TY - JOUR
T1 - Constructing the Self-similarity Concept
AU - Hershkowitz, Rina
AU - Dreyfus, Tommy
AU - Tabach, Michal
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2023/8
Y1 - 2023/8
N2 - Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpiński triangle, working in small group and whole class settings in an inquiry-based MA level mathematics education course. We follow shifts of knowledge from individuals to groups and/or to the whole class community during the process of constructing the self-similarity concept. Our theoretical and methodological approach is based on networking between Abstraction in Context and Documenting Collective Activity. We found that the knowledge constructing processes of different students varied, some thinking recursively about finite cases and others thinking more directly about the infinite case. Some students acted as knowledge agents, with shifts of knowledge occasionally occurring in chains. We also observed a tendency to report results of group discussions back to the plenum only partially and in a purified manner.
AB - Fractals describe many natural phenomena; their strong visual-figurative nature found its mathematical conceptualization in the concept of self-similarity. In the current study, we investigate how students construct (fully or partially) the self-similarity concept while recursively constructing the Sierpiński triangle, working in small group and whole class settings in an inquiry-based MA level mathematics education course. We follow shifts of knowledge from individuals to groups and/or to the whole class community during the process of constructing the self-similarity concept. Our theoretical and methodological approach is based on networking between Abstraction in Context and Documenting Collective Activity. We found that the knowledge constructing processes of different students varied, some thinking recursively about finite cases and others thinking more directly about the infinite case. Some students acted as knowledge agents, with shifts of knowledge occasionally occurring in chains. We also observed a tendency to report results of group discussions back to the plenum only partially and in a purified manner.
KW - Abstraction in context
KW - Construction of knowledge
KW - Documenting collective activity
KW - Knowledge agent
KW - Self-similarity
KW - Shifts of knowledge
UR - http://www.scopus.com/inward/record.url?scp=85128832374&partnerID=8YFLogxK
U2 - 10.1007/s40753-022-00173-0
DO - 10.1007/s40753-022-00173-0
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AN - SCOPUS:85128832374
SN - 2198-9753
VL - 9
SP - 322
EP - 349
JO - International Journal of Research in Undergraduate Mathematics Education
JF - International Journal of Research in Undergraduate Mathematics Education
IS - 2
ER -