From Context to Algebraic Procedures: A Praxeological Analysis of Knowledge Construction in a Gakko Tosho Mathematics Textbook

Ika Wulandari; Didi Suryadi; Sufyani Prabawanto; kusnandi

doi:10.33541/edumatsains.v11i2.8822

Authors

Ika Wulandari Universitas Pendidikan Indonesia
Didi Suryadi Universitas Pendidikan Indonesia
Sufyani Prabawanto Universitas Pendidikan Indonesia
kusnandi Universitas Pendidikan Indonesia

DOI:

https://doi.org/10.33541/edumatsains.v11i2.8822

Keywords:

praxeological analysis, algebraic techniques, mathematical justification, linear equation systems, mathematics textbooks

Abstract

Mathematics textbooks not only introduce procedures for solving systems of linear equations in two variables but also provide mathematical reasons for their validity. This study examines the construction and justification of elimination and substitution techniques in the Indonesian Grade VIII Gakko Tosho student textbook and teacher guide (2021). A qualitative document analysis was conducted within the Anthropological Theory of the Didactic. Seven types of tasks were examined through practical blocks (tasks and techniques) and theoretical blocks (technologies and theories), complemented by epistemic and systemic analyses. The findings reveal a progression from contextual problems and simultaneous solutions to elimination, substitution, strategy selection, and mathematical modelling. Elimination develops from relationships between contextual quantities before being formalised through operations on equations, whereas substitution draws on replacing expressions of equal value. The teacher guide explicitly provides operational justifications based on properties of equality, addition and subtraction of equations, and equal-valued substitution. Both resources also support checking solution pairs and comparing strategies. However, these explanations mainly concern particular operations and examples; a general account of why equivalent system transformations preserve the entire solution set was not found explicitly stated. The study identifies an established connection between contexts, techniques, and operational justifications while highlighting an opportunity to make the general mathematical basis of valid system transformations more visible in the organisation of knowledge.

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