PCMI TLP: Repository of Wisdom of Practice: Shana Henry, Sharon Goodman, Tun Bhothinard

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Proportional Reasoning in the Formative Years Are you down with O.P.P. (Organizing Proportional Reasoning Problems)? Shana Henry, Sharon Goodman, Tun Bhothinard

In a 90 minute PD workshop, middle school math teachers will explore the differences in proportional thinking from 5th to 8th grade. Heavy emphasis will be on the conceptual understanding for creating cohesive learning which should lay the foundation for functions in high school.

What we do:

Proportional reasoning is heavily highlighted in the middle school. Proportional reasoning can be organized into four contexts of tasks. To increase flexibility in their mathematical thinking, students should be proficient in all four contexts. However, many classrooms only focus on two types of thinking tasks: rate and part-part-whole. Our aim is to build awareness of two additional types (mixture and similarity) to deepen holistic understanding of proportional reasoning.

How we do it:

Learning Objective #1: Participants will be able to distinguish between four types of proportional reasoning tasks.

Learning Objective #2: Participants will be able to state at least one connection between middle school and high school tasks requiring proportional reasoning.

Research:

De la Cruz, J. A. (2013). Selecting proportional reasoning tasks. Australian Mathematics Teacher, 69(2), 14 – 18. https://files.eric.ed.gov/fulltext/EJ1093097.pdf

Holzrichter, Rebecca, "Proportional reasoning in middle level mathematics textbooks" (2016). Honors Program eses. 221. https://scholarworks.uni.edu/hpt/221

Thompson, Charles, S. & Bush, William, S. Improving Middle School Teachers’ Reasoning about Proportional Reasoning. Mathematics Teaching in the Middle School, NCTM, Vol. 8 No. 8, April 2003, 398 – 403. http://cunycci.pbworks.com/f/improving%20middle%20school%20teacher%20reasoning%20about%20proportional%20reasoning.pdf

Van de Walle, J., & Lovin, L.A. (2006). Teaching student-centered mathematics: Grades 5-8. Boston, MA: Allyn & Bacon.

Files developed during PCMI 2018:

download zipped folder tan.zip [generic login required]

  #PCMIsummer
  #proportionalreasoning
  #mixture
  #similarity
  #rate
  #part-part-whole
  #multiplicativereasoning
  #ratios
  #scaling

View TLP PCMI | IAS YouTube channel for an overview of the Teacher Leadership Program, ideas for your classroom, resources for you and your colleagues, and short clips of important things to think about as teachers.