Refusing to Recognize

In one of my courses this semester, we have an ongoing assignment as we work through the reading list. As we read, we are to pull out quotations that can be unpacked multiple ways. Rather than looking for passages that succinctly sum up one point, our goal is to pull out passages that can be connected to other aspects of the piece (and to other readings from the course) in multiple ways. To point out the connections we see, we’re tagging these multi-spoke quotations with themes.

One of our early readings in the course was Seymour Papert’s Mindstorms. There is one passage I picked out that I’ve been mulling over ever since:

Dynaturtles can be put into patterns of motion for aesthetic, fanciful, or playful purposes in addition to simulating real or invented physical laws. The too narrowly focused physics teacher might see all this as a waste of time: The real job is to understand physics. But I wish to argue for a different philosophy of physics education. It is my belief that learning physics consists of bringing physics knowledge into contact with very diverse personal knowledge. And to do this we should allow the learner to construct and work with transitional systems that the physicist may refuse to recognize as physics. (Papert, 1980, p. 122, emphasis added)

I really liked this passage for a lot of reasons. First, I noted the bold phase, because it illustrates the way Papert argues against the separation between play and learning — a separation I believe we as educators need to keep pushing against every single day. I also liked his reference (shown in italics) to “very diverse personal knowledge,” which I interpret as attention to equity. He doesn’t just mention personal knowledge. He mentions very diverse personal knowledge. I think this reflects a theme that runs through his book: he believes every student can and should find a personal connection to content.

Even though I like this quotation for multiple reasons, it’s the last highlighted phrase, in bold italic, that has been niggling in the back of by brain for a while. At the end of the passage, Papert argues that students and educators should take advantage of “transitional systems that the physicist may refuse to recognize as physics.” The word refuse is what first caught my eye, I think. Papert doesn’t say that physicists cannot or do not recognize work with dynaturtles as physics. He says they refuse. There’s an intentionality in that word. An implication of a decision to deny any connection between dynaturtles and physics.

I have not worked with any physicists in any educational pursuits, but I’m willing to believe that refuse was an appropriate word choice. In mathematics education, at least, one only has to look as far as the “Where’s the math?” debates (Heid, 2010; Martin, 2010; Battista, 2010; Confrey, 2010) to realize that there is evidence of refusal to recognize certain experiences as mathematics learning. While I do not go so far as to claim that disciplines have no boundaries, I do worry about refusals to recognize experiences as related to mathematics. As the incomparable Stephen Hawking (may he rest in peace!) once said, “People have the mistaken impression that mathematics is just equations. In fact, equations are just the boring part of mathematics” (Overbye, 2018). I think that such misconceptions stem from the refusals of professional mathematicians to recognize informal pursuits as mathematics — and I further believe that these misconceptions have contributed making the “I’m not a math person narrative” so prevalent and socially acceptable.

When I first read the Papert quotation above, some part of my mind thought it might be connected to computer science education, but I was not able to articulate the thought right away. A few days ago I finally put my finger on it.

The ongoing efforts to bring computational thinking into K-12 education have led to some discussions about whether or not the CT-related practices already happening in mathematics and science courses can rightfully be considered CT. As I wrote on this blog a couple of weeks ago, I do think there is CT all over elementary mathematics. I also think that explicit connections between these math-embedded CT ideas and CT as applied specifically to computing need to be made for kids. But in order to effectively develop instruction that facilitates those connections, I think we need to recognize CT — everywhere that it lives, in all the “diverse personal knowledge” (Papert, 1980) kids bring to and gain in school — as CT.

Why do I worry that we’re not doing that? Consider this passage from a recent study:

“[I]n our study, the result of student classroom observations, interviews with teachers, and participatory engagement rarely led to activities that fit the prototype of CT if CT means using elements easily recognizable to computer scientists as computer science, that is, creating algorithms and meta-level descriptions of code, coding, engaging in explicit acts of structure creation, structured top-down problem-solving, and so forth. Instead, we found important opportunities to address proto-computational thinking (PCT). PCT consists of aspects of thought that may not put all the elements of CT together in a way that clearly distinguishes them from other human intellectual activity.” (Tatar et al., 2017, p. 65)

At first, I was on board with “proto-CT” as a label for the mathematical and scientific ideas that have elements of CT. Now I wonder, though, if calling that knowledge by a different name is a refusal to recognize it as CT (as Papert would say). And if it is a refusal, I think we need to examine the implications of that refusal for bringing computer science to all.


Battista, M. T. (2010). Engaging Students in Meaningful Mathematics Learning: Different Perspectives, Complementary Goals. Journal of Urban Mathematics Education, 3(2), 34–46.

Confrey, J. (2010). “ Both And ”— Equity and Mathematics: A Response to Martin, Gholson, and Leonard. Journal of Urban Mathematics Education, 3(2), 25–33.

Heid, M. K. (2010). Editorial: Where’s the Math (in Mathematics Education Research)? Journal for Research in Mathematics Education, 41(2), 102–103.

Martin, D. B., Gholson, M. L., & Leonard, J. (2010). Privilege in the Production of Knowledge. Journal of Urban Mathematics Education, 3(2), 12–24.

Overbye, D. (2018). “Stephen Hawking Dies at 76: His Mind Roamed the Cosmos.” The New York Times. Retrieved from

Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books.

Tatar, D., Harrison, S., Stewart, M., Frisina, C., & Musaeus, P. (2017). Proto-computational Thinking: The Uncomfortable Underpinnings. In P. J. Rich & C. B. Hodges (Eds.), Emerging Research, Practice, and Policy on Computational Thinking (pp. 63–81). Cham, Switzerland: Springer.


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