My intention in this session was to learn more about the Common Core Mathematical Practices. Kristen and Samuel provided details on these practices embedded in the standards, but even more importantly, they suggested ways of implementing the standards in a high school mathematics classroom.
The Practices are defined as follows (the links were not provided in the session):
Kristen and Samuel noted that these practices require students to "do" mathematics rather than just following mathematical procedures laid out by the teacher. They suggested that "doing" mathematics requires the following:
- Students participate in complex and non-algorithmic thinking.
- Students explore mathematical concepts.
- Students self-monitor their problem-solving processes.
- Students access relevent knowledge.
- Students examine task restraints.
- Often, students will experience a level of anxiety as they wrestle with mathematics in a more real way.
Kristen and Samuel promoted the importance of modifying tasks to promote mathematical reasoning. They provided several ideas for doing so:
- Ask students what happens in the nth case of a pattern.
- Ask students to justify their conjectures.
- Reduce scaffolding, so that students are prompted to seek out strategies for problem-solving.
- Ask students to identify prior knowledge that they assume is true and justify the use of this knowledge.
- Ask students to define key mathematical objects.
- Ask students to model a problem through visual representations.