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1500 questions
24
votes
6 answers
What is a good way to explain the Lebesgue integral to non-math majors?
A few days ago I had my last discussion session on probability theory as a TA. In the end I asked students to ask me questions as this is the last class. One of the student asked me about the (real) definition of expectation; he said he is confused…
Bombyx mori
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24
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2 answers
Should geometric algebra be presented early on in undergraduate education?
The Cambridge University GA Research Group’s website along with the “Geometric Calculus R & D Home Page” should serve as a good introductions to geometric algebra, along with the Wikipedia reference – “Geometric algebra”. A somewhat more advanced…
user89
24
votes
10 answers
Pi or Tau? How should the circle constant be taught?
Tau ($\tau = 2 \pi$) has more merits in its application, but pi is the established standard in industry and education. Is the trade-off of teach-ability of circle concepts worth the subsequent confusion due to pi's omnipresence?
How can both be most…
jpd527
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24
votes
4 answers
Keeping quicker students engaged and interested throughout a course
In a college math course one is bound to find a fairly broad range of students in terms of their quickness in understanding the material. This is due to many reasons, including differing mathematical backgrounds. Inevitably, there are always a…
Jared
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24
votes
5 answers
Do all high school students need the same 3-year sequence of math courses?
I continue to be troubled by the amount of symbolic manipulation in a typical Algebra 2 course. Once a student has completed Algebra 1 and Geometry, shouldn't there be another option for them if a math/science field is not in their future? What…
Jennifer Silverman
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24
votes
13 answers
What is a free and simple 3D plot software for students?
I need any plot software on Linux or Windows that my students should use it for plotting 3D functions.
I want introduce any software that be free and useful for bachelor students.
Huseyin
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24
votes
14 answers
What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?
I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, optimization and (more recently) machine learning.…
Fraïssé
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24
votes
5 answers
Correcting how a student writes symbols
One of my college students writes the Greek letter $\pi$ as a script n with a bar over it, like $\bar{n}$. [There is actual space between the letter and the bar.] I have never seen this before, and Googling didn't get me anywhere. I feel compelled…
Nick C
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24
votes
10 answers
How to encourage young student to think in unusual ways?
I tutor a young girl aged 11 (grade 4).
She is doing OK for her age, but I have observed that she has a tendency for rigid ways of thinking. She is usually more inclined to follow rules and stick to known ways of doing things which I think limits…
BKE
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24
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9 answers
Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?
The assumed age of the students is 10-15 years old.
What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to me like the term "congruent" is an unnecessarily rigorous term to…
Improve
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24
votes
4 answers
Non-answerable questions on exam: What to do?
What is a good strategy when you realize (e.g. while grading the exam) that a question on an exam was incomplete/wrong?
More concretely:
If it is decided that additional points should be given:
How many additional points should one give to the…
Markus Klein
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24
votes
3 answers
Why aren't logarithms introduced earlier?
I've always been puzzled by the unequal treatments of square roots and logarithms in school mathematics. In the United States, most students know what a square root is before they enter high school (9th grade, age 14 or so), and can answer…
Jim Belk
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24
votes
5 answers
How does a teacher come up with plausible wrong answers for multiple choice tests?
When taking a MOOC in calculus the exercises contain 5 options to select from. I then solve the question and select the option that matches my answer. Obviously only one of the options is correct. But there are (quite a few) times where my solution…
Marcus
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24
votes
6 answers
Should we stop teaching "interchange $x$ and $y$" when finding the inverse function?
In one textbook I use for College Algebra, the author teaches that one should interchange $x$ and $y$ when looking for inverse functions. For example, the inverse function of $$y=2x+2$$ is $$y=0.5x-1.$$
In a calculus textbook the author does not…
Zuriel
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24
votes
1 answer
Has Benezet's teaching experiment ever been reproduced?
In the 1930's, Louis Bénézet, a superintendent of several schools in New Hampshire made the interesting experiment of teaching no formal arithmetic until grade 6:
In the fall of 1929 I made up my mind to try the experiment of abandoning all formal…
Michael Bächtold
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