than a handful of students seem to think the graph of $y=x^2$ on $-1\le x\le 1$ is part of a circle! Here is a quiz question I posed: Consider the part of…
Brendan W. Sullivan
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Is algebra really the gatekeeper to higher math, or is it multiplicative reasoning?

The National Mathematics Advisory Panel final report states that algebra is the gateway to higher math, to a college degree, and higher earnings from employment. It also states that success in algebra is dependent on understanding multiplicative…
Burt Furuta
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Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th century, but I'd like to supplement it with…
Conifold
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Making standards for "showing work" explicitly clear to students

I do not mean for this thread to be a discussion of whether or not students should show work on an exam, whether they should be docked points for just "seeing" an answer and writing it down, whether using a calculator is fine, etc. etc. Rather, I…
Brendan W. Sullivan
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How to prove Taylor formulas?

I will soon have to teach Taylor's formulas (with Lagrange and Peano¹ remainder terms) to first-year students in math-related curricula (computer science, physics, engineering), and I am not terribly satisfied with the proofs I have seen. I do not…
Benoît Kloeckner
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Worldwide collection of final examinations in mathematics

I am interested in comparing mathematics (and also physics) final examinations from all around the world for the highest secondary school qualification in the particular country. Especially I am interested in countries which ranked high in…
Julia
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Teaching manifolds to high schoolers

I would like to introduce the concept of a manifold to a high school student. This person isn't familiar with the axioms of set theory nor topology. However, despite these deficits, I would like to get the general point across that manifolds are…
Stan Shunpike
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Probability Misconception: Two Bags with Black and White Marbles

I asked this question in a class of 13-year-old students: Bag 1 contains 2 black marbles and 1 white one. Bag 2 contains 20 black marbles and 10 white ones. Which bag is more likely to yield a black marble? Or maybe the chances are equal? We were…
Behzad
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Books that every aspirant mathematician should read

I am a student and I would love to become a research mathematician one day. So I would like to ask you---experts in mathematics but also in education---what are some influential ($\star$) books that I (and everyone in my situation) should ($\star…
Dal
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