David Ebert
• Member for 7 years, 9 months
• Last seen more than a week ago

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...