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
- 3.4 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)
3.1 Beginning to Reason: Definitions and Conjectures
The Difference between a Mathematical Argument and a Proof
The CCSS for mathematical practices do not use the word “proof”. This is because many people are familiar with a narrow definition of proof (e.g., a two-column geometry proof). The term “argument” is intended to be more general in form but ultimately has the same purpose of constructing a logical sequence of steps that justify and communicate a given conclusion from a set of agreed premises.
As stated in California’s CCSS for Mathematics (p.1):
Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments."
When students begin to reason, they need to establish definitions (e.g., clear and logical descriptions of what they are reasoning about). They also may need to make conjectures — informed guesses of what is true — that they then set out to explain through reasoning.
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.
