This paper presents initial findings from a project investigating sociomathematical norms in two ... more This paper presents initial findings from a project investigating sociomathematical norms in two grade five classes. Here I focus on the different sociomathematical norms perceived by students in the two classrooms and how these norms contributed to students' sense of inclusion.
In this paper, we report findings of a research project that involved students evaluating and off... more In this paper, we report findings of a research project that involved students evaluating and offering feedback on mathematical arguments claimed by the author, usually a fellow student, to constitute a proof of a given statement. The focus of this study is on the norms related to what makes a "good" student-written "proof". We conclude that our research participants engaged in reading and presenting proofs in appropriate ways, as they identified and provided revisions based on criteria that are similar to what mathematicians believe makes a good proof. Furthermore, our data indicates that students should not be expected to merely identify simple errors or shortcomings of "proofs", as they should be able to offer more complex and explicit analysis, suggestions, and revisions.
How can understanding grow when students encounter ideas that are inconsistent with their prior k... more How can understanding grow when students encounter ideas that are inconsistent with their prior knowledge? We draw upon the Pirie-Kieren Theory's construct of folding back (Pirie & Kieren, 1994) and elaborate on it to describe how, when building on existing understandings for a mathematical concept, teachers may need to encourage students to 'set aside' specific, context-limited ideas in order to build a more generalizable understanding. Folding back offers a way to characterise how learners can build understanding through returning to and 'thickening' existing knowledge for a concept. We theorize 'setting aside' as a specific instance of thickening, and suggest that it can be seen as a process of reconstructing and reorganizing of context-dependent knowings. To locate, develop, and illustrate 'setting aside' within teaching, we draw on three data sets from different levels, all involving teachers who had experience with the Pirie-Kieren construct of folding back. We propose that 'setting aside' is a cognitive act that can be deliberately encouraged by teachers and, as such, is of interest to both mathematics educators and those who train them.
The TI-Navigator project was a mixed methods study to investigate use of the TI-Navigator in grad... more The TI-Navigator project was a mixed methods study to investigate use of the TI-Navigator in grade 9, 10 and 11 mathematics. The study began in 2006 and continued into 2009. The key questions for the research were:
World Conference on Educational Multimedia, …, Jul 1, 2010
Abstract During a three year study of implementation of the TI-Navigator in secondary school math... more Abstract During a three year study of implementation of the TI-Navigator in secondary school mathematics, by 'typical'teachers, we identified a number of unexpected support needs. Some could be addressed by the researchers in conjunction with the teachers, but others ...
This paper presents initial findings from a project investigating sociomathematical norms in two ... more This paper presents initial findings from a project investigating sociomathematical norms in two grade five classes. Here I focus on the different sociomathematical norms perceived by students in the two classrooms and how these norms contributed to students' sense of inclusion.
In this paper, we report findings of a research project that involved students evaluating and off... more In this paper, we report findings of a research project that involved students evaluating and offering feedback on mathematical arguments claimed by the author, usually a fellow student, to constitute a proof of a given statement. The focus of this study is on the norms related to what makes a "good" student-written "proof". We conclude that our research participants engaged in reading and presenting proofs in appropriate ways, as they identified and provided revisions based on criteria that are similar to what mathematicians believe makes a good proof. Furthermore, our data indicates that students should not be expected to merely identify simple errors or shortcomings of "proofs", as they should be able to offer more complex and explicit analysis, suggestions, and revisions.
How can understanding grow when students encounter ideas that are inconsistent with their prior k... more How can understanding grow when students encounter ideas that are inconsistent with their prior knowledge? We draw upon the Pirie-Kieren Theory's construct of folding back (Pirie & Kieren, 1994) and elaborate on it to describe how, when building on existing understandings for a mathematical concept, teachers may need to encourage students to 'set aside' specific, context-limited ideas in order to build a more generalizable understanding. Folding back offers a way to characterise how learners can build understanding through returning to and 'thickening' existing knowledge for a concept. We theorize 'setting aside' as a specific instance of thickening, and suggest that it can be seen as a process of reconstructing and reorganizing of context-dependent knowings. To locate, develop, and illustrate 'setting aside' within teaching, we draw on three data sets from different levels, all involving teachers who had experience with the Pirie-Kieren construct of folding back. We propose that 'setting aside' is a cognitive act that can be deliberately encouraged by teachers and, as such, is of interest to both mathematics educators and those who train them.
The TI-Navigator project was a mixed methods study to investigate use of the TI-Navigator in grad... more The TI-Navigator project was a mixed methods study to investigate use of the TI-Navigator in grade 9, 10 and 11 mathematics. The study began in 2006 and continued into 2009. The key questions for the research were:
World Conference on Educational Multimedia, …, Jul 1, 2010
Abstract During a three year study of implementation of the TI-Navigator in secondary school math... more Abstract During a three year study of implementation of the TI-Navigator in secondary school mathematics, by 'typical'teachers, we identified a number of unexpected support needs. Some could be addressed by the researchers in conjunction with the teachers, but others ...
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Papers by Amanda Allan