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)
3.2 Beginning to Reason: Definitions and Conjectures
Higher order questions generally challenge the student to provide additional information and engage in deeper understanding and reflection, and ultimately promote greater conceptual development."
Nathan & Kim, 2007
Explaining and justifying are at the heart of mathematical reasoning. By becoming aware of the language patterns of students, teachers are able to scaffold mathematics instruction and support students in moving toward justifications and generalizations.
Two studies that focused on discourse (Mendez, 2004) and teacher elicitation (Nathan & Kim, 2007) found that explanations, justifications, and generalizations coincide with the reasoning practices of students. This work provides the basis for a hierarchy of questions and responses between teachers and students. The researchers found that teachers move up and down the hierarchy of questioning in response to student needs.
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.
