
06426597
j
2015c.00148
Lee, Hyung Sook
Yim, Jaehoon
Pursuing coherence among proportionality, linearity, and similarity: two pathways from preservice teachers' geometric representation.
Math. Enthus. 11, No. 3, 541554 (2014).
2014
Information Age Publishing (IAP), Charlotte, NC; University of Montana, Department of Mathematical Sciences, Missoula, MT
EN
C39
F80
I20
concepts
modes of representation
proportionality
linearity
similarity
algebraic aspects
geometric aspects
proportional reasoning
coherence
geometric representations
developmental perspective
covariation
understanding
preservice teacher education
http://www.math.umt.edu/TMME/vol11no3/Lee%20&%20Yim_6.pdf
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.