# All Questions

2,279 questions
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### The royal road to calculus

In the early 1900s Felix Klein lay out his vision for secondary mathematics curriculum. He wanted schools to teach calculus, so that universities would not be burdened by it. And at the core of the ...
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### Topics in Mathematics for a 15 minute demonstration

I need to appear for an interview for the post of Assistant Professor in Mathematics in an undergraduate college. My Backgorund : I have studied topics like Algebra comprising of Group Theory,Ring ...
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### Where can I get a sample assessment brief for BTEC HN Engineering Unite 39 further mathematics (H/615/1507)

http://www.sbcs.edu.tt/wp-content/uploads/2017/07/Unit-39-Further-Mathematics.pdf I just want some questions to workout so I will be prepared for tests that cover these learning objectives.
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### Is is a bad idea to use an old textbook such as Differential and integral calculus, with examples and applications for calculus course?

I am wondering if it is a bad idea to use an old textbook, such as Differential and integral calculus, with examples and applications by George A. Osborne. This book was published in 1906 and there ...
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### Difference between high school and college calculus courses

I am curious why students who take calculus in high school often do so poorly in college calculus. I am an instructor at an engineering college and I've noticed a decent number of students who have ...
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### Making modular arithmetic interesting for school kids

This is a pattern even school kids could discover (when gently pointed to). I never did conciously, and cannot remember to have been pointed to explicitly, neither at school nor later: \color{red}{\...
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### Presenting ways to find a resultant force

To begin with I am working in a high school classroom where the students are working on the applications of vectors. The beginning of the lesson is about calculating direction and magnitude of vectors ...
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### In what grade do kids (New York, US) learn common differences?

I'm teaching an after school workshop for a few 7th graders. I was having them try to predict the next item in a complicated sequence. After some failed attempts, one of the kids started analyzing the ...
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### Open Rings-First Abstract Algebra Text

Building off my own experience and the responses to "Rings before groups in abstract algebra?" I've decided to teach Abstract Algebra using a rings-first approach. However the various texts mentioned ...
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### Is there any example of a “forwards/backwards” induction?

I like to make the "dominoes" analogy when I teach my students induction. I recently came across the following video: https://www.youtube.com/watch?v=-BTWiZ7CYoI In this video, a sequence of ...
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### How to make students understand/remember that $x^2 = a$ has two solutions?

I teach math in university, in France. This semester I have first-year bachelor students. I am becoming increasingly annoyed that they cannot remember the simple fact that $x^2 = a$ has two solutions ...
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### Why do inequalities flip signs? [closed]

Is there a mathematical reason (like a proof) of why this happens? You can do it with examples and it is 'intuitive.' But the proof of why this happens is never shown in pedagogy, we just warn ...
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### How to explain angle hunting to students

$I$ is a point of the circle of diameter $JK$. The perpendicular bisector of $JK$ cut the semi-circle not containing $I$ at $M$. Let $N$ and $P$ be the orthogonal projections of $M$ on $IJ$ and $IP$. ...