Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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1500 questions
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6 answers

Do I really need to cover solids of revolution in my Calculus I class?

I will be teaching Calculus 1 soon, using Stewart's Calculus: Early Transcendentals as a reference. I can't help but recall my time in high school AP Calculus and my first semester undergraduate calculus, and how much I (along with many other…
Justin Champagne
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How should I teach logarithms to high school students?

I have some very basic questions about how to teach the logarithm to high school students: First of all, is it better to introduce it as a function with a graph or is it better to treat it like a black box with certain properties at first with which…
Matt N.
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9 answers

What is the rationale for distinguishing between proper and improper fractions?

I cannot recall ever hearing the terms "improper fraction" and "proper fraction" outside of an elementary and middle school setting. At some point in my mathematics education people began to simply say "fraction". Has there been any research into…
Improve
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1 answer

How much time to spend on a single question?

When I was self-studying as an undergraduate, I would spend up to two weeks working on a single problem or trying to understand a proof in Rudin's Principles of Mathematical Analysis. I realize now that I wasted a lot of time and could have learned…
Student
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How does one tutor an A-level student past the derivative paradox?

EDIT (two years later): I was saddened to realise that no-one seems to care at the school level. Everything I thought might be a problem ended up as a non-issue because no-one challenged anything. The word limit is used in class but no one stops to…
FShrike
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2 answers

Emphasizing the discrete in early undergraduate education?

From time to time, I have come across course ideas emphasizing the discrete over the continuous, such as Peter Saveliev's Fantasy Math curriculum (update: see also his material on discrete calculus) and Kelemen et al's article Has Our Curriculum…
J W
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9 answers

Children's counting problems: Is this question phrased correctly?

Look at the following example: Which picture has four apples? A B C D B is the expected answer but should not the correct answer be BCD? Technically if a set has exactly $m$ elements, then it has $k$ elements if $k\leq m$. This is also how we…
Zuriel
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Why use the word Quadratic?

While talking about different types of equations, a student in my class asked: Why we use the word quadratic to refer to second-degree equations? Here is some context: 1) Linear ($x^1$) equations make sense, because the graph of a linear equation is…
David Ebert
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Why do some linear algebra courses focus on matrices rather than linear maps?

I hope the essence of the question is clear from the title. There are obvious advantages to making the linear map the central notion of a linear algebra course: the notion can be illustrated with nice, intuitive geometric (or otherwise) examples,…
Kostya_I
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5 answers

Is required reading of the text effective, and how can it be assessed?

This will likely depend on the class, of course. But I've asked calculus students in the past if (a) they regularly read the textbook and (b) whether this is helpful for them and (c) whether they like the book. The responses have been mixed for (a)…
Brendan W. Sullivan
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8 answers

Prisoner's dilemma formulation for children

I am preparing an introductory course on Game Theory for children (between 10 and 17 years old). In the course description, I want to include a prisoner's dilemma in order to catch children's attention and persuade them to attend the course.…
Kikolo
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3 answers

Implementing oral exams

In the USA most mathematics undergraduate classes seem to base the final grade on the following items Homework / quizzes Midterms / exams. I believe that there can be a lot of value in oral exams, so my question is: What is a concrete model for…
Thomas
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8 answers

Is there a place to buy physical models to demonstrate the Calculus shell, disk, and washer methods?

I know a math teacher who is going to teach a calculus class that will include the shell, disk, and washer methods for calculating volumes. My question is, is there some 3D kit she could use to demonstrate these methods physically? Ideally for…
Eugene
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4 answers

Why we don't normally teach chord, versine, coversine, haversine, exsecant, excosecant any more?

It seems that the following functions are not only excluded from a course in trigonometry, they are almost never taught in any course: Chord Versine Coversine Haversine Exsecant Excosecant I could have asked the same question with the title "why…
Zuriel
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Adding irrelevant humorous questions to a quiz exam

Sometimes, when preparing some calculus exams I try to have a "funny question" such as: T/F I love mathematics T/F Calculus 2 is easier than Calculus 1, ... So my questions are: Do you think it is a good idea to have such questions in an…
Muath Karaki
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