Exploring the intersection of algebraic and computational thinking

Abstract

This article investigates how the recent implementation of programming in school mathematics interacts with algebraic thinking and learning. Based on Duval's theory of semiotic representations, we analyze in what ways syntax and semantics of programming languages are aligned with or divert from corresponding algebraic symbolism. Three examples of programming activities suggested for school mathematics are discussed in detail. We argue that although the semiotic representations of programming languages are similar to algebraic notation the meanings of several concepts in these two domains differ. In a learning perspective these differences must be taken into account, especially considering that students have to convert between registers with both overlapping and specific meanings.

The Integration of Programming in Swedish School Mathematics: Investigating Elementary Mathematics Textbooks

“…In computer programming in elementary school, as it is represented in our data, an algorithm is connected to the representation of stepwise instructions to achieve a specific goal, not necessarily a mathematical problem and rarely a class of problems. The results mirror our findings when analyzing government-provided teaching materials (Bråting & Kilhamn, 2020) and are well in line with the Swedish syllabus. By removing the term algorithm from arithmetic and inserting it into the section on programming in the syllabus, a transposition of the what and the why of algorithms has occurred.…”

“…The use of variables is of course a tacit ingredient that will become explicit when they move on to text programming in higher grades, but the concept is not explicit in the textbooks for grades 1-6. Working with variables would be a way of making the algorithms applicable to a class of problems rather than used to solve a specific problem, thus bridging the gap between programming and mathematics (see also Bråting & Kilhamn, 2020). More tasks including the action "envisage" could achieve this, for example by posing questions like "What would happen if the variable is changed?"…”

“…However, examples of typical introductory examples of algorithms within the context of programming often describe everyday activities that are far removed from arithmetic. Such algorithms are not generalizable outside the activity described, in contrast to mathematical algorithms which are always applicable to a class of problems (Bråting & Kilhamn, 2020).…”

“…Such concepts are for example code, loop, conditional and bug. Some words, for example algorithm, have slightly different meanings within a mathematical context and a programming context and could therefore be treated as different concepts (Bråting & Kilhamn, 2020). We have classified algorithm as a computational concept if it is defined as such and/or refers to an algorithm used to achieve a specific goal without being applicable to a class of (mathematical) problems.…”

Integration of computational thinking in K-12 mathematics education: a systematic review on CT-based mathematics instruction and student learning

“…Related studies have also advanced the instructional design, including the programming tasks to facilitate students' mathematics learning. These studies encompass Kotsopoulos et al 's (2017) pedagogical framework for CT activities, designing for unplugged, tinkering, making, remixing in K-12 mathematical problem-solving in the domains of combinatorics (e.g., De Chenne & Lockwood, 2022), algebra (Bråting & Kilhamn, 2021), number theory and mathematical modelling (e.g., and geometry (e.g., Miller, 2019). Significantly, these studies evidence the reciprocal relationship between computer science and mathematical concepts, in the sense that the application of CT deepens mathematical disciplinary knowledge, while the context of CT-based mathematics learning improves one's CT skills (Pei et al, 2018).…”