# MATH-ish

# Chapter 2: Learning to Learn

## Summary:

In this chapter Boaler discusses the importance of helping our students build metacognition. John Flavell, a pioneer in cognitive studies, introduced the concept of metacognition, which involves understanding one’s own cognitive processes, the tasks at hand, and the strategies to address them. Research such as the 2015 Programme for International Student Assessment (PISA) demonstrated that students who adopt memorization techniques in math scored lower globally, while those using relational or self-monitoring methods achieved higher. Further supporting this, John Hattie's meta-analyses found that strategies where students report their own progress, engage in metacognitive thinking, and participate in classroom discussions and problem-solving are more effective compared to methods like individualized instruction or ability grouping.

Boaler talks about a teacher she worked with at Railside School, whom she has great respect for, Carlos Cabana. Cabana emphasized metacognitive strategies by encouraging varied approaches and validating student work by celebrating both correct and incorrect work equally and continually questioning his students by asking questions like Why? How do you know that to be true? How do you know that's false?

These strategies include drawing problems to visually connect concepts, simplifying them, and exploring different approaches to foster a deeper understanding and flexibility in problem-solving. By promoting group work, journaling, and the use of rubrics for assessment, educators can enhance students' respect for diverse ideas and develop a growth mindset, further embedding metacognitive practices in education.

## Key Math-ish Principle(s):

## The importance of teaching students how to learn.

## Key Ideas/Themes:

8 Different types of metacognitive thinking: listen respectfully, talk out loud, think about what someone was going to present, consider different strategies, understand and value errors, think about and notice why methods work, notice color coding and technical drawing, and think back on what you learned.

Encouraging metacognition through eight mathematical strategies: take a step back, draw the problem, find a new approach, think about why?, simplify, conjecture, become a skeptic, and try a smaller case.

Encourage metacognition through: journaling, group work, and assessment

## Reflection Questions:

### After reading this chapter reflect on the following questions. Think about:

What makes sense?

What can you apply in the classroom right now?

What do you still need help with?