
Math Mistakes - DanBC
http://mathmistakes.org/
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ggambetta
This concept of "teaching with keywords" absolutely terrifies me.

I distinctly remember encountering Metric Geometry* in high school. It didn't
teach me geometry, it taught me how to think, and I'm forever grateful.
Teaching math with keywords is the opposite of this.

[*] Probably not the correct name in English. It was geometry without algebra;
proving theorems and finding loci based on some axioms about angles, parallel
lines and so on. What is this called? Euclidean Geometry?

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tokenadult
_It was geometry without algebra; proving theorems and finding loci based on
some axioms about angles, parallel lines and so on. What is this called?
Euclidean Geometry?_

"Euclidean geometry" would do for a name, but to specifically emphasize the
point that algebra is not involved, you can say "synthetic geometry." The
geometry of the plane can also be taught from an analytic geometry perspective
(using ordered pairs of points on the Cartesian plane) as a first high school
course, as in the book _Vectors and Transformations in Plane Geometry_ by
Tondeur.[1]

[1]
[http://www.mathpop.com/bookhtms/tondeur.htm](http://www.mathpop.com/bookhtms/tondeur.htm)

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eru
Interesting enough, you can also build your whole geometry on the operation of
reflection and a bunch of axioms. See Calculus of Reflections at eg
[http://rd.springer.com/article/10.1007%2Fs00022-012-0123-5](http://rd.springer.com/article/10.1007%2Fs00022-012-0123-5)
(surprisingly for Springer, not behind a paywall).

There's algebra and calculating, but with reflection operations here, not with
coordinate pairs.

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eru
> (surprisingly for Springer, not behind a paywall).

OK, that was only true at work.

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jamessb
People interestd by this may also be interested in 'The Most Common Errors in
Undergraduate Mathematics':
[http://www.math.vanderbilt.edu/~schectex/commerrs/](http://www.math.vanderbilt.edu/~schectex/commerrs/)

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Sniffnoy
This particular entry is quite interesting, it gets at a distinction I'm not
sure I had explicitly thought about before:
[http://mathmistakes.org/recursive-and-relational-thinking-
an...](http://mathmistakes.org/recursive-and-relational-thinking-and-the-
feedback-each-deserves/)

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gizmo686
I think the author of that post undervalues the strength of the recursive
approach. It is, in general, much easier to apply a recursive approach, and
once you have done so you can often mechanically convert your solution into a
relational one. Even if you cannot, you have still converted the question into
a standard notation math problem, which is normally the hardest part of the
problem.

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RevRal
Can anyone think of a "writing mistakes" version of this blog?

Making public another's writing may be too far.... But it would be interesting
to mine the data and classify non-grammatical writing mistakes, specifically
to ease the stress of grading college junior research papers -- some of which
are written at a middle-school writing level -- by parsing sentences and auto-
applying applicable writing mistake classification, to which I can gently
glide my eyes to and convert to something intelligible.

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DanBC
I had a quick look and I didn't see anything on the site about whether
dyslexia or dyspraxia have common errors that show up in math.

There was an interesting programme on BBC Radio Four this morning about how
dyslexia and dyspraxia can show up in art.
[http://www.bbc.co.uk/programmes/b06d2fxf](http://www.bbc.co.uk/programmes/b06d2fxf)

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tempestn
In theory the relatively recent adoption of Common Core math teaching
techniques should help with many of these sorts of mistakes. I'm not well
versed enough to know whether there's any sign of that already, but certainly
the intention of teaching students to actually _think_ about how math works
and why a certain technique produces the right answer is laudable.

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Johnny555
Maybe Math Mistakes needs a related site "Grammar and Spelling Mistakes":

I notice that the kid didn’t write them as (x,y) but wrote them as x,y. I
wonder how come he did that? Or, more precisely, I wonder if he doesn’t see
much of a difference between (x,y) and x,y or if three is some other reason
for leaving off the parentheses.

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daniel-levin
It is interesting to see kids invent their own perfectly adequate, if
peculiar, notation. In the first example with the quadrilaterals, the answers
were all right. The math is not wrong, just written differently.

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gohrt
That gave me mixed feelings. On the one hand, the teacher did an admirable job
(for a teacher) of seeing the correct thinking behind the "wrong" notation. On
the other hand, the teacher still accused the student of making a mistake.

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Gibbon1
If I were a teacher and I saw a student come up with a peculiar but correct
notation, I'd be ecstatic.

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jacobolus
Indeed, developing new notation should be not only allowed, not only
encouraged, but even required as an assignment at various points during
mathematical training, at every age level. Also to be encouraged is
conscientious analysis and critique of existing notations, algorithms, and
explanations.

Society advances in two ways: in small incremental steps, and in large leaps.
When we stick to existing notations and concepts we can make incremental
improvements. But the large leaps often come from creating better notations
and better conceptual understandings, which can turn substantial amounts of
knowledge and logical thinking into obvious consequences of an organized and
intuitive system.

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daniel-levin
Agreed. Feynman diagrams are a great example of this phenomenon. They might be
'pictures', but they are still mathematical notation.

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zipbooks
It would be interesting to see a new teaching methodology develop around
teaching mostly just the concepts that people get wrong with the assumption
that most people don't need much help with the stuff everyone is getting
wrong.

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deeteecee
haha i totally remember that "law of sines" example. nothing to do with the
"law of sines" over time, i would regularly just exhaust my brain and i would
just imaginarily throw random variables to give me solutions, making my
homework full of errors lol.

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softprodigy
Amazing blog!

