Options
Cognitive characteristics and contextual influences in mathematical problem posing
Loading...
Type
Thesis
Author
Quek, Khiok Seng
Supervisor
Soh, Kay Cheng
Abstract
This inquiry into mathematical problem posing started on a tentative basis with informal observations of the activity in practice. It had appeared odd to me that different people (e.g., pupils and academic mathematicians) are likely to make up textbook-like mathematics problems when asked to engage in the activity of mathematical problem finding or posing. Initial observations and analyses of the activity led the inquiry to focus on the cognitive characteristics and contextual influences associated with the activity of mathematical problem finding or posing. The methodology of a grounded theory approach was identified as appropriate for deriving a conception of mathematical problem finding and posing that would inform classroom practice.
As the inquiry progressed, it became clear that it would be inadequate to conceptualise the cognitive aspects separately from the contextual aspects of mathematical problem posing. Context conceptualised as dynamic and continuously constituted by individuals in interaction meant that individual cognition intertwined with the context prevailing. The inquiry, in the spirit of a grounded theory approach, investigated this interlocking nature of cognition and context in problem posing. A comparative analysis of data from extant literature, lived experiences, testimonies, anecdotes and initial observations of problem finding and mathematical problem posing suggested a conceptualization of mathematical problem posing as an activity system.
Next, a series of observations of mathematical problem posing in classroom practice was carried out to substantiate, refine, or reject the proposed conception. Altogether, eight intact classes (average class size of 25) of preservice teachers tutored by me from the Diploma in Education programme for non-degree holders and from the Postgraduate Diploma in Education (Primary) programme for degree holders, participated in making up mathematics problems under different conditions. One group of 11 student teachers from my Postgraduate Diploma in Education class agreed to be interviewed for their views of mathematics and to think-aloud when making up mathematics problems. The session was audio-taped.
This inquiry found that a popular conception of mathematical problem posing is one consisting of willing individuals (students or research participants) making up mathematics problems under different conditions at the request of someone else (teacher or researcher). It revealed that the meaning and object/motive a person has for engaging in mathematical problem posing direct the person's actions and determines its outcome. Contextual and cognitive factors impinged on the construal of meaning and object of the activity for that particular individual.
This inquiry recommends treating mathematical problem posing in classroom practice as an activity system. An activity theory perspective should provide a means of organising the dynamic and continuously changing context that is characteristics of mathematical problem posing. Contradictions from within and between the components of an activity system, and from interactions with other activity systems, should sensitise an observer (a teacher) to initiate actions to locate and resolve the contradictions. The transformative power of the components of an activity system viz, rules, division of labour, and artefacts, that mediate between subject (e.g., students) and object (e.g., formulating or discovering a mathematics problem) has practical implications. The evolving nature of an activity system of mathematical problem posing requires further research to realise its potential for managing and theorising about the many activity systems in a classroom.
As the inquiry progressed, it became clear that it would be inadequate to conceptualise the cognitive aspects separately from the contextual aspects of mathematical problem posing. Context conceptualised as dynamic and continuously constituted by individuals in interaction meant that individual cognition intertwined with the context prevailing. The inquiry, in the spirit of a grounded theory approach, investigated this interlocking nature of cognition and context in problem posing. A comparative analysis of data from extant literature, lived experiences, testimonies, anecdotes and initial observations of problem finding and mathematical problem posing suggested a conceptualization of mathematical problem posing as an activity system.
Next, a series of observations of mathematical problem posing in classroom practice was carried out to substantiate, refine, or reject the proposed conception. Altogether, eight intact classes (average class size of 25) of preservice teachers tutored by me from the Diploma in Education programme for non-degree holders and from the Postgraduate Diploma in Education (Primary) programme for degree holders, participated in making up mathematics problems under different conditions. One group of 11 student teachers from my Postgraduate Diploma in Education class agreed to be interviewed for their views of mathematics and to think-aloud when making up mathematics problems. The session was audio-taped.
This inquiry found that a popular conception of mathematical problem posing is one consisting of willing individuals (students or research participants) making up mathematics problems under different conditions at the request of someone else (teacher or researcher). It revealed that the meaning and object/motive a person has for engaging in mathematical problem posing direct the person's actions and determines its outcome. Contextual and cognitive factors impinged on the construal of meaning and object of the activity for that particular individual.
This inquiry recommends treating mathematical problem posing in classroom practice as an activity system. An activity theory perspective should provide a means of organising the dynamic and continuously changing context that is characteristics of mathematical problem posing. Contradictions from within and between the components of an activity system, and from interactions with other activity systems, should sensitise an observer (a teacher) to initiate actions to locate and resolve the contradictions. The transformative power of the components of an activity system viz, rules, division of labour, and artefacts, that mediate between subject (e.g., students) and object (e.g., formulating or discovering a mathematics problem) has practical implications. The evolving nature of an activity system of mathematical problem posing requires further research to realise its potential for managing and theorising about the many activity systems in a classroom.
Date Issued
2002
Call Number
QA63 Que
Date Submitted
2002