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What topic can I use in an Introduction to Proofs course that would introduce students to a wide variety of proof methods?
What topics are appropriate for an Introduction to Proofs course which is:
Aimed at Freshman who have taken integral calculus and nothing else
Is designed to introduce them to formal reasoning and writing proofs
Includes a unit/chapter on proof…
Brian Rushton
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11
votes
4 answers
Should homework be graded in an undergraduate math course?
It seems like the internet has made it very difficult to prevent cheating -- simply looking up the solutions to textbook problems -- on undergraduate math homework. So there is a danger that grading math homework assignments could be unfair to the…
eternalGoldenBraid
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11
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3 answers
Middle / High School Math Teachers and LaTeX
All of the middle and high school math educators I´ve encountered choose not to use LaTeX in preparing their documents or presentations. I would assume that most of them had to use the program in the past for their Bachelors or Masters programs. …
MichaelLink
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11
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3 answers
In math courses with writing requirements, how should large papers be graded fairly?
In a course I am teaching this semester, I am required to have my students write a large (6-12 page or so) paper worth 40% of their grade. Many other colleges have courses with similar requirements, e.g. a capstone major course involving writing, or…
Brian Rushton
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11
votes
4 answers
What are the best places online where math educators can discuss their experience?
As a math teacher I often experiment new things (for instance non obvious ways to use technology in the classroom, or new ways to teach something), and I think it would be useful if I could share my results without having to write my own blog that…
d. zeffiro
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1 answer
Motivation for uniform continuity
What are some problems or theorems that motivate the distinction between continuity and uniform continuity? In particular, I would like:
a) A useful, appealing theorem that applies to uniformly continuous functions but not arbitrary continuous…
benblumsmith
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11
votes
4 answers
How would you introduce Frullani integral to students?
Some integration techniques are just "tricks", while some integrals are analytically significant in that they connect different fields of math or they embody higher level concepts.
In the commonly stated form, the Frullani's integral is a definite…
Lee David Chung Lin
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11
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4 answers
How to teach a student algebra who misses too much previous knowledge?
I am now tutoring a student in Grade 9, who falls behind in math study. He lacks the basic understanding of operations and inverse operations, and have trouble dealing with negative numbers and fractions.
As a consequence, he knows how to solve an…
Mathis
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votes
1 answer
Is Lax's Linear Algebra and its Applications comprehensive or idiosyncratic?
I'm looking for a good abstract linear algebra text (i.e., not matrix crunching) for students who have completed a Strang-level linear algebra course plus exposure to a proof writing (e.g., induction and contradiction are not foreign concepts).
The…
user9185
11
votes
3 answers
Should one ask questions directly to specific students in a lecture or exercise group?
In the question Encouraging class participation there are some answers how to encourage class participation in general.
Sometimes, there are some smaller lectures (in particular in graduate courses) or you have smaller exercise groups where you know…
Markus Klein
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11
votes
4 answers
How to design multiple choice questions
I've seen the previously-asked questions about the effectiveness of multiple choice problems, but I want to know about design. What are best practices in multiple choice problem design? The "common" understanding I've come to is based on perennial…
Nick C
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11
votes
3 answers
Difficulty with word problem interpretation
I've tutored math SAT prep for some years now, and have developed a routine with certain texts and exercises that I have found to be fairly successful in improving scores overall. I recognize that many students face a challenge in translating word…
bloomers
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11
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5 answers
Book request: teaching proving and reasoning at an American university
I am a European postdoc who recently teaching at a large public university in the United States. I will have to teach a course for undergraduate students that introduces them to proving and reasoning in mathematics.
The students have possibly no…
shuhalo
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11
votes
1 answer
How cheating on homework affects student questions
I am teaching Calculus 2 and 3 this semester from a common text, and a significant number of my students are handing in perfect homework assignments that are clearly copied from Chegg, et al. As homework grades are a minuscule part of their overall…
AegisCruiser
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11
votes
1 answer
Using number theory instead geometry to introduce proof in Basic School?
It seems there is an overall agreement that Geometry is the right place to introduce proof in Basic School. However, number theory (arithmetic) looks like to be a more simple environment (consider, for instance, a sentence like this one: "if n is…
Humberto José Bortolossi
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