New paper: Learning Trajectory for Variables

I’m pleased to report that a new paper from the Learning Trajectories for Everyday Computing (LTEC) project is now available online in Computer Science Education (Rich et al., 2020). This paper, which has been in development, review, and revision for roughly two years, is likely the last paper we’ll put out focused on a specific learning trajectory (LT). The LT discussed in this paper is about a topic we didn’t originally intend to address in our curriculum but found we couldn’t avoid: Variables.

In addition to completing the publication of our set of six computational thinking LTs (Sequence, Repetition, Conditionals, Debugging, Decomposition, and now Variables), this paper differs from our earlier publications in a couple of important ways. First, in previous papers we identified a set of consensus goals for a particular trajectory that served as the waypoints or stepping stones in learning of the overall topic of the LT. We did that again for variables, but in this paper we delve deeper into the theory underlying the learning trajectory construct and differentiate two kinds of consensus goals. Levels of thinking about variables, which are ways of thinking about and cognitively operating on mental objects related to variables, are contrasted against fact- and skill-based goals, which are more tangential and declarative types of knowledge that support the use of variables within code. The levels of thinking form a kind of core or backbone to the LT, whereas the fact and skill goals can facilitate progress through levels of thinking for kids.

There are a couple of reasons we included these ideas in this Variables LT paper and not in the other papers. One simple reason is that the journal format gave us much more space to explain and elaborate the concepts than our previous conference papers did. But another, equally important reason is that our other papers came out either before we started or as we were in the thick of developing our accompanying curriculum, Action Fractions (Strickland et al., 2021). By the time were writing this paper, curriculum development was almost done. The timing of this last LT paper provided the time and space to reflect on how the LT influenced our curriculum development, which allowed us to articulate more of these ideas in communicable form than we could have sooner.

That leads me to the second important way this differs from other our LT papers: In this one we talk in much more detail about how the LT and curriculum development processes worked together. There is also some very preliminary student and teacher data in the paper. Unfortunately, the pandemic did not allow us to do a more detailed study with students, but we are glad we got to share a bit of the data we did collect about their experiences with variables.

I really hope CS ed folks enjoy the paper. The LTEC team put a lot of time and effort into it. And on a personal note, this paper serves as a kind of capstone on a line of work that served as my first real foray into research and academic discourse. As I prepare to complete my PhD and find new avenues to contribute to the education research field, I’m grateful for the opportunities the LTEC project offered me and proud of the way the efforts came out.


Rich, K. M., Franklin, D., Strickland, C., Isaacs, A., & Eatinger, D. (2020). A learning trajectory for variables based in computational thinking literature: Using levels of thinking to develop instruction. Available online in Computer Science Education.

Strickland, C., Rich, K. M., Eatinger, D., Lash, T., Isaacs, A., Israel, M., & Franklin, D. (2021, March). Action Fractions: The design and pilot of an integrated math+CS elementary curriculum based on learning trajectories. To appear in Proceedings of the 2021 ACM SIGCSE Technical Symposium on Computer Science Education. ACM.

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