FIRST JOURNAL ARTICLE! Synergies and differences in mathematical and computational thinking

I have reached a milestone in my academic career: My first peer-reviewed journal article has been published!

Written with my UChicago colleagues Liesje Spaepen, Carla Strickland, and Cheryl Moran, the article is called, “Synergies and differences in mathematical and computational thinking: Implications for integrated instruction.” It is currently available online (this link will get you to a free eprint) and will eventually appear in a special issue on computational thinking from a disciplinary perspective in Interactive Learning Environments.

The history of this piece, and the special issue that will contain it, is rather interesting. Back in 2016, I attended a PI meeting for the NSF Cyberlearning program. I wasn’t a PI at the time, but the program invited interested folks to apply and come for learning and discussion. I applied and got accepted. That meeting included time for working groups to meet and discuss potential collaborations. There was a working group on computational thinking, and one of the outcomes of that working group was a structured poster session at AERA 2017. In the discussion period at the end of that session, the idea of a special issue came up. Several years later, the issue is finally close to finished!

The Everyday Computing project contributed two posters to the AERA poster session. One of those posters was the debut of our first learning trajectories, on Sequence, Repetition, and Conditionals. But during the time between the poster session and official start of work on the special issue, we published those LTs in the 2017 ICER proceedings. We were left, then, with the choice to either drop out of the special issue or come up with something else to contribute. I am reluctant to give up opportunities, so I campaigned for the latter.

Knowing the special issue was not focused just on CT, but specifically on looking at CT from disciplinary perspectives, I spent some time thinking about the discussions we were having (and continue to have) as a team about the relationship between CT and the kinds of thinking kids are already doing in elementary mathematics. Kids do decomposition and abstraction as they engage in mathematics, sure. And they put things in order, and repeat steps, and develop algorithms. But are all those things CT? When do to they start being CT?

During our processes of integrated curriculum development, we explored some of connections that really seemed to hold promise for leveraging mathematics to get kids ready to engage in meaningful computing. But we had also explored lots of them that fell apart under scrutiny. I was interested in seeing if we could come up with a way to systematically look across the elementary mathematics curriculum and make sense of the opportunities for connecting mathematics to computing.

So, we ended up doing a document analysis of the K-5 Common Core State Standards for Mathematics, mining it for potential connections to CT. We used our own trajectories as a starting point for the CT ideas we used to code the standards — a choice that was self-serving but, I would argue, justified given the work and detail we put into the articulation of those LTs and the ways in which they have been readily taken up by others. We looked, thoroughly and systematically, for ways in which general ideas connected to CT — like precision, completeness, order, identifying repetition, and examining cumulative effects — appear in K-5 mathematics. Then we scrutinized each connection, asking ourselves in each case if the thinking happening in mathematics could be built upon to forge a pathway into computing.

Unsurprisingly, we found lots of variation, including both connections that surprised us in their potential — like ways third graders think about when to stop counting as they subtract, and how well those map onto different kinds of loops — and surface-level connections that got thorny when we thought through the details — like the many subtle differences among examples of conditional-like thinking in K-5 math, and how few of the examples seemed synergistic with computing (or at least the kinds of computing kids might do in elementary school or shortly after).

There are lots of both kinds of examples in the paper, although we did not have enough room to explain most of them at the level of detail I might have liked.

More than the specific examples, though, there are two bigger ideas that I took away from writing this paper.

First, the question of whether or not CT-like ideas that appear in mathematics are useful leverage points for starting computing instruction, or even building readiness for later computing instruction, can’t be decided at a general level. There is no overall, general answer to this. Not all of mathematics is going to support computing instruction. On the other hand, not all integration of CT into mathematics is meaningless. We have lots of work to do figuring out our best avenues.

Second and even more importantly, working on this paper helped me (or at the risk of speaking for my coauthors, us) to articulate for myself a truth I think is both fundamental and often forgotten in debates about unplugged CT: Skilled curriculum development can’t be done one activity at at time. Ideas aren’t learned through one activity. They are developed across a curriculum. Evaluations of whether what students are doing is or is not CT don’t make sense to me when pointing to one activity completed in one hour of one school day. The finish line could be miles away, but that doesn’t mean kids aren’t making progress towards it. We need to think about development of ideas across time and give kids and teachers the space to think and learn.

I’m becoming less and less interested in debates about what CT is or is not. It needs to be decided, perhaps, but I’m willing to let others hash that out. I’m more interested in using the admittedly ill-articulated conceptualizations of CT I have so far, and imagining and studying how we can psychologize it for kids a al Dewey (1902) and spiral a curriculum around it a la Bruner (1960). Go ahead and keep shifting the finish line a bit. I’ll just keep trying to point my elementary school students in the right direction.

References

Bruner, J. S. (1960). The process of education. Vintage Books.

Dewey, J. (1902). The child and the curriculum (No. 5). Chicago, IL: The University of Chicago Press.

 

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