Developing design principles to enhance pre-service teachers’ understanding of number structure and mathematical equivalence in early grade mathematics

Abstract

Research on mathematical equivalence, and to some extent, on number structure in early grade mathematics, has shown that most students at primary and secondary levels understand these concepts instrumentally rather than relationally. The study reported in this paper uses a design research approach to explore both mathematical equivalence and number structure in a primary pre-service teacher education programme at a university in South Africa and reports on an intervention strategy intended to culminate in developing design principles comprising guidelines for the effective teaching of number structure and mathematics equivalence in primary pre-service teacher education programmes. The mixed method study comprises 70 first-year primary pre-service teachers (PSTs) and a teacher educator. The PSTs wrote pre- and post-tests, and were interviewed following the pre-test. Skemp’s notion of relational and instrumental understanding guided the design of the intervention and the analysis of the data. The results from the study indicates that PSTs’ understanding of the notion of equivalence is similar to what has been reported for students in schools, and that there were some learning gains in the post-test results. Based on the findings from the study in general, some emergent design principles are proposed.

Keywords:

• Mathematical equivalence
• number structure
• design principles
• early grade mathematics
• equal sign
• instrumental and relational understanding
• design research

Acknowledgements

This work is based on the research supported by the National Research Foundation South African Numeracy Chair at Wits (grant number 74703). Any opinion, finding and conclusion or recommendation expressed in this material is that of the authors and the National Research Foundation does not accept any liability in this regard.

Disclosure Statement

No potential conflict of interest was reported by the authors.