Utilization of Algebraic Habits of Mind According to Types of Algebraic Demands

Abstract

This study aims to explore the utilization of algebraic habits of mind according to types of algebraic demands. To this end, algebraic demands in middle school mathematics textbooks were examined and evaluated through content analysis, employing a document analysis design. The research design of this study is document analysis. The findings indicate that algebraic demands can be categorized into four groups: (1) demands requiring the construction of rules, (2) demands requiring the application of a constructed rule to a specific case, (3) demands requiring the validation of a rule, and (4) demands requiring the use of a known rule. Results show that different types of algebraic demands directly influence the ways in which algebraic habits of mind are activated. For instance, when students are asked to explain why a given rule holds, explicit justification is expected; however, when students are engaged in constructing the rule themselves, justification emerges naturally within the process. Thus, the same habit of mind may function differently depending on the nature of the algebraic demand. In conclusion, the study highlights that algebraic thinking extends beyond the mechanical application of rules. It emphasizes the importance of exposing students to diverse types of algebraic demands in order to enrich their algebraic habits of mind. Accordingly, teachers are encouraged to develop awareness of these habits, to critically consider the nature of algebraic demands in textbooks, and to design learning environments that foster their effective development.