Abstract
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.
Highlights
While algebra has a long history, both as a research field in mathematics and as content taught in schools, computer science is a recently developed field of knowledge
Computational thinking may seem more inclusive than the term programming suggests, we focus our discussion in this article on aspects of computational thinking that can be developed through programming
The aim of the present paper is to explore how semiotic representations related to computational thinking compare and interact with algebraic thinking and, how this may affect students’ learning of algebra
Summary
While algebra has a long history, both as a research field in mathematics and as content taught in schools, computer science is a recently developed field of knowledge. We will analyze syntactic rules and the meaning of the concepts algorithm, equality, variable, and function within registers related to programming and algebra This example is directed to grades 1–3 when students learn the basics of programming by means of stepwise instructions. This is not the case in Example 2, since in Scratch the equal sign ð1⁄4Þ is always used as a relational operator and the double equal sign is not included in the syntax We can summarize this as follows: In programming, the relational equality can be represented differently, for instance, as 1⁄41⁄4 in JavaScript and as 1⁄4 in Scratch, which means that a student needs to be able to convert between these two registers when learning to program. Variables in programming registers can be non-numerical and can change values as an effect of time in the execution of a program, which is not the case in algebraic notation used in school algebra
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