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Research on how mathematics skills transfer to other areas
Briefly: I am looking for research on the extent to which learning mathematics (let's say "college algebra" if we want to be specific) impacts problem solving skills, abstract reasoning, etc.
Less briefly: I teach a college algebra class in an…
David Steinberg
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Explaining the symbols in definite and indefinite integrals
I teach the definite integral before the indefinite for a few reasons, one of which is that I want students to recognize that the definite integral means area (not anti-derivative). If we do indefinite integrals before the Fundamental Theorem of…
Sue VanHattum
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What are questions from students that improved the teachers understanding of mathematics?
Once my professor told me that sometimes questions that she gets from her students turn out to be precious inputs for deepening her own mathematical understanding or for doing some new research in mathematics.
Did this happen to some of you too?…
Dal
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Explaining subjects whose justification requires demanding technical content
This is my first question and I hope it's appropriate.
Often in the process of teaching a subject I start with examples of a phenomenon, exhibiting similar properties between the examples and building an abstract concept of something. Turns out that…
Jonas Gomes
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Math activities for gifted second and third grade math circle students
What are some ideas for math topics to teach to gifted second and third grade math circle students? Let's assume the math circle meets for one hour every week.
One example activity is learning about various types of ciphers that can be used to send…
littleO
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How to deal with students copying?
In university courses with compulsory homework, I quite often find students copying their work from others. Now, you can simply ignore this since they are responsible for their learning. If not, usually a very annoying game starts, where students…
Anschewski
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14
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The interplay of memory and mathematical performance
As mathematicians and mathematics educators we very often see the Dunning-Kruger effect in action. Our calculus students are certain that they are masters of Calculus because they took the AP exam. To be fair, we ourselves are not immune: I often…
Jon Bannon
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Physics-based mathematical courses
I've seen many courses labelled as 'mathematical physics', but I'm interested in knowing about the opposite: 'physical mathematics'.
I've noticed that some areas of mathematics which I found extremely abstract and not interesting were directly…
Brian Rushton
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14
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3 answers
Why do we prove things we already know?
As math majors and math educators we take for granted the importance of proofs and being precise. However with I have found that non-math majors are content with anything that looks reasonably quantitative, whether the logic is correct or not. I…
john mangual
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Teaching advanced math using books with cartoons
Could an effective and 'comprehensive' course on advanced math be taught through a series of fun comic books, say a fun and adventurous series of stories each exploring advanced math principles somehow entangled in the story. I know of a fair amount…
user128932
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Why are hyperbolic functions given "short shrift" at "low" levels of math?
Starting with "precalculus," students learn trigonometric functions. After they've spent a semester or more learning how to differentiate and integrate these trigonometric functions in calculus, students are then introduced to "hyperbolic"…
Tom Au
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When is a good time to teach linear algebra?
When I was a student (in the 1970s) I was taught linear algebra as an "adjunct" to "engineering mathematics" such as differential equations. That was during my sophomore year, which seems a bit late, but those were the days when "calculus" was all…
Tom Au
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What is a good "simplification policy" for a college course with no calculators?
This is a detail, but getting the details right means a lot when you design your course. For the purposes of this question please assume calculators are not allowed in the course, which is true in many college calculus courses and is a debate I do…
Chris Cunningham
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Resources for teaching Riemann integration in higher dimensions and on submanifolds, with view toward Stokes' theorem?
Question
I am looking for suggestions of good resources (textbooks or lecture notes preferably) for teaching Riemann integration in $\mathbb{R}^d$ with $d\geq 2$ and also for Riemann integration along (smooth) hypersurfaces of $\mathbb{R}^d$…
Willie Wong
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According to Common Core standards, what math skills are beginning Kindergarteners supposed to have?
I remember looking once at what chikdren in Kindergarten were expected to know, and it was quite a bit. I have a young son, and would like to know:
What is a Kindergartener expected to know about numbers and shapes and other mathematical concepts?
Brian Rushton
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