Details of Thesis

Title Na´ve and Yet Knowing: Young learners portray beliefs about mathematics and learning
Author McDonough, Andrea M.
Institution Australian Catholic University
Date 2002
Abstract This is a report of an investigation of children’s beliefs about the nature of mathematics, the nature of learning and helping factors for learning mathematics. The study aimed to investigate whether beliefs held by eight learners of eight to nine years of age could be articulated and portrayed. It aimed also to develop procedures to facilitate this process, to portray children’s beliefs from their responses to the research procedures, to provide insights into possible complexities and subtleties of young learners’ beliefs, to reflect upon the significance for the mathematics classroom of the insights gained, and to reflect upon the value of the procedures developed for the study.  The research took the form of individual case studies of four girls and four boys of eight to nine years of age from two schools in suburban Melbourne. Four children were teacher-perceived low achievers in mathematics and four were teacher-perceived high achievers in mathematics.  The children were each interviewed on ten occasions over a five-month period using thirty semi-structured, creative interviewing procedures that were developed or adapted for the study that included drawing, writing, discussing scenarios presented through photographs, video snippets and other children’s drawings, ordering of descriptors, and responding to questionnaires presented verbally. The interview data consisted of transcripts and artefacts. Some class administered tasks, lesson observations and interviews with the mathematics teachers provided background information.  Analysis of interview responses was undertaken through a criss-cross examination in which themes were drawn from each child’s data. Responses were not judged for correctness or for a match to any predetermined categories and the researcher sought to take a stance of neutrality to the phenomena under study.  The research suggests that teachers and others involved in the education of young learners of mathematics should know that: it is possible to gain insights into children’s beliefs about maths (the term used most commonly by the children), learning, and helping factors for learning maths; to gain insights into young children’s beliefs, it is important to have dialogue with the children to avoid making assumptions about their interpretations or meanings; the creative interviewing procedures developed for the present research are helpful as they can stimulate reflection and prompt conversation; young children’s beliefs can be complex, subtle, broad and deep; young children’s beliefs are individually constructed and differ from child to child; children may not see mathematics concepts in the same ways as their teachers and other adults; beliefs are sufficiently diverse and significant to affect the way children see the mathematics learning situation; although the beliefs of children of eight to nine years of age may, on the surface, appear simplistic and na´ve, they are not necessarily so. Young learners are able to reflect on their own and others’ experiences and often construct complex beliefs. There is a lot happening in the minds of these children.  The research suggests also that it is important that educators do not to make assumptions about: what children see as maths (or mathematics); what children see as learning; and what children see as helping factors for learning maths.  A key factor facilitating children’s reflection and expression was the range of visual, verbal, and text-based creative interviewing strategies developed for the present study. The individual procedures provided suitable prompts to allow young children to articulate or represent their beliefs. The semi-structured procedures, through which ideas were explored on multiple occasions, followed by theme-based, criss-cross analysis of interview transcripts and artefacts, resulted in rich and trustworthy portrayals of beliefs, increasing the validity of the findings.  The research provides the education community with insights into young children’s beliefs that are unlikely to emerge within the day to day activity of the classroom and, through the availability of the research procedures, facilitates further gaining of insights into beliefs either by classroom teachers or other researchers.
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