Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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Recommend a vector calculus textbook/resource with an algebraic geometry flavor

Is there a resource or textbook that presents the basics of vector calculus, specifically the gradient, directional derivatives, curves and surfaces, and extrema, from a more algebraic geometry flavored perspective? I suppose I mean algebraic…
Mike Pierce
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Computational Software for the whole curriculum and beyond

Our (United States, undergraduate) math program is considering the idea of putting more mathematical modeling and computation into all levels of our curriculum. One of the hang-ups is that we can't decide on a specific mathematical software that…
Aeryk
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Algebra best practices for students

One thing I notice frequently is that students don't have 'best practices' for doing algebra. Let me given an example: If students are trying to differentiate, say, $f(x) = (x^2 + x)^2$, they will often write: $2 (x^2 + x) [2x + 1]$, where the…
Elle Najt
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How to teach Leibniz and Newton's notation

There has been many posts here and in MSE about different notations of differentiation. See for example this, this and this. However, those questions only deal with the common misunderstanding about Leibniz notation. But none of them really tell how…
Harto Saarinen
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High School Math Course focused on Sports

I am an high school math teacher and want to develop a math course that is totally focused on sports. It would be a senior level course and would focus on the math and analytics of sports. I just wanted to see if anyone out there has created a math…
Chris Woloch
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teach that $\frac10$ not defined properly

there're some students, who belive that $$\frac10 = \infty $$ I need to teach them that this is not true and $\frac10 $ is undefined, mathematically and give a good picture (for their minds) what is the proper way to teach them without to telling…
Bad English
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Cognitive demands of a mathematical task

I'm looking for a theoretical framework to classify a task based on its cognitive demand. I only have the Smith and Stein's (1998) proposal and PISA framework such as my principal references. In particular, the PISA categories which help us to…
Carlos Torres
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What is known about discrimination and difficulty in test questions?

I am interested in looking at any design resources or "guiding principles" on the distribution of different types of question difficulties on evaluative examinations. We can use Item Response Theory and other data analysis techniques to get a…
Nate Bade
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How to teach a weak student?

I am tutoring a 9th grade student. And he is terribly weak in mathematics. He doesn't remember the multiplication tables, can't divide efficiently. Doesn't know how to proceed with solving a mathematical expression. He says he is not interested in…
Shad
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How to effectively use colors on a whiteboard?

I will be teaching assistant for an analysis course next semester: I'll present the solutions of the exercices to the class. Syllabus is sequences and series of functions, Riemann and Lebesgue integrals, L^2 spaces, etc. Solutions of the harder…
Olivier
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Studies into the effects of having fewer classes per term

Have there been any studies done into the effect of having fewer classes per term on a student's comprehension of their mathematics course material? Also are there any examples of schools that have shorter class terms with fewer classes per term? I…
Mike Pierce
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Drumming up interest in journal-problem-solving and competition prep

I teach at a small liberal-arts college and advise our Math Club. In past years, I have talked a few students into taking the Putnam Exam. I've found that I pretty much have to "coerce" them into taking it at all, let alone prepare for it…
Brendan W. Sullivan
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Activities for biology undergraduates taking integral calculus

After searching for applications of calculus for biology students, I've found that many of the results are all either contrived exercises, or are way over the heads of students that are seeing calculus for the first time (like activities for a…
Mike Pierce
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Math for Social justice curriculum

Recently, a friend of mine who plans to work as a "social-impact consultant" (she is currently a College senior with a background in intro statistics) requested that I offer some kind of curriculum that targets "math for social justice." I took this…
Andres Mejia
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Surrounding a subject and strangling it to death versus concentrating on the main point

Standard calculus textbooks begin by introducing limits, including limits of a fraction as the numerator and denominator approach $0,$ limits of a fraction as the numerator and denominator approach $\infty,$ limits of continuous functions as their…
Michael Hardy
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