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�Lesson 5: ��Effective Explanations

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Today’s Plan

  • Goal: To explore what makes a drawing with an explanation effective
  • We will revisit a task from Homework 4 and look at two responses from other pre-service math teachers.
  • In groups, you’ll analyze these explanations and drawings

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�Activity 1: ��What Makes a Good Explanation? ���

GROUP WORK

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Task:�� Homework 4, �Question 4

  • A zookeeper made a batch of Monkey Chow. Two of the ingredients are 4 cups of pumpkin and 9 cups of oatmeal. The zookeeper would like to make a larger batch of monkey chow that will taste the same as the original batch. If she uses 10 cups of pumpkin, how much oatmeal should she use?
  • Solve this problem using a multiplicative comparison of oatmeal to pumpkin.
  • Use well-labeled drawings and explain your thinking.
  • Don’t use the proportion algorithm or any calculations, such as reducing fractions. If do perform a calculation, it needs to be shown in the drawing

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Groups Share

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  • List every part of the explanation and drawing that is effective:

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  • What could be improved?

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  • List every part of the explanation and drawing that is effective:

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  • Identify several problems with the explanation and drawing:

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Main Differences Between the Explanations:

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Reflect

What have you learned from this experience of looking at other people’s explanations and drawings that you will bring to your future explanations and drawings?

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Tips for Writing Good Explanations

  • Don’t just present a labeled drawing. Write text to go with your drawing that provides a running account of your reasoning
  • Think about an audience for your explanation. What would you say to students to help them make sense of your drawing and approach?
  • Don’t calculate and then illustrate the result of your calculation. Instead, use the drawing to solve the task.

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Now It’s YOUR Turn to Create Great Explanations!

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�Activity 2: ��Creating Effective Drawings and Explanations ���

GROUP WORK

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Activity 2A: Explanation using multiplicative comparison reasoning

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Activity 2B: Explanation using composed unit reasoning

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Task:

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Groups Share �

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Compare �

  • What differences do you notice between these two types of proportional reasoning: composed unit reasoning and multiplicative comparison reasoning?

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Homework 5

  • The reading is a set of 4 explanations that you will read and analyze for Homework 5

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The development of these videos were supported by the National Science Foundation through Awards DRL-1416789 and 1907782. The views expressed here are not necessarily those of the NSF

Acknowledgments

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Dr. Joanne Lobato, PI, San Diego State University (SDSU)

Dr. John Gruver, Co-PI, Michigan Technological University (MTU)

Dr. Michael McKean, Technical Specialist, SDSU

Dr. Alicia Gonzales, Postdoctoral Scholar, MTU

Isabel White, Doctoral Student Research Assistant, SDSU & UCSD

Dr. Michael Foster, Postdoctoral Research Associate, Rochester Institute of Technology

Dr. C. David Walters, Creator of Teacher Support Materials, Weber State University