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1500 questions
13
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3 answers
Are there any applications of $x^x$?
I'm teaching Calculus I. It's time for the derivative of $x^x$. In previous semesters, I've told
students we mainly do this just for closure, so that we know that we can find derivatives of every function possible.
Are there any applications of…
Sue VanHattum
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13
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10 answers
Why don't all teachers use clickers?
As a school project we've developed a web based tool (similar to a clicker) which helps the teacher understand how large proportion of their students actually understand what she/he says. Now we've been approached by our school's business incubator…
Johan Wikström
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3 answers
Finding the Balance in a Math Question (Teaching)
As we try to work and teach in the midst of this pandemic, some problems arise when making online math exams. My question is simple: What could be an interesting basic differentiation question such that students doing the online exam still have to…
sam wolfe
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13
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7 answers
Why don’t American school textbooks recognize negative numbers as whole numbers?
Looking up for definition for whole numbers on Google yields a result which mentions:
The whole numbers are also called the positive integers (or the nonnegative integers, if zero is included).
I was suspicious about this answer and I decided to…
codespeare
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13
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11 answers
When do college students learn rigorous proofs?
I teach in a regional university.
In my department, students take their "proof course" (a course that sole focus on writing proofs) in the third or even fourth year.
All the courses before that have minimum proof component.
E.g., even linear algebra…
user13395
13
votes
7 answers
Content for a 40-minute lecture on graph theory for high schoolers
I'm due to deliver a session on graph theory for 16–17-year old students (UK sixth formers) as a taster of what studying mathematics at university is like. What would you recommend as content, and a 'route' through the content for such a talk? There…
dbmag9
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13
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5 answers
How to read chained equalities out loud?
I find that my community-college students are usually very hazy on the status and meaning of chained equality statements (or other relational statements). This seems like a really critical element of mathematical grammar that is almost never…
Daniel R. Collins
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13
votes
5 answers
An application-heavy functional analysis textbook?
I took functional analysis from Conway's book. I thought it was just as abstract and dry as homological algebra, if not more. I knew of no applications.
Then I learned that standing waves on a drum were related to functional analysis, and then that…
Brian Rushton
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13
votes
8 answers
Should true-false questions ask for an explanation?
I like to ask true-false questions on exams, because I feel that they can be an efficient way to assess students' understanding of concepts and ability to apply them to somewhat unfamiliar situations. In general, I'm very happy with true-false…
Mike Shulman
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13
votes
6 answers
Is it a bad idea to offer variants of a final exam based on the type of allowed calculators?
Background/rant:
I am in charge of teaching our single quarter course on vector calculus (don't ask me why the department head thinks the area can be covered in half a semester). The two biggest groups of students in that course are A)…
Jyrki Lahtonen
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13
votes
2 answers
Introductory real analysis before or after introductory abstract algebra?
What are the pros and cons for students of taking introductory real analysis before or after introductory abstract algebra, assuming they are going to take both?
I recognize that the overlap between the two courses is minimal, and therefore they are…
J W
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13
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11 answers
How to explain what's wrong with this application of the chain rule?
Yesterday a student in my calculus class attempted something like this:
Problem statement: Find the derivative of $3^{(5x+1)}$ with respect to $x$.
Proposed solution:
Let the inner function be given by $g(x)=3,$ and the outer by…
Michael Bächtold
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13
votes
6 answers
Why do some students struggle so much with fractions?
I read on multiple web pages something that implies that that some students really struggle with fractions but I could never find a detailed explanation of why. This question is different from Are fractions hard because they are like algebra?. I'm…
Timothy
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13
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3 answers
Is it 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 are no known copy right restrictions, which means…
Zuriel
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13
votes
9 answers
Why do inequalities flip signs?
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 students to remember to flip the inequality…
Lenny
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