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
- 3.3 Identifying Flaws in Reasoning
- 3.3.1 Discourse
- 3.3.2 Language
- 3.3.3 Definition of “Rule”
- 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)
3.3.3 Definition of “Rule”
Three groups of students in the classroom demonstrated misunderstandings when asked to define what a mathematical "rule" was.
Their confusion was influenced by everyday experiences with school rules and expectations. For example, one group explained that an example of a rule was that you couldn't play tag on the cement because it is easy to get hurt. However, they explained, there are exceptions made to the rule for physical education classes.
In the following video clip, Leslie similarly explains exceptions to rules. The notion of exception allowed students to see 9 as a multiple of 2 as an exception to the rule of even.
Teachers may assume that students understand that a mathematical rule is a statement that is always true. The definition exercise demonstrated that in the daily activities of students, rules often have exceptions.
In your Metacognitive Journal, consider how you would help students understand what "rule" means in mathematics.
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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.
