The focus of our second meeting is to deepen our own understanding of the specific content we chose for our research lesson - proportional reasoning.

In preparation, participants should read the following: 

• Three Balloons for Two Dollars: Developing Proportional Reasoning (8 pages) 
  

Cynthia W. Langrall and Jane Swafford

• Teaching Ratio and Proportion in the Middle Grades (6 pages)
  

 NCTM Research Brief

Recommended Resources for Deepening Teacher Understanding of Ratio and Proportional Reasoning

• Ratios - Chapter 8 of Understanding the Math You Teach, Grades K-8 (24 pages)
  

Suzanne Chapin

• Developing Concepts of Ratio and Proportion - Chapter 18 of Elementary and Middle School Mathematics (18 pages)
  

John A. Van De Walle

• Developing Essential Understanding of Ratios, Proportions & Proportional Reasoning, Grades 6-8 (85 pages)
  

 National Council of Teachers of Mathematics   

• Ratios and Proportional Relationships (15 pages)
  

Progression Document for the Common Core Standards in Mathematics

More Readings on Proportional Reasoning

• Giant Pencils: Developing Proportional Reasoning (5 pages)
  

S. Megan Che 

• Problems that Encourage Proportion Sense (5 pages)
  

Esther M. H. Billings 

• Proportionality and the Development of Prealgebra Understandings

Thomas Post, Merlyn Behr and Richard Lesh 

• Building on "Building Up": Proportional Reasoning Activities for Future Teachers (4 pages)
  

Melanie Parker 

• Improper Applications of Proportional Reasoning (6 pages)
  

 Wim Van Dooren, Dirk De Bock, Lieven Verschaffel and Dirk Janssens   

• Improving Middle School Teachers' Reasoning about Proportional Reasoning (6 pages)
  

 Charles Thompson and William S. Bush   

Additional Recommended Print Resources

• Teaching Fractions and Ratios for Understanding by Susan Lamon 

• Math Matters: Understanding the Math You Teach, Grades 6-8 (Chapter 8) by Suzanne H Chapin - available above
  

• Elementary and Middle School Mathematics: Teaching Developmentally (Chapter 18) by John Van de Walle - available above
  

• Keeping Things in Proportion from the EMPower Series