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1500 questions
26
votes
6 answers
What is the quantitative data on effectiveness of "modern" teaching methods?
What research has been done on how much and in what circumstances various non-lecture types of teching are effective with regards to student knowledge and performance? Meta/review studies preferred over single case studies, of course.
I am thinking…
Džuris
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26
votes
4 answers
Lesson plan to self-teach real analysis to student with comp-sci background
For my background, I'm a software engineer currently studying for his master's degree in information security. But when that's all done, I plan on going back to mathematics to keep me busy. But with wife and kids, taking more college classes is…
avgvstvs
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26
votes
6 answers
How do you go about writing your own lecture notes for a new course?
In advanced graduate courses, there are often no textbooks on the material being covered, and sometimes no good introductory material at all. Even when there are textbooks, many professors prefer to write their own notes on the subject.
As a fairly…
Brian Rushton
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26
votes
5 answers
Should we "program" calculus students, like the physicists seem to want us to?
If it is true that we first learn formalism...how to do things that we don't understand, should we regard teaching students mathematics as programming dumb machines with formal rules (to the greatest extent possible) and allow them to eventually…
Jon Bannon
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26
votes
6 answers
How to present $\Bbb Z/n\Bbb Z$ to highschool level audience
I have the oportunity to talk to a highschool class about mathematics, the topic I got to present are the integers modulo $n$, ie, $\Bbb Z/n\Bbb Z$ , however I don't want to be very heavy and formal, because I don't want to lose them. For the talk I…
Ana Galois
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26
votes
8 answers
"We already passed that course!" How to overcome this?
I've heard the phrase "we passed that course already!" too many times when asking for e.g. the derivative of a simple rational function or a simple integral, getting blank stares, and digging deeper. This in a second-year discrete mathematics…
vonbrand
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25
votes
5 answers
When did US mathematics programs start failing to prepare incoming students for books like "Baby" Rudin?
I've seen in a lot of questions about "which textbook to use for intro analysis", and inevitably Rudin's Principles of Mathematical Analysis comes up, with the (almost cliche) rejoinder that "today's incoming US freshmen cannot handle Rudin."…
user5661
25
votes
2 answers
Student Poisoned Experience with Math
I’d like to start off with saying I am not a teacher so I don’t know how much of this is already trying to be addressed in math education throughout the world.
In talking to and tutoring fellow students, I have seen that most students think of math…
ruler501
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25
votes
8 answers
What are the historical reasons for the hostility against standardized testing in the US?
NB. Some answers appear to be for a question I did not ask, namely, "Why is standardized testing bad?" Indeed, these answers tend to underscore the premise of my actual question, which can be found above.
As a foreigner who has spent some time in…
user378
25
votes
1 answer
Is there a Piagetian age at which proofs can be comprehended?
I am wondering if there is literature on the developmental age
(pre-adolescent?, adolescent?) at which the notion of a "proof"
can be understood? I am less interested in mathematical proofs
and more interested in "water-tight arguments"—at
what age…
Joseph O'Rourke
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25
votes
4 answers
How should one tutor a student in undergraduate real analysis?
I am an undergraduate. Other undergraduates sometimes ask me to tutor them in an introductory real analysis course that covers the equivalent of the first half-dozen chapters of Rudin's Principles of Mathematical Analysis (baby Rudin). We meet once…
Potato
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25
votes
6 answers
How can you explain to students that they should not use the same variable in an integrand and in the limits of integration simultaneously?
When teaching Calculus, one thing that many teachers emphasize is that the variable of integration is a `dummy variable' that is unimportant.
Around the same time, we introduce integrals with variables in the limits of integration. Students are told…
Brian Rushton
- 11,680
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- 137
25
votes
2 answers
Are there science-backed effective teaching strategies?
As a math teacher, I am always trying to self-assess my teaching methods. I am trying a lot of different methods but I would like to organize my study on the subject without weighing too much on the kids with a trial and error approach, so I'm…
marco trevi
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25
votes
5 answers
What is the proper verb for "doing" an integral?
It's time to write exams, and when writing in committee we often discover differences in usage between various instructors. Here's an example I noticed today.
What is the proper verb to use in a question of the form: "____ the following integrals"?…
Matthew Leingang
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25
votes
6 answers
Practical experience with teaching differentials in freshman calc?
There is a well known essay by Dray and Manogue which argues that differentials should be brought back into freshman calculus, and that we shouldn't worry too much about choosing a specific way of formalizing them, or about giving students a formal…
user507