INTRODUCTION
The idea of building on the methodology used in the Ratio Project, but addressing a different topic, was raised at more than one annual conference, and was finally realised at the 2018 conference in Gävle with regard to the concept of functions. This, like ratio, typically forms a major part of mathematics curricula, and also occurs in science curricula (just two examples being wave functions and velocity-time functions). Appropriate teaching is therefore very important, and work on suitable tasks and representations has featured in research for many years. A study of prospective teachers' content knowledge and pedagogical content of the topic in different countries can contribute to the identification of areas of strength and weakness that figure cross-nationally.
FIRST PHASE OF THE STUDY, 2018-19
During RDC meetings in Gävle, the instrument initially used for data collection in the Ratio Project - and modified over the years to improve some of the items - was adapted to the new topic. It was agreed that RDC members who were present (and who wished to be involved) would aim to collect data and share it during the academic year 2018-2019. The research questions to be addressed were:
(a) What meanings do prospective teachers for primary and secondary levels, attending selected institutions in different countries, give to the term ‘function’?
(b) What multiple representations do these prospective teachers associate with the term ‘function’?
(c) What implications do the prospective teachers’ descriptive meanings and representations have for teacher education courses with regard to functions?
Data were collected in participants' institutions in four countries (the Netherlands, Portugal, Ireland and the USA - the USA data being only from faculty members so far). A poster describing initial results from the Portuguese data was presented at the 2019 Winter Conference in Braga, and is displayed above. The preliminary collective findings from the prospective teachers' data were reported at the 2019 Annual Conference in Bath, and a separate account of the Irish data was also presented. Analysis continued after the conference; the resulting two papers are in the Conference proceedings.
The idea of building on the methodology used in the Ratio Project, but addressing a different topic, was raised at more than one annual conference, and was finally realised at the 2018 conference in Gävle with regard to the concept of functions. This, like ratio, typically forms a major part of mathematics curricula, and also occurs in science curricula (just two examples being wave functions and velocity-time functions). Appropriate teaching is therefore very important, and work on suitable tasks and representations has featured in research for many years. A study of prospective teachers' content knowledge and pedagogical content of the topic in different countries can contribute to the identification of areas of strength and weakness that figure cross-nationally.
FIRST PHASE OF THE STUDY, 2018-19
During RDC meetings in Gävle, the instrument initially used for data collection in the Ratio Project - and modified over the years to improve some of the items - was adapted to the new topic. It was agreed that RDC members who were present (and who wished to be involved) would aim to collect data and share it during the academic year 2018-2019. The research questions to be addressed were:
(a) What meanings do prospective teachers for primary and secondary levels, attending selected institutions in different countries, give to the term ‘function’?
(b) What multiple representations do these prospective teachers associate with the term ‘function’?
(c) What implications do the prospective teachers’ descriptive meanings and representations have for teacher education courses with regard to functions?
Data were collected in participants' institutions in four countries (the Netherlands, Portugal, Ireland and the USA - the USA data being only from faculty members so far). A poster describing initial results from the Portuguese data was presented at the 2019 Winter Conference in Braga, and is displayed above. The preliminary collective findings from the prospective teachers' data were reported at the 2019 Annual Conference in Bath, and a separate account of the Irish data was also presented. Analysis continued after the conference; the resulting two papers are in the Conference proceedings.
LATER WORK
Work was interrupted by the COVID-19 pandemic. Individuals did further research in the area, but to date (2025) it has not been reported to the RDC..
Work was interrupted by the COVID-19 pandemic. Individuals did further research in the area, but to date (2025) it has not been reported to the RDC..
