Table of Contents
- Content Home
Welcome
Module Overview- Pre-Assessment
- Unit 1: Teaching and Learning the Standards for Mathematical Practice
- Unit 2: Overarching Habits of Mind: MP1 and MP6
- Unit 3: Reasoning and Explaining (MP2 and MP3)
- 3.0 Unpacking MP2 and MP3
- 3.1 Beginning to Reason: Definitions and Conjectures
- 3.2 Explaining and Justifying
- Taxonomy of Questions in Mathematical Discourse
- 3.2.1 Levels of Explanations: Level 1
- 3.2.2 Levels of Explanation: Bridging Level 1 and 2
- 3.2.3 Levels of Explanation: Level 2
- 3.2.4 Levels of Explanation: Level 3
- 3.2.5 Levels of Explanation: Include All Students
- 3.3 Identifying Flaws in Reasoning
- 3.4 Making Arguments More Viable
- 3.5 Summary
- Unit 4: Modeling and Using Tools (MP4 and MP5)
- Unit 5: Seeing Structure and Generalizing (MP7 and MP8)
- Unit 6: Summary and Next Steps
- Post-Assessment
Certificate of Completion- Glossary
Resources- Acknowledgements
Module Evaluation
Unit 3: Reasoning and Explaining (MP2 and MP3)
3.2.2 Levels of Explanation: Bridging Level 1 and 2
Single Case or Example
When learning to explain their thinking, students will provide one example and believe it is enough evidence to argue their conjecture. This is referred to as a “perceptual proof” (Sowder & Harel, 1998).
View the student work below for examples of a perceptual proof:
Student writing on posters:
Even. Yay 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. All cookies have partners. Even means there are no numbers left out when you count by twos.
Boo! Odd, Boo! Not all ghosts have partners. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29. Odd means there is a number left out when you count by 1s, 3s, 5s, 7s, or 9s
In the video below, Jason and Jonathan use a single example to demonstrate what an odd number is.
Notice that in the two examples presented, students are satisfied with one case as sufficient evidence to validate their claim.
Mathematics: Kindergarten through Grade Twelve (K–12) Standards for Mathematical Practice. Brought to you by the California Department of Education, the Regents of the University of California, and the California Mathematics Project.
For questions or feedback, please e-mail commoncoreteam@cde.ca.gov.
