From Jo Boaler: "I have a new op-ed that was just published this morning, on the need to slow down math and stop advancing students when they really need depth not speed."
Wayne, as an exercise in personal discipline, see if you can manage to comment critically on this opinion piece without attacking the author personally. While I realize you're going to disagree automatically given who wrote it, that's rather ancient news. What would be useful, not to mention classy, not to mention a personal breakthrough for you, would be to take the "low-hanging fruit" that doesn't require libeling anyone, mud-slinging, or argument ad hominem. Then there would be a basis for a debate instead of what we generally get here.
Carleton Washburne wrote:
>> From Jo Boaler: "I have a new op-ed that was just published this
>> morning, on the need to slow down math and stop advancing students
>> when they really need depth not speed."
> Wayne, as an exercise in personal discipline, see if you can manage to
> comment critically on this opinion piece without attacking the author
> personally. While I realize you're going to disagree automatically given
> who wrote it, that's rather ancient news. What would be useful, not to
> mention classy, not to mention a personal breakthrough for you, would be
> to take the "low-hanging fruit" that doesn't require libeling anyone,
> mud-slinging, or argument ad hominem. Then there would be a basis for
> a debate instead of what we generally get here.
I happened to read the article just now and was going to comment
on it, then I noticed it's the same article you cited yesterday.
(It didn't load for me yesterday, at least not within 10 to 15 seconds,
so I didn't read it then.)
Relating to your quote above, the following excerpt is especially significant
"Memorizers are the lowest achievers and other Common Core math surprises"
by Jo Boaler, The Hechinger Report, 7 May 2015.
** Part of the problem in the U.S. is the desperation of many parents to
** advance their children in math, pushing them to higher levels of math
** faster and sooner, somehow believing that a resume packed with advanced
** math courses will guarantee their future. Bill Jacob, a mathematics
** professor at the University of California, Santa Barbara, speaks openly
** about the dangers of students being pushed to higher levels of mathematics
** too soon. "I know it is hard to persuade parents that their students
** shouldn't race to get calculus, but I really wish they wouldn't. Too much
** content and depth is left out when they do." said Jacob, who is not alone
** in saying that he would rather have students in his university mathematics
** courses that have breadth in their mathematical experiences than any
** additional Advanced Placement courses.
I think this is one of those things no one here disagrees with. Wayne has
been calling for more in-depth reasoning and coverage in high school geometry,
and Robert has been calling for more in-depth reasoning and coverage in high
school algebra and precalculus. It's a topic David Bressoud has devoted many
of his monthly columns to. It's something I've been trying to "show by example"
for many years in my posts, such as the following I put up yesterday by copying
one of my past math-teach posts:
On the other hand, the following from near the beginning irked me a little:
** Mathematics classes of the past decade have valued one type of
** math learner, one who can memorize well and calculate fast.
First, why the past decade? Since the late 1980s there has been this constant
push to de-emphasize memorization and emphasize understanding, critical thinking
skills, and writing skills. The intent of the statement above is mostly a strawman
anyway (see below), but by saying "of the past decade" it's so much of one that
I'm left scratching my head. Maybe this was an unconscious transition phrase
that should have been removed during editing?
Anyway, I remember previously reacting to something like this and found
the following post of mine.
math-teach thread "Safety Glasses in Algebra?" (15 November 2012)
I haven't listened to the video and don't really have
a comment about the teaching method (getting students
engaged is good, assuming it's in a way that leads to
appropriate learning), but I did want to complain about
something I see way too often (and have complained about
before), which is the tendency of advocates of "the latest
new thing" to misrepresent the past. The first sentence of
the article follows:
** When many of us were in school, math class was about
** word problems and memorization.
Since when was math class about memorization? Math has always
involved the least amount of memorization of any subject I
can think of, with the possible exception of P.E. classes.
And, now that I think about it, I took a number of multiple
choice tests on volleyball rules and other sports rules
in my high school P.E. class, tests whose preparation for
involved nothing but memorization.
