7. Diversity in Practice and Feedback

• Boaler uses the term diversity a lot in this book. Applied problems, mental representations, and ongoing feedback give math education a diverse look and this is important. As for feedback, most teachers just give kids aggregate scores and answers are either correct or not. We need to go beyond this.
• Deliberate practice is also important and mentioned in many other books I have summarized. This goes beyond mindlessly doing lots of the same kind of problems and on to struggling with open ended problems that focus on concepts rather than procedures.

8. A New Mathematical Future

• If you look at who succeeds in traditional math and moves on to advanced classes and who ultimately succeed in STEM majors, you will find that poor students and students from Black and Hispanic racial minorities are disproportionately left out. Boaler believes that if you can follow her methods more students will enjoy and understand math and be able to use it to advance.
• Her work and ideas have been challenged and called controversial by people who support traditional and narrow teaching methods that rely on lectures, timed tests, and narrow one right answer problems that lack visualization and classroom discussion. She encourages teachers to push for changes that can make math more diverse and that give students who are more diverse a better chance to find joy and purpose in math.

Jo Boaler

• Jo is a British education author and is Professor of Mathematics Education at the Stanford Graduate School of Education. She is involved in promoting math education reform and equitable mathematics classrooms. She is the CEO and co-founder of Youcubed, a non-profit organization that provides mathematics education resources to parents and educators of K–12 students. Her most recent book is Limitless Mind. Another important book is Mathematical Mindsets. Her work also appears in many popular publications. Follow her on X at @joboaler.

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