# Learning to teach upper primary school algebra: changes to teachers’ mathematical knowledge for teaching functional thinking

## Abstract

A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students’ functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers’ interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

## Keywords

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

### Acknowledgments

The author would like to acknowledge with appreciation the teacher participants and School Mathematics Leaders from the Contemporary Teaching and Learning of Mathematics project, funded by the Catholic Education Office, Melbourne, who contributed to the study on which this article is based.

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