1. Andrew Izsak
  2. Professor
  4. University of Georgia
  1. Sybilla Beckmann
  2. https://faculty.franklin.uga.edu/sybilla/
  3. Meigs Distinguished Teaching Professor
  5. University of Georgia
  1. laine bradshaw
  2. https://coe.uga.edu/directory/profiles/laineb
  3. Associate Professor
  5. University of Georgia
  1. Torrey Kulow
  2. Post Doctoral Researcher
  4. University of Georgia

Investigating Proportional Relationships from Two Perspectives

NSF Awards: 1420307

2016 (see original presentation & discussion)

Grades 6-8

The Investigating Proportional Relationships from Two Perspectives project is investigating how future mathematics teachers in preparation programs at the University of Georgia develop facility reasoning about proportional relationships in terms of quantities. We are attempting to make three significant contributions to teaching and research about proportional relationships—arguably the most central mathematics in the middle grades. First, we are investigating a new, potentially transformative approach to proportional relationships that is based on two complementary perspectives, one that makes co-variation visually explicit with double number lines and one that makes multiplicative relationships between quantities visually explicit with strip diagrams. The central hypothesis for InPReP2 is that, taken together, the two perspectives may facilitate both key features of proportional relationships and open new pathways that make subsequent topics, like linear equations and statistical samples, more accessible. Second, we are investigating new, potentially transformative methods that coordinate detailed case studies with recent advances surveying multiplicative reasoning in large, national samples. Third, we are examining how different initial strengths and weaknesses with multiplicative reasoning affect how future teachers make sense of the two perspectives on proportions and applications. By examining a potentially transformative approach to ratio and proportional relationships, the project will generate results about multiplicative reasoning that can inform improved teacher education content courses and professional development that prepare teachers cross the nation for standards that emphasize sense making with quantities, including the Common Core State Standards. Thus, the project has high potential for improving teaching and learning middle grades mathematics fundamental to subsequent college readiness.

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