Excepts from Justin Reich’s blog entitled Don’t Use Kahn Academy
without Watching this First, June 21, 2012
In a send-off of the Comedy Central
classic Mystery Science Theater 3000, two teacher-educators sit in front of a
Khan Academy video on multiplying and dividing fractions and offer their
critical commentary. Dave Coffey
and John Golden are the hosts
here (they really do need at least one talking robot), and they clearly are not
big fans of Mr. Khan or his patron Mr. Gates.
The two
teachers systematically dissect the video, noting a variety of missteps. There
are a few unquestionable errors of mathematics: Khan uses incorrect terminology
at a couple of points. Khan is also inconsistent in his language about positive
and negative numbers (using plus when he means positive, or minus when he means
negative), which is perhaps a lesser sin, but poor practice and misleading for
students. He's also inconsistent in his use of symbols, sometimes writing
"+4", sometimes writing "4", never explaining why he does
or doesn't. He making the kind of mistakes that would reduce his score on the
Mathematical Quality of Instruction observational instrument, used in the
Gates-funded Measures of Effective
Teaching Project.
Coffey
and Golden are probably most savage when Khan makes these outright mistakes,
but I think the true fuel of their satire is their broader critique of Khan's
approach. Khan teaches students to memorize a small set of procedural rules for
dealing with multiplying negative numbers, with essentially zero effort
expended to explain conceptually what the symbolic manipulations represent. In
fact, in the final minute of the video, Khan says verbatim, "In your own
time, think about why these rules apply."
For
many math teachers, the most important work to do is to get kids to think about
why the rules apply, to help them derive them where applicable, and to help
them contextualize them when derivations are impractical.
Khan
Academy pulled down the video satirized in MTT2K, Episode 1 within a day or so
of publication. It will be interesting to see if they simply fix the outright
errors, or if they address some of the broader pedagogical concerns.
My Response:
Justin,
Once again you point out what should be
obvious, but sadly is not. In mathematics today the ongoing debate about
teaching for conceptual understanding versus procedures continues with the
concept side losing, no doubt thanks to teaching to the high stakes
standardized tests under NCLB. But as my wife (a PhD in Mathematics Education)
would say, the debate continues among mathematics teachers themselves as many
do not buy into the Cognitively Guided Instruction (CGI) ideas set out by the
National Council of Teachers of Mathematics (NCTM).
Too often people who are “good at math” think
they are because they are good at learning and memorizing procedures, yet they
may not understand the concept or its applications. This becomes a problem if
they become mathematics teachers as they can only tell students the procedure,
which merely represents one way to solve a given problem, and they will not
able to explain the concept or applications of the procedure. One result, people
who don’t think or learn that way begin to see themselves as “bad at math” at an early age.
This may once again be a negative effect of
“teaching to the test” and may actually be made worse by some aspects of Common
Core standards as more ideas, in the form of procedures, are to be taught to
students with little time devoted to conceptual understanding.
As one of my professors says, the result is
exposure to information that is, “a mile wide and an inch deep.”
Link to Justin's Blog:
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