# Upper primary school teachers’ mathematical knowledge for teaching functional thinking in algebra

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## Abstract

This article is based on a project that investigated teachers’ knowledge in teaching an important aspect of algebra in the middle years of schooling—functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research project funded by the Catholic Education Office, Melbourne (2008–2012). Analysis of the survey responses revealed that two-thirds of teachers demonstrated content knowledge on a pattern generalisation task appropriate for upper primary levels of schooling (8- to 12-year-old students), but less than half demonstrated reasonable pedagogical content knowledge (PCK). On a paired variable (function machine) task, only one quarter of teachers demonstrated appropriate PCK. Although two-thirds of the teachers indicated that they currently taught content from the “Patterns and Algebra” strand of the new Australian Curriculum, less than half were able to provide examples of appropriate learning experiences for students. More than two-thirds of teachers expressed concern about their ability to teach this area of mathematics. Implications for the professional learning of teachers to improve their mathematics knowledge for developing students’ functional thinking are presented.

## Keywords

Teacher professional learning Functional thinking Content knowledge Pedagogical content knowledge Algebra Mathematics education Middle years of schooling## Notes

### Acknowledgments

The author would like to acknowledge with appreciation the teacher participants from the *Contemporary Teaching and Learning of Mathematics* project who contributed to the study on which this article is based. I am indebted to Anne Roche and Associate Professor Vince Wright for their helpful feedback on data instrumentation and participation in the check-scoring process.

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