If you only read the headlines, you might think that education is rapidly moving towards a monumental shift. Venture capitalists, tech start-ups, and Bill Gates himself hold the idea that with better data management, we can revolutionize education. Many of these ed tech companies employ some sort of “flipped classroom”, where students are autonomous beings who are given scaffolding to learn skills at their own pace. There are various reports to the efficacy of these practices, but they are drawn to the Mathematics world more than other domains.

## Pursuing the Dream

I want to discuss the methodologies, pros and cons of one such system: Dreambox learning. Dreambox promises to “meet students where they are” with respect to their mathematical abilities and then to “accelerate” their mathematical learning. Their methodology for accelerating students is a simple GUI where students are to complete various tasks, such as adding fractions or comparing numbers with decimals.

Let me say first that I do not wish to single out Dreambox or any other “flipped” classroom approach such as watching videos and taking subsequent quizzes at Khan Academy. However, the debates center around logical (and rarely empirical) arguments, and conclude that these approaches are good and that therefore we must spend money on them.

As I wrote last week, there seems to be a plethora of jargon on the systems used by many of these educational systems. Here are some jargon-y words from Dreambox’s FAQ: differentiated; adaptive; learning engine; gaming fundamentals; rewards; aligned (to Common Core standards); intervention; proven; and real-time reports.

Dreambox promises that for every *minute* that a student is engaged with their software, their engine analyzes 800 different pieces of information. Everything from the keys they press to the duration between those presses is analyzed and spit out to… somewhere. “The kids love it because Dreambox looks like a game”. I don’t really take issue with anything that they’re trying to do so far, with one large, glaring exception. The headline that Dreambox promises states explicitly that “Every child can think like a mathematician!”. Dreambox also markets itself like a teaching assistant with “unlimited patience and a perfect memory”.

The “game” I tried on Dreambox had students practicing identifying decimal values on a number line. Here’s a screenshot of the software in action.

And since I really am terrible at knowing my decimal places, I put the pin in the wrong place:

After I guessed incorrectly a couple of times, the narrator of the “game” said she would help me and gave me an entirely different problem. She led me through using the magnifier and basically solved a similar problem for me. I think as a teacher, this is exactly what I would want a teaching assistant to do: solve similar problems with the student giving scaffolding, assistance and problem solving. But how did this particular game meet me where I currently am? Did it analyze why I might have gotten a question wrong? As a human being that can ask questions that aren’t so binary, I *still* struggle with determining students misconceptions. Call it the experts’ (ha!) blindspot. But this system is no more adaptive than the “teaching machines” the behaviorists created.

(One more thought: Game like? I mean.. there’s definitely color? There’s a funny shaped character with what I believe to be a monocle. But I’m not sure where the playfulness of a game exists here.)

## Behaviorist Approaches

In the above video, we can see the emergent technology of the behaviorist: the teaching machine. Although it might be comical to watch the antiquated technology of the 1950s, they hold striking parallels to the emergent technologies of today.

Listen to Skinner’s opening line. “These young people are studying in a new way. The class is in spelling, but it might as well be in arithmetic, or in algebra or grammar, or anything involving the use of words or symbols.” This approach of content agnostic technology is what gets at me the most. The idea that mathematics should be taught in the same way as spelling or grammar is beyond fundamentally flawed – it loses the idea of divergence completely. Forget the connections of divergence to GDP, or economy or even being happy. If we’re dealing with a dichotomous world – wrong or right answers only – we lose the reason that we studied any of these topics at all. As Paul Lockhart said, we don’t study Mathematics for its usefulness; we study Mathematics because it’s so damned interesting.

Second, listen to the words that Skinner uses to describe these teaching machines: effective study; immediate knowledge (feedback); leads to *correct behavior*; motivating; free of uncertainty or anxiety about being wrong; scene of intense concentration; and quick report. I do not know the history of teaching machines or why they failed, but the connection between yesteryear’s and today’s “teaching machines” is fairly obvious.

So if this technology has been around for over half a century, why is it just now that their use is being so proliferated? Is it a political issue (grandstanding on the idea of improving education) or an efficacy issue (only now do we have the processing power to truly utilize these machines). I am unclear which it is. However, I do have one question: how would a teaching machine of the past or present handle a divergent question like this:

## Conclusions

Dreambox’s ultimate goal is to have every student think like a mathematician. Nowhere in their software could I find the use of thinking in extremes, solving a simpler problem or analyzing assumptions – all key components of how mathematicians think.

If there’s any message I could get across to these ed tech companies, it’s this: A skill-based approach will not a mathematician make. Mathematicians are interested in good questions, not how to follow instructions. Trying to predict what a student might say to a convergent question is easy – and you can get many data points. But is it useful? Will it help a student think creatively? These are the kinds of questions that will drive innovation in flipped classrooms and self-pacing. However, it doesn’t seem like we’ve made much progress there.