id: 06426597
dt: j
an: 2015c.00148
au: Lee, Hyung Sook; Yim, Jaehoon
ti: Pursuing coherence among proportionality, linearity, and similarity: two
pathways from preservice teachers’ geometric representation.
so: Math. Enthus. 11, No. 3, 541-554 (2014).
py: 2014
pu: Information Age Publishing (IAP), Charlotte, NC; University of Montana,
Department of Mathematical Sciences, Missoula, MT
la: EN
cc: C39 F80 I20
ut: concepts; modes of representation; proportionality; linearity; similarity;
algebraic aspects; geometric aspects; proportional reasoning;
coherence; geometric representations; developmental perspective;
covariation; understanding; preservice teacher education
ci:
li: http://www.math.umt.edu/TMME/vol11no3/Lee%20&%20Yim_6.pdf
ab: Summary: The importance of using multiple representations of a mathematical
concept and connecting the representations has been discussed in
learning and teaching mathematics. The Common Core State Standards
further the discussion with an emphasis on focus and coherence in
teaching mathematical concepts across grades. Preservice teachers in
our problem solving class were asked to use geometric representations
to solve a problem that required proportional reasoning. They were also
asked to sequence the works of their peers as well as their own from a
developmental perspective. Sequencing geometric representations with
various levels was challenging because it required showing a coherent
understanding of proportionality, linearity, and similarity. In this
article, we present two pathways of developing proportional reasoning
and discuss how proportionality, linearity, and similarity can be
developed coherently. We also discuss the significance of engaging
preservice teachers in others’ thinking and having them sequence
others’ works in the journey of pursuing focus and coherence in
teaching.
rv: