Mathematics Educators Stack Exchange
Mathematics Educators Stack Exchange

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How important is making definitions plausible?

During my studies I observed that while most lecturers try to explain theorems and their proofs, only very few of them try to explain definitions. However, in my opinion, definitions are the base of maths education. In principle, it is possible to…
Photon
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Pros and cons of randomised question generation

I am developing an assessment piece where the content is the same but the particular numbers are different for each student. It involves finding Triangle Centers given points using coordinate geometry. The particular skills it is assessing…
pdmclean
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Use of Lockhart's *Measurement* in a course?

I greatly admire Paul Lockhart's Measurement (Harvard Press). Many of you know him through A Mathematician's Lament. One review of Measurement said, “Here Lockhart offers the positive side of the math education story by showing us how math should…
Joseph O'Rourke
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Vocabulary for giving just numbers, not a full answer

I am a math teacher from China, teaching a course in English. Some students of mine are really good at finding answers for math problems designed in a quiz, however they are unable to write down full answers with details or explanations. How do I…
Hoa
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Students who have succeeded before but are not succeeding now

Here is a common process I witness in office hours: Student struggles with a difficult concept. Student gains understanding of the concept. Student, now bewildered since the concept is mastered, declares "Oh! That's it??." They not only learned…
Chris Cunningham
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Is $180^\circ = \pi$?

I want to ask a question that causes confusion. In the trigonometry, we use some units of measure of angle: degree and radian. Which is/are correct? $$ 180^{\circ} = \pi $$ or $$ 180^{\circ} = \pi \ \ \ \text{radians}$$ In the other words: Is…
scarface
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Looking for a specific female maths writer, who has written on infinity

I once read a book on infinity that was written by an American female maths writer. Her writing was very easy to read and she was a great explainer of concepts. A very distinct aspect of her books was that there were only a few words on each line to…
bill
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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 curriculum was to be the notion of function, which…
Manya
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Formats for Calculus instruction at different colleges and universities

In the comments under another question, a couple of people expressed interest in how Calculus is taught at the University of Michigan. I'm not convinced a question that narrow is appropriate for this site, so I am opening the topic up to a broader…
mweiss
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Is the constant term a coefficient?

I'm a baby boomer who was taught that the constant term of a polynomial is a coefficient, being the constant factor for the x^0 term. That's not what's taught today. Current text books are vague on their definition of coefficient, but, when they ask…
Thomas Martin
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'Low-algebra' examples of induction

What are good examples of proofs by induction that are relatively low on algebra? Examples might include simple results about graphs. My aim is to help students get a sense of the logical form of an induction proof (in particular proving a statement…
dbmag9
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Why don’t all professors let students use notes, books, etc. on exams?

Last semester I had a teacher who let us use any type of information in the exam, for example the course notes, books, solved exercises, etc. The only thing he did not let us use was something electronic like smartphone. Of all the teachers that…
user10026
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Appropriate education level for this geometry problem

What's the appropriate education level for the following concise but non-trivial geometry problem? Points $A$, $B$, $C$ are collinear; $\|AB\|=\|BD\|=\|CD\|=1$; $\|AC\|=\|AD\|$. What is the set of possible $\|AC\|$ ? To check one's answer,…
fgrieu
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How to resolve the new definition of subtraction and division seen in college algebra?

Here's the foundational thing that irritates me the most when teaching college algebra. Up through the secondary level, I think that instructors and students are trained to understand subtraction and division in terms of the inverse operation.…
Daniel R. Collins
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Analogies or explanations for duality, at the college sophomore level

This semester I taught the third semester of my college's freshman physics sequence. Nearly all the students are engineering majors. Compared to previous semesters when I've taught this course, I went into a little more detail on quantum mechanics,…
user507
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