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1500 questions
9
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7 answers
Examples of arithmetic and geometric sequences and series in daily life
In this part of the course I am just trying to show that we actually see a lot of sequences and series every day in our regular life.
I already found some examples such as the house numbers when you drive down a street, the number of people you…
Michelle_B
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Does there exist an international certification of mathematical skill?
I think that an international certification of math level would be really important also for non-math educators. Here in Italy primary school teachers actually teach math without being proficient at it. I was wondering, does there exist an…
marco trevi
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3 answers
What is abstraction and generalization ?
Mathematicians does something when they mean by doing "abstraction" or "generalization". I can't exactly decipher what they mean, but I suppose
i. Abstraction is of finding patterns from some objects(and conctretizing something is probably adding…
user6330
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votes
3 answers
Applications of MVT for Integrals, suitable for calculus 1
I'm about to give a first-semester calculus lecture covering the mean value theorem for integrals:
If $f$ is continuous on $[a,b]$, then there is some $c\in(a,b)$ such that $(b-a)f(c)=\int_a^b f(x)\,dx$.
In past semesters, I've shown examples in…
swensonj
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5 answers
Primary/Elementary Math Resources for Homeschool
I'm a homeschool mom, my daughter is 7. She will be in second grade next year. I appreciate the different ways of doing math, rather than just stacking the numbers and adding/subtracting. I'm not sure how to go about teaching it. Any good resources…
Shannon
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1 answer
How do you assign a grade to a proof?
This question is very similar to one I posed two years ago: How to assign grades to proofs: what do(es) theliterature/experts suggest?
I would like to ask the more general question of: what do you actually do? Specifically, what do you look for…
David Steinberg
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votes
2 answers
What is the failure rate of students in Algebra 1?
Hello fellow educators,
I've been hearing a lot recently that many students struggle with Algebra 1 in the US. The dropout rate is supposedly very high and some educators argue that Algebra 1 and higher math should be pulled from the school system…
Wmol
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9
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1 answer
Alternative limit for e
I have recently worked with some students motivating the development of $e^t$ and $e^{t i}$ as summing change over time, basically informally solving differential equations. My motivation for this is that the students are already used to programming…
Richard
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9
votes
2 answers
Developing mathematical stories
In a comment on a recent post, Steven Gubkin pointed out that in doing mathematics he likes to develop stories. This motivation for mathematics is perhaps familiar to many practicing mathematicians. Calculations can even become stories. I do not…
Jon Bannon
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9
votes
2 answers
How can we neatly explain chain rule of differentiation
My students are often getting confused while using chain rule for complicated functions. For example
$$f(x)=\tan^3\left(\sqrt{x^2+x+1}\right)$$ Most of the students wrote $f'(x)$ wrongly as
$$f'(x)=3 \tan^2\left(\sqrt{x^2+x+1}\right) \times…
Ekaveera Gouribhatla
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9
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3 answers
Standard word for a formula that is always true
If it is known from context that variables $x$ and $y$ represent integers, an open Boolean formula such as $x \ge y \Rightarrow x+1 > y$ evaluates to true regardless of the value assigned to variables $x$ and $y$, at least in the standard…
Theodore Norvell
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9
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3 answers
Defining vertical tangent lines
In looking at the definition of vertical tangent lines in some popular calculus texts,
I noticed that there are a few different definitions for this term, including the following:
A function $f$ has a vertical tangent line at $a$ if
$\;f$ is…
user84413
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9
votes
1 answer
Do mathematics teaching professional organizations publish hiring recommendations?
Suppose that a secondary school intends to hire a new math teacher, math department head, or math and science director. Do any professional mathematics or educational organizations such as the MAA, NCTM, or NAIS publish a list or summary of…
Andrew
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9
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1 answer
Advice on Proof-based Math Topics for High Schoolers
I have a handful of high school students that are all prospective math/physics majors and have pooled their resources to hire me to teach them a proof based math course because it has become apparent to them in my physics class that proof and…
Zaid Khalil
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9
votes
2 answers
When higher grades are more common than lower grades
The usual assumption in education is that grades follow some sort of normal curve.
My question is about situations where the grade distribution curve is a rising one. More A's than B's, and more B's than C's, etc. In educational setting: Is there a…
Maesumi
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