For questions in Mathematics Education as a scientific discipline. For more hands-on questions on teaching Mathematics, please use the tag teaching. There is also a Stack Exchange community http://matheducators.stackexchange.com/
Questions tagged [mathematics-education]
277 questions
63
votes
20 answers
What should we teach to liberal arts students who will take only one math course?
Even professors in academic departments other than mathematics---never mind other educated people---do not know that such a field as mathematics exists. Once a professor of medicine asked me whether it is necessary to write a thesis to get a Ph.D.…
Michael Hardy
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26
votes
6 answers
What are the advantages and disadvantages of the Moore method?
Describe your experiences with the Moore method. What are its advantages and disadvantages?
Paul Kieger
- 39
25
votes
5 answers
Simple but serious problems for the edification of non-mathematicians
When people graduate with honors from prestigious universities thinking everything in math is already known and the field consists of memorizing algorithms, then the educational system has failed in one of its major endeavors.
If members of the next…
Michael Hardy
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23
votes
16 answers
What are your experiences of handouts in mathematics lectures?
There are many different styles of lecturing, and many different aspects that are blended together to give a whole "lecturing style". That said, I'm particularly interested in hearing people's experiences with so-called "handouts". At one extreme…
John Jones
- 95
22
votes
9 answers
How do you motivate a precise definition to a student without much proof experience?
When introducing students to highly technical definitions for seemingly intuitive concepts (e.g., homotopy, continuity), how do you motivate the necessity of the definition? On the one hand, you would hope that the students are mathematically…
user4759
- 141
17
votes
2 answers
Where and when did "transition to abstraction" courses start?
I often find myself debating the content and structure of such courses and I would find it useful to know the basic history.
I don't remember any such offerings during my own undergraduate days in the '70s. I have always supposed these courses…
David Feldman
- 17,466
16
votes
12 answers
Motivating Algebra and Analysis for Average Undergraduates
I work at a small liberal arts college, where many of our mathematics majors will not attend graduate school in mathematics. My hope in asking the following question is to gather innovative ideas for motivating an average student for the development…
Jon Bannon
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16
votes
5 answers
Why is a topology made up of 'open' sets? Part II
Because the display was getting quite cluttered, I thought I'd post a second part to this question separately. I hope the Gods of Math Overflow don't take too much offense. I'll go now into some details with which I wished intially to avoid…
Minhyong Kim
- 13,471
14
votes
1 answer
Classroom platonism
I'd like to know whether any form a certain hypothesis about the
learning of higher mathematics has entered the mathematical or
educational literature. I'll frame the hypothesis here but not defend
it since this is not a blog-in-disguise; likewise…
David Feldman
- 17,466
12
votes
2 answers
Teaching and students
Sometimes I get stumped by students' questions in my classes I teach. I am an algebraist by training and have just started teaching. Sometimes I have to teach analysis courses. My question is: Is it normal to get stumped by questions from students…
Rachel J
- 129
9
votes
4 answers
Differential Equation Examples for Calculus Students
I've been teaching calculus courses for a while now, and something always bothers me each time I teach it. Students always seem to have trouble connecting with the differential equation material for the following reason: I always tell them that…
Brent Werness
- 183
9
votes
4 answers
Name for a basic principle of calculus?
$$
[\text{size of boundary}] \times [\text{rate of motion of boundary}] = [\text{rate of change of size of bounded region}]
$$
This differs from the fundamental theorem of calculus in that it does not mention antiderivatives and you can present it…
Michael Hardy
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9
votes
12 answers
How do I explain the number e to a ten year old?
Hardly a research level question, but interesting nonetheless, I hope. Pi is easy, but not e. Where could I start?
James Smith
- 107
8
votes
1 answer
Self-taught undergrad math: ordering of topics?
After some initial research on math topics, it seems there are about 4 main streams as follows:
1) calculus -> analysis -> complex variables
2) linear algebra -> abstract algebra -> topology
3) discrete mathematics -> number theory
4) statistics
By…
mathmoggy
- 93
8
votes
3 answers
Specializing early
Topic: this is a mathematics education question (but applies to other sciences too).
Assumptions: my first assumption is that most mathematical concepts used in research are not intrinsically more complicated to grasp than high-school and…
Thomas Sauvaget
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