The solving of problems from the Kängaru competition by student dyads
First commenced with students in grade six, this project follows dyads on two more occasions, by which time students are in their grade seven and high school in the Swedish school system. The problems from the Kängaru are utilised to offer students with differing abilities and aptitudes at school mathematics neither any advantage nor disadvantage in their ability to solve problems. This offers opportunity to investigate the range of abilities and strategies that students exhibit in arriving at solutions. The aim of the project is to look beyond finding out if students can or cannot solve the creative problems offered by the Kängaru and to understand the nature of cues or prompts they utilise and find useful in solving problems. Such insight could in turn throw light on the kind of training that students may be wanting of towards solving mathematical problems.
Participating departments and units at Umeå University
This project relating to the solving of problems by students pairs arose in the same grade six in which the conduct of the project on narrative inquiry took place, by which time all students had taken part in the Kängaru competition. Keeping the curriculum for mathematics at grade six in mind, a choice of four problems was made which was set for students to solve as pairs or dyads. Eleven student pairs participated in such problem solving sessions, on the conclusion of which six volunteered to participate in similar sessions even when they moved to their next grade at new and different high schools. These six dyads are now working at another selection of problems from the Kängaru on at least two more occasions, a practice that could continue further if they are willing. Apart from drawing on data that was revealed through narrative inquiry, as well as field notes made during their problem solving sessions, all attempts of students dyads have been audio-recorded. Student inscriptions while solving problems are also at hand.
The conduct of the initial round of problem solving sessions point to the fluent command that the more able have on their verbal abilities and reasoning, one which they use to their advantage towards arriving at their solution. Such abilities combined with greater numerical proficiency as for example in mental computation placed them at an advantage in showing readiness to attempt the problems at hand. The use of language as a tool to solve mathematical problems is thus under investigation in this study, besides the Vygotskian construct of Zone of Proximal Development or ZPD within which cues and prompts assist them to solve the given problems. Two other aspects that will contribute to the final analysis of the attempts of students is literature in small group problem solving as well as research pertaining to creative problem solving.
The above project extends the deployment of perspectives utilised in problem solving by small groups in a classroom and doctoral study and is supported financially by a post-doctoral scholarship provided by the Kempe foundation, Sweden.