161 reputation
16
bio website
location United States
age
visits member for 1 year, 5 months
seen 14 hours ago

"My life is spent in one long effort to escape from the commonplaces of existence. These little problems help me to do so." (Sherlock Holmes)

I sometimes enjoy embedding puns and subtle self-references into many of my answers and comments.

Remember, context is everything.


Never make the mistake of thinking that a tiny preposition has only one meaning.


14h
comment Visually stunning math concepts which are easy to explain
@DanielM - You're right, the experiment isn't a proof. Then again, neither is the formula. I just wanted to draw attention to how my math teacher's technique left a lasting impression that the formula by itself could never manage to do.
Apr
22
revised If there are obvious things, why should we prove them?
deleted 1 character in body
Apr
20
answered If there are obvious things, why should we prove them?
Apr
20
comment If there are obvious things, why should we prove them?
Not my downvote, either, but: Immoral? Sacred? For someone professing such strict adherence to rigor, those words are a bit over-the-top.
Apr
20
comment Are there 3 trig functions or are there 6 trig functions?
The bottom line answer always seems to be "it depends." Great link, btw.
Apr
13
comment Visually stunning math concepts which are easy to explain
@Travis - That's why I gave up and constructed my own image. (Hopefully one that illustrates my point a little better.) I left the other image in my answer so as not to render all these comments obsolete.
Apr
13
awarded  Editor
Apr
13
revised Visually stunning math concepts which are easy to explain
added 411 characters in body
Apr
13
comment Visually stunning math concepts which are easy to explain
@Travis - Yes, a few folks have made that observation. Perhaps I didn't choose the best examples. I'll stand by my point, though: diagrams showing little more than a polygon, some labels, and an equation often lead a student toward a plug-and-chug mindset that isn't as instructive as it could be. I still think first diagram has plenty of room for improvement; it could be drawn in a way that would do a better job of nudging a student toward your line of reasoning.
Apr
7
awarded  Good Answer
Apr
7
comment Visually stunning math concepts which are easy to explain
@LaC - I'd think the first picture would be fine, too, if it had a rectangle drawn around it, so that it's plain to see that the four triangles that form the rhombus cover half the rectangle. My beef with the first drawing is that most middle schoolers would not think to do that; I'm afraid they'd simply follow the formula without any thought about why it works.
Apr
7
awarded  Nice Answer
Apr
7
comment Visually stunning math concepts which are easy to explain
@WillOrrick - You make a good point. Yet I'm still disappointed in the first image because it doesn't really nudge the learner toward thinking about the area of a rhombus as the area of two adjacent triangles with related dimensions. It just shows the formula; a two-color rhombus might have worked better. (As for the second image, I agree, it doesn't look as square as it should.)
Apr
7
comment Can a coin with an unknown bias be treated as fair?
Even if the SD card comes up as "heads" 2/3rds of the time, you only have a 50-50 chance of picking the favorable side, assuming you have no data to nudge you toward the correct choice. I think this answer helps answer the O.P.'s question: Does not knowing contribute to "fairness"?
Apr
5
awarded  Teacher
Apr
5
answered Visually stunning math concepts which are easy to explain
Feb
16
comment Plotting Primes
I want this as a poster.
Feb
14
awarded  Informed
Jan
20
comment Splitting a sandwich and not feeling deceived
A great theoretical answer of limited practical use. :^) This cake will be little more than crumbs by the time it is divided up. You'd better have an awfully sharp knife.
Jan
9
comment Pedagogy: How to cure students of the “law of universal linearity”?
I've used this technique often – just substitute some concrete values and make sure your last operation makes sense and is valid. That said, though, I've also learned to avoid using 2's and 4's, as you used in your example, because, when x=2, x+x=x*x, and 4-x = 4/x, so you could get a false positive. I feel a little safer using 5's and 3's instead.