New paper: Applying levels of abstraction to mathematics word problems

A new paper stemming from the CT4EDU work just came out in TechTrends. I think of this paper as a companion piece to this one that came out last year in Journal of Computers in Mathematics and Science Education. That article was an empirical analysis of student work, showing that looking at mathematics problem solving through the lens of levels of abstraction—an idea I drew from the computer science education literature—could provide a new and interesting perspective on what is going on with students’ reasoning when they make common errors. This new TechTrends piece is theoretical and looks at how we could adapt an instructional framework from CS education research for use in elementary mathematics (and perhaps more importantly, why it makes sense to attempt such an adaptation). In short, the empirical piece establishes a problem, or at least demonstrates a new perspective on a problem. This new theoretical piece looks at how we might solve it.

(Here is a link to a free view-only version if you don’t have access to TechTrends. As always, contact me if you’d like a preprint.)

The principal mathematics instructional issue that these papers focus on is the ways in which our culture of schooling tends to lead children to produce answers to mathematics problems without adequately attending to context. Every elementary school teacher, and probably every parent with kids old enough to have gone through elementary school, has likely watched a child skim over a contextualized problem, pick out the numbers, make a guess at which operation to use on them, and report a numerical answer without ever considering whether that answer makes sense in context. Even though a number of instructional frameworks have been developed to combat this issue (a few are cited in the paper), the problem continues to endure. Yesterday a colleague lamented to me that her daughter had produced an answer of 1/3 of a frog to a word problem. I’m also teaching math methods to preservice elementary teachers this semester, and last week, in response to an assignment requiring him to do a task-based interview with a child, one of my students expressed surprise that his interviewee was perfectly capable of executing the arithmetic required for the task, but seemed to have no idea how to make sense of what the word problems were asking him to do.

The framework that we (my coauthor Aman Yadav and I) present in this paper has yet to be tested empirically, so I can’t make any claims as to its efficacy for solving this issue. However, as someone who finds herself solidly situated at the intersection of two domains, I see a major part of my work as identifying ways that mathematics and computer science education might work together. Sometimes, that collaborative work can take the form of integrated instruction. Other times, I have found that the import of ideas from one of the disciplines into the other was really useful, even if the benefit is only children’s learning in one of the disciplines rather than both. In this case, I have found the focus on moving among levels of abstraction as a skill to be fostered in students, often mentioned in computer science education literature, to be very useful for highlighting a common instructional issue in mathematics. And I figure that new ways of looking at enduring problems might be helpful—and certainly can’t hurt.


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