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.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/6618 |
| Date | 05 1900 |
| Creators | Kelleher, Heather |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Relation | UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/] |
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