When tech folk dabble in education (and tech writers cover it), the
excess of hype is sometimes matched only by their breathtaking lack of
knowledge about education. Even so, the above headline to the July 1 post by Forbes
contributor Jordan Shapiro must rank as one of the most stupid and ignorant
statements in human history.
It would be somewhat less ludicrous, though still open to debate, if
the headline had said “learn some algebra.” But “algebra”? All of
it?
Almost certainly, Shapiro himself did not write the headline—writers
rarely do. In fact, the article itself is fine. I have no problem with what
Shapiro wrote. But the fact that the ludicrous headline had not been changed 24
hours later indicates that Forbes’ editors feel happy with it. Sigh.
What the article itself reports is that, on average, students who
played a particular video game (DragonBox, of which more
later) completed a sufficient part of it in 42 minutes. Since the game itself
is based on algebraic principles, they could, therefore, be said to have
engaged in algebraic thinking. (I would be inclined to say just that, though
with any kind of machine learning—and human teaching if the instructor is not
paying close attention—one should always be on the lookout for an instance of
Benny’s Rules.)
Whether such performance in a video game justifies saying that the
students learned some (!) algebra in 42 minutes depends on what
metric you use to determine what learning has taken place.
Of course, if you define algebra to be (or to include) symbolic
manipulation, then successful completion of any video game is not going to
count as “doing algebra.” That is why I used the term “algebraic thinking” a
couple of paragraphs back. (See my previous blog post What is Algebra? for a
discussion of the distinction.) But is that the appropriate measure? What do we
want K-12 students to learn under the title “algebra”?
[ASIDE: There is another definitional question as to the classification
of DragonBox as a video game. Game developers have different views as to what
constitutes a video game. Some would describe DagonBox as an entertaining,
interactive, digital app, but would stop short at classifying it as a game.]
Before I go any further, I should give some disclaimers. First, as
readers of my blog profkeithdevlin.org (or my book Mathematics
Education for a New Era) will be aware, I am a strong proponent of the
use of video games in mathematics education. In fact, I advocate an approach to
the design of math ed video games that definitely includes DragonBox. I’ve met
the developer, Jean-Baptiste Huynh, and one of the co-founders of his company WeWantToKnow, and I used their game as an example in a
feature article on math ed
video games I wrote for American
Scientist in March of this year. I am about three-quarters of the way
through the second, greatly expanded version of the game, DragonBox2. Among the
designs for math ed video games that my own company, InnerTube Games, has been working on for several years,
are a couple that have much in common with DragonBox. (We are due to release
our first one, Wuzzit Trouble, this summer, but chose one based on arithmetic
and number theory to be our initial release, with algebra-based games to come
later.) So I am not a dispassionate outsider here.
For his Forbes article, Shapiro interviewed Jean-Baptiste Huynh, and
everything the DragonBox designer says, I agree with 100%. Here is my take on
the benefits of playing DragonBox (besides the fact that is it fun).
A student who plays through the new, greatly expanded version of the
game will undoubtedly engage in a substantial amount of (contextualized) algebraic
thinking focused on the solution of linear equations in one variable. The score
they obtain in the game will provide a good measure of how well they have
mastered that form of thinking (i.e., solving single-variable linear equations).
Does that mean the student can then sit down and ace a standard
written algebra exam? Not at all. Even though the later stages of DragonBox and
DragonBox2 involve on-screen manipulations of the standard symbolic
representations of equations, the step from physically moving digital objects
to manipulating symbolic expressions on a page is a much harder cognitive
challenge than one might first think. The human mind simply finds it very
difficult to reason in a purely abstract fashion. (In my book The Math Gene, published in
2000, I investigated the reasons for that difficulty.)
At issue is the notorious transfer problem, which, roughly
speaking, is the difficulty humans face in taking something that has been
learned in one context and applying it in another.
Huynh is of the opinion that it requires a human teacher to help the
student take the difficult step from completion of his game to mastery of
symbolic algebra, and I agree with him. I suspect that not everyone will be
able to make the transition, no matter how good the teaching, but many will.
There is certainly a lot to be gained from mastery of symbolic
algebra. First of all, learning at that level of abstraction is readily
applicable to any specific domain. Second, being able to reason free of the
complexities of any application domain is extremely powerful.
On the other hand algebra (or, more accurately, algebraic thinking)
was successfully used in commerce for many hundreds of years before the modern,
symbolic variety was introduced in the sixteenth century. So acquiring useful
algebra skills is not totally dependent on mastery of symbolic algebra.
A major question is, will playing DragonBox increase the likelihood
that a student will be able to master symbolic algebra, compared with a student
who does not have that game experience? There is good reason to assume the
answer is “Yes,” but that remains to be fully tested—something that can be
done only now the game (and others like it) is out. (The analogous question
remains to be answered for my own company’s forthcoming games.)
My reason for suspecting that playing video games like DragonBox is
highly beneficial in learning symbolic mathematics—the kind that is tested in
our school system—is perhaps best explained by an analogy from Hollywood. In
the 1984 movie The Karate Kid (I can’t bring
myself to watch the 2010 remake) and its sequel (KK2), martial arts instructor
Mr Miyagi prepares his
young pupil Daniel for Karate tournaments by getting him to polish a car, sand a
floor, catch a fly with chopsticks, and paint a fence, all of which develop the
reflexes and muscle memory required for key Karate moves, which Daniel uses to
great effect later in the movies.
True, this is not sound educational theory, though many teachers (and
most athletic coaches) adopt a similar approach. (This is a blog, remember, not
a research journal.) But until we have something more concrete, the analogy
works for me. Indeed, I am betting my company on it—as is Jean-Baptiste
Huynh.