David Ebert
  • Member for 7 years, 9 months
  • Last seen more than a week ago
How do you explain why perpendicular lines have negative reciprocated slopes?
Accepted answer
9 votes

A proof following from the Pythagorean Theorem: Claim: If two lines are perpendicular, then their slopes are negative reciprocals of one another. Proof: Assume WLOG that two nonvertical lines with ...

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Counterintuitive consequences of standard definitions
8 votes

Here's an analagous situation: http://en.wikipedia.org/wiki/Clopen_set. Intuitively, open and closed seem like mutually exclusive concepts, but their definitions allow for 'clopen' sets. More ...

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Ideas for high school pure maths projects
7 votes

Here are a few projects done at my high school: 1) Given a quadratic in the form $y=ax^2+bx+c$, determine what changing $a$, $b$ and $c$ does to the turning point (vertex) of the parabola and prove ...

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Evidence showing that returning tests helps students
6 votes

As Richard pointed out, it may be helpful to understand the difference between formative and summative assessment. Here's a good link if you're not familiar with the terms. Your question suggests the ...

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Is $e^{i\pi}+1=0$ a good motivation for introducing $e$ or $i$? Why (not)?
5 votes

Let me take on a different meaning of "introducing" and argue why I think Euler's identity is a great way to introduce the concept: I teach primarily remedial students in grade 8, 9, and 10, and I ...

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Cost and benefits of compartmentalization in k-12 curriculum
5 votes

The opposite of compartmentalization as the question describes it may be connections. Connections is a process standard of the U.S. National Council of Teachers of Mathematics (NCTM), and they have ...

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How to justify teaching students to rationalize denominators?
4 votes

Why assume that your students should learn to rationalize the denominator? It's true that there are instances when rationalizing a denominator is helpful, but my guess is that in your college algebra ...

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Do all high school students need the same 3-year sequence of math courses?
4 votes

NO! Absolutely not! This answer became resoundingly clear to me when I moved from learning high school and undergraduate math in the U.S. to teaching high school maths in South Africa. The ...

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What can be done to improve the standard of mathematics in South Africa?
3 votes

I believe your question refers to the World Economic Formum rankings. As the government and Mail & Guardian noted in their responses, the WEF rankings are based on outside perception, not student ...

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Fun games for children
3 votes

The NCTM website has many mathematical games: http://illuminations.nctm.org/. The site lists over 20 games in the "pre-K-2" grade category, though some of them are a bit advanced. For offline games, ...

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Adoption / penetration rates for dynamic geometry software in secondary school
3 votes

I've found very little good information about how many classrooms use DGS, though Sketchpad does boast on its website: "Each new school year, tens of millions of students around the globe encounter ...

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What are some good rules for handling student questions during exams?
3 votes

Don't neglect the students in your class with unasked questions! If one student in your class asks you a question, then it's safe to assume that at least one or two also have the question somewhere ...

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Are puzzles a good way to interest pre-college students?
3 votes

As a grade 8, 9, and 10 maths teacher I can testify that good puzzles often do motivate my students. Here are a few observations I have about the puzzles I've given in class: 1) A good puzzle must be ...

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Research/Anecdotes supporting WebWork, MyMathLab and other computerized, immediate feedback HW
2 votes

I likewise have mainly anecdotal experience to offer, having used 3 different online homework systems in the last 3 years, including Khan Academy, WebAssign, and WileyPlus. Here are the top 3 issues I ...

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Given a 3 4 5 triangle, how do you know that it is a right triangle?
2 votes

Cut out four identical 345 triangles and put the biggest angle from each triangle together at a point. Then observe that all 4 identical angles fit to make a revolution, which implies each of the ...

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How do you revise?
2 votes

The most helpful aid to my undergraduate exam preparation was writing 3 x 5 notecards. I usually wrote the name of a theorem/term/concept on the front and on the back gave the definition/description ...

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I wanna learn math!
0 votes

Khan Academy has a nice overview of primary, secondary, and some university mathematics, presented in a way that is clear and easy to self assess. I would encourage you to start there, and then when ...

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