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1500 questions
20
votes
8 answers
What is the point of teaching variance?
I am a teaching assistant for a sophomore engineering laboratory. We use standard deviation a lot during the semester. It is an incredibly useful concept that can be used in a lot of engineering applications. We also teach students how to calculate…
BobTheAverage
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20
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8 answers
Why do no students know to change the limits of integration when doing substitutions?
I've TAed and tutored calculus for years and of the hundreds of students I've interacted with, it is always a shock when I tell them to change the limits of integration when they do substitutions. When I tell them to do that, they are always…
user5108
20
votes
5 answers
Why is multiplication taught using cross notation at first?
Alert: I am not a math educator.
It seems to me that multiplication is first taught using the cross notation, for example $3\times 5=15$.
First question - is that even correct? Maybe not all schools in every country even teach this?
Later on in…
Džuris
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3 answers
Why are $m$ and $b$ used in the slope-intercept equation of a line?
The slope-intercept form of the equation of a line is often presented in textbooks (in the US) as
$$y = mx + b\,,$$
where $m$ is the slope of the line and $b$ is the $y$-intercept. How did $m$ and $b$ become the standard variables used for the…
Mike Pierce
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20
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9 answers
Memorizing Trig Identities
I adjunct for a local community college teaching College Algebra and College Trigonometry. Every year, the community college math department insists on students memorizing each of the trig identities. I can understand why students should have the…
MathGuy
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6 answers
Answers in exact form (e.g. including radicals) vs. Decimal Approximations
I was tutoring a student on early trigonometry. Solving for the hypotenuse of a right triangle, but with sine, not Pythagoras.
The student went through getting the sine of a 45° triangle, and gave me the correct answer to 3 digits after decimal.…
JTP - Apologise to Monica
- 9,770
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20
votes
2 answers
Tips for Teaching Math in a Language Foreign to the Teacher
I retired after 25 years of teaching and moved to Israel a year ago. My Hebrew is okay, but before moving here, I had no experience talking about math in Hebrew. I have been learning Hebrew math vocabulary by reading math textbooks and taking an…
Amy B
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20
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6 answers
How to learn math from textbooks in the right way?
I am a freshman studying math.
Everytime I learn Mathematics, I do it the slow-way. I tend to read the definitions until I make sense of what is written in the texts. I can spend a whole day trying to get one page of the textbook. I also do all the…
Minh Khôi
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1 answer
Problems which require interpreting definitions
I'm trying to find more problems suitable for early college students (students who know algebra and calculus) that involve translating words into mathematical notions. A nice example is this one:
Show that on the graph of any quadratic polynomial…
Henry Towsner
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20
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3 answers
Group theory for high schoolers, want the opinion of other educators
So I am going to be teaching the basics of group theory to high schoolers in a few weeks, and I want to hear what the Stack Exchange network has to say on the matter.
What are the applications and insights I should show them in order to excite them…
user338102
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20
votes
2 answers
Literature on learning from errors in mathematics
In teaching undergraduate mathematics, I implemented some strategies to encourage the students to look at errors they made or at "typical errors" in the current topic. One attempt was to compile a commented list of errors which appeared in the…
Christian
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20
votes
5 answers
Source of conceptual, multiple choice calculus questions
I'd like to give my Calculus 1 class periodic multiple choice questions that really test conceptual understanding. Ideally, I'd like these questions to require very little computation. I know that a lot of textbooks have true false questions, which…
Jared
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20
votes
7 answers
How can I motivate the formal definition of continuity?
In order to teach continuity of real valued functions $f:D\to\mathbb R$ one may start with the (in some sense wrong) intuition
$f$ is continuous when its graph can be drawn without lifting the pen.
I guess this is the intuition many students start…
Stephan Kulla
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20
votes
4 answers
Students' Messy Sheets: The Big Problem of Exams and Homeworks
Students' messy exam and homework sheets (which are messy because of a bad handwriting or an irregular logical argument in proofs) cause many serious problems. e.g.
Reading their arguments takes too much time.
Messy sheets could be confusing.…
user230
20
votes
12 answers
What could be good non-mathematical analogies to explain the difference between the words theorem, proposition, lemma and corollaries?
What could be good non-mathematical analogy/analogies to explain the difference among the words - theorem, proposition, lemma and corollaries to high school students?
I am looking for analogies that would explain their meaning and their usage by…
vivek kumar
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