Problem-posing and problem-solving at grades five and six
This project is extension to an earlier project in this database titled "Development of students' communication at a grade four mathematics classroom" and studies how students pose and solve mathematical problems.
Despite a change in their teacher, this longitudinal study through grades five and six, has student groups pose mathematical problems as before, as well as solve problems in small groups as part of everyday instruction. Such an approach enables understanding of problem posing as well as problem solving in classroom practice, with analytical emphasis on classroom talk, pedagogy and the formation of student identity.
Participating departments and units at Umeå University
Being conducted across grades five and six, this project builds on an earlier project titled 'Development of students' communication at a grade four mathematics classroom'. Long association during the grade four project had allowed for fruitful teacher-researcher collaboration. It was possible to perceive in particular, a shift in researcher position from being a participant observer with a practical disposition to becoming an action researcher with a critical-emancipatory disposition. Students participating at grade four were well accustomed in addition, to participating in activities whose design and conduct were based on Vygotskian perspectives. The current project, at grades five and six, builds upon such student participation and enables new directions in research in relation to problem-posing as well as problem-solving within everyday classroom practice.
In continued conduct of the activity of formulating questions mediated by textbook vocabulary, it was observed that students took actions of posing and challenging their peers with their problems, by the time they were in grade five. Such actions were met with inspired guesses as well as accurate answers. On occasion students were observed to verify the accuracy of their numerical answers by resorting to the use of calculators. It is intended to study the continued participation of students in this and similar activities, shedding light on the nature of problem-posing by students. As argued in a recent symposium at an international conference (PME35, Turkey) such nature of research in mathematics education has many unanswered questions, one of which relates importantly to students' voice.
The conduct of specific activities at grade four to facilitate communication in student pairs has since led to their working in groups of two or more at grades five and six. Organised around mathematical problems such grouping has called for discussion and acceptance of rules of talk that are to be followed, both within one’s own group (cooperation) as well as across student groups in the classroom (collaboration). The very constitution of groups as well as the presentation by student groups of their solutions, at the whiteboard, enables the study of two specific aspects. First, the nature of talk and reasoning that students utilise in solving mathematical problems, as well as the nature of student identity that is intertwined in such nature of participation within classroom practice.
This project acknowledges that social practices are situated and students learn by engaging in these practices. It is while working with multiple resources found available in activities within, that children also achieve specific forms of student identity.