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.
Lee, Hyung Sook and Yim, Jaehoon
"Pursuing Coherence Among Proportionality, Linearity, and Similarity: Two Pathways From Preservice Teachers’ Geometric Representations,"
The Mathematics Enthusiast: Vol. 11
, Article 7.
Available at: http://scholarworks.umt.edu/tme/vol11/iss3/7