The role of syntax in numerical and mathematical processing

Mathematics employs various symbols (e.g., 3, y, +, Δ) and combines them into expressions (35+Δy). The rules for these combinations are called syntax, by analogy to language, wherein syntax combines words into sentences. The present chapter discusses syntactic processing, the cognitive ability to handle such rules. Syntactic processing is challenging, yet it is crucial for several concrete mathematical operations, such as number reading, number writing, and calculation. An open question is whether it also supports the development of higher-level skills, such as abstract mathematical reasoning. We present two theoretical approaches to explain syntactic processing: one highlights the large variety of cognitive mechanisms that handle syntax; the other emphasizes their commonalities, proposing that they rely on a shared cognitive capacity. We discuss the benefits of each approach and consider how a better understanding of syntactic processing might improve math education.