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theses

How mathematical ideas and ways of reasoning are built, over time, is an important aspect of the concept development for a student in his or her learning process. Using a qualitative, phenomenological approach that is backed by newly constructed video narratives (VMCAnalytics) to illustrate Stephanie’s growth in understanding over time, this study analyzes archived data from a ten-year longitudinal study to trace the growth of mathematical understanding of a participant in the longitudinal study from the lens of the Pirie-Kieren model for studying growth in mathematical understanding. Using archived video data, published VMCAnalytics, transcripts, student work, and publications, the study traces growth in mathematical understanding of one student, Stephanie, as she engages in non-routine mathematics problems in formal and informal learning environments. A learning progression was created, attentive to Stephanie’s movement in mathematical understanding through various layers of the Pirie-Kieren Model, starting from primitive knowing to formalizing, structuring, and inventising. Attention was given to following Stephanie’s folding back in tracking her growth in understanding, particularly as she makes connections and recognizes the structural relationships between and among task solutions. The VMCAnalytics created to trace Stephanie’s growth illustrate how she revisits inner layers of understanding to rebuild and extend that understanding. This study contributes to addressing gaps in the literature by focusing on Stephanie’s reasoning as she works with a partner, small group, and in whole class settings. It extends the Pirie-Kieren work by attending to Stephanie’s growth in collaborative settings. Also, analyses of response to researcher moves and interactions with others, and the influence of these on Stephanie’s growth extend earlier work using the Pirie-Kieren framework. This study demonstrates growth in and among layers of understanding though video narratives, with a learning progression showing visual evidence of mathematical growth in understanding. A major finding includes a proposal for an addendum to the Pirie-Kieren model for studying growth in mathematical understanding that encompasses collaboration’s effect on individual learners’ growth. Another finding highlights the significance of folding back on growth in mathematical understanding. A third finding indicates that interaction with researchers were instrumental in advancing Stephanie’s growth in understanding and development of mathematical ideas.

ETD_9880

Ph.D.

Includes bibliographical references

doi:10.7282/t3-6w2c-qm85

ETD doctoral

The author owns the copyright to this work.