UBC Theses and Dissertations
Making sense of number : a study of children’s developing competence Kelleher, Heather
This study investigated young children's construction of meaning for number and explored ways to more comprehensively assess and portray the development of number sense in young children. Greeno's (1991) conceptualization of number sense as situated knowing in a conceptual domain was used to consider both the mathematical tools available to the child and the extent to which the child makes use of these tools. The data consisted of four videotaped interviews for each of sixteen children between the ages of six and eight. Each of the four interviews involved a different number context: doubling, finding missing parts, sharing, and working with money. Each context involved a task presented in a series of increasingly difficult items, with number size predominantly determining the difficulty level. A dynamic interview format was used to encourage children to work beyond their independent level, or "number comfort zone." Cues and scaffolds were provided to support children's construction of meaning within their "number construction zone" and towards the outer limits of their understanding. Analysis focused on the strategies children used to make sense of each item, and the cognitive, affective and contextual aspects which enhanced or constrained their mathematical activity within the number construction zone. Results were reported two ways. The first, specific task performance across children, provided a means of describing the diversity of developmentally appropriate ways children made sense of the different tasks and provided a frame of reference for considering individual performance. The second approach to reporting results considered individual children's performance across tasks, and provided a means of focusing on characteristics of emerging competence. Results of this study illustrate how the nature and use of children's reasoning strategies can provide an indication of developing competence. Results highlight specific conceptual, procedural, functional, and affective characteristics that most directly affected children's capacity to make sense of number situations. No single characteristic alone accounted for children's success or lack of success, rather the inter-relationships of the different characteristics was apparent, with strengths in one area compensating for weaknesses in another. Though conceptual and procedural abilities appeared to shape to a great extent the nature of the number knowledge available to children, affective considerations and functional competence played a major role in shaping the extent to which children drew on this existing knowledge. Issues of context influenced both aspects of number sense: available knowledge and the nature of its use. Number size, context of the tasks, and presentation of tasks influenced children's mathematical activity in important ways. Children's personal number contexts were considered in terms of how they influenced their approaches to tasks. Overall, dynamic assessment techniques proved to offer a viable alternative for exploring the limits of children's ability to make sense of number situations, and for considering children's construction of meaning for number in developmental terms.
Item Citations and Data