As someone who always had great difficulty with memorization
(I had to transfer to another undergraduate university due to
Foreign language requirements, I got a 60 (under 70 was an F)
on my 3rd quarter 9th grade English report card because I was
making 30s to 50s on the spelling tests our class began taking
that quarter, I almost failed a supposedly easy classics elective
because I couldn't remember the various painting and
sculpture and architecture styles we needed to distinguish
on tests, etc.), I'm EXTREMELY AWARE of the amount of
memorization in various subjects. Sure, I often forgot
things in math too (e.g. is the derivative of u/v equal
to (u'v - uv')/v^2 or (uv' - u'v)/v^2), but almost always
you can "see the complete picture" by filling in the missing
parts by using some alternate method. For example, in the case
of the quotient rule, see which of the two possibilities work
for the case of u/v = 1/x (whose result you know by using the
Dave L. Renfro
In reply to this post by Carleton Washburne
Dave L. Renfro Posted: May 8, 2015 10:26 AM
>First, why the past decade? Since the late 1980s there
>has been this constant push to de-emphasize memorization
>and emphasize understanding, critical thinking skills,
>and writing skills. The intent of the statement above is
>mostly a strawman anyway (see below), but by saying "of
>the past decade" it's so much of one that I'm left
>scratching my head. Maybe this was an unconscious
>transition phrase that should have been removed during
You will have to scratch your head a little harder.
In reply to this post by Dave L. Renfro
This was eloquent testimony from a non-memorizer.
The whole point of math exercises for non-memorizers
is "derivation" i.e. they're puzzles to be solved, not
facts to be committed to memory. One turns one's
wheels. Such a relief to *not* have to commit a
thousand and one arbitrary facts to memory, such
as the English word for this thing in Russian and
vice versa. Such redundancy in the first place! Let
robots do that drudge work!
This is part of why I drive so hard in the direction of
having Russian and Chinese language computer science
texts (Devanagari, Burmese etc. etc.) that only cover
enough English to make the keywords intelligible.
For mnemonic reasons it helps to know what print()
means (i.e. the Indonesian equivalent), as well as:
if else in return -- whatever symbols are likely in your
math notation du jour.
So yes, English helps and business English is useful
to learn, but don't detour your whole career as a Python
programmer to try to achieve much higher fluency in
Better to find highly literary and glowing examples of
native language perspicuity and share those, openly
and freely, on such as Wikieducator. If you live in
Brazil, master Python primarily by reading Portuguese,
but you'll be glad for the little English you'll need to
get the meaning of these:
False, None, True, and, as, assert, break, class,
continue, def, del, elif, else, except, finally, for, from,
global, if, import, in, is, lambda, nonlocal, not, or,
pass, raise, return, try, while, with, yield
This sounds a lot like Mandelbrot, whom I've both read
and heard in person. He was great at deriving stuff, in
many ways thinking far more geometrically than the exercise
Yet by geometric deduction he was able to ace tests and
impress the judges. He grew to prominence in his domain.
The Mandelbrot Set is but one of his legacies.
Chaos Math in general owes a huge amount to this other
good example of a non-memorizer mathematician.
Lets remember though, in the K-12 Catechism of the Mafiosi,
"math facts" are "things to remember" like the "times tables".
You don't want to "pause to derive" and many "flash cards"
There's an approach to fluency based on memorization (rote)
which those good at memorizing want to use just to get to a
level where they can't be bullied anymore.
Memorizers are on the defensive, as their ability to derive on
the spot is less advanced. So do we punish them as God's
less chosen? They may have other gifts. No one is superman
in all dimensions except the Great Flying Spaghetti Monster.
Memorizers seek careers where a memorized set of math
facts is likely to be sufficient and if there are any puzzles
to be solved, they'll have a different nature (actually, a
computer language can be a great bridge, in showing how
both modes of thought fit together).
It's the religious value of Compassion that means we try
to Close the Gap between those who can derive on the spot,
impromptu (call them Improvs or Intuiters) and those who get
through life by remembering what intelligent people have said
on some topic, maybe their parents or an uncle, or a school
teacher or other authority in some magazine or on TV (call
them Authoritarians or Rememberers). I think we're all really
a combination of both, with some, tapering to a few, at
either extreme. Yes, another Bell Curve, surprise surprise.
Quoting authorities is a way to gain political office, even
become president. Living by rote is part of what we do.
Those who "derive" are often considered "absent minded"
because they forget where they parked the car, such a
trivial and accidental fact, not obtainable in pure principle
(so hardly worth one's attention).
Those who can just look at a problem and solve it are
more like Iron Man of the Avengers. We can't all be like
him. Lets cut ourselves slack and not be too hard on the
freaks at either extreme.
Do we believe this guy or is this an illusionist team?
You be the judge:
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