# Mathematical Mindsets

Are you looking for ways to implement the new BC curriculum? Look no further! Mathematical Mindsets is packed with many great ideas and is a fantastic place to start.

Jo Boaler is a professor of mathematics education at Stanford University. Mathematical Mindsets builds on the work and research of Carol Dweck, author of the book Mindset: The New Psychology of Success, and Boaler’s own extensive research. Mathematical Mindsets provides concrete methods and suggestions that can be used to transform students limiting mindset messages about math like – “I’m not good at math” or “I really struggle with mathematics” – into an understanding and a belief that ALL students can do math.

The book starts by walking the reader through an understanding of the brain and how we learn. The opportunity to struggle and make mistakes is key to learning. “More successful people make more mistakes.” It also takes into consideration the skills today’s students need to be successful: problem solving, interpersonal skills and teamwork. These are the 3 most valued skills listed by Fortune 500 companies. In comparison, computational skills, #2 in 1970, has dropped to #12 in 1999. Building on this knowledge and the goal to develop growth mindsets in all students, Boaler provides specific, concrete suggestions, techniques and activities we can use in the classroom (and at home) that encourages students to make mistakes and practice the 3 most valued skills for the 21st century.

Like, how to:

- Provide rich mathematical tasks and problems. In other words, provide problems
- that have multiple methods, pathways and representations that students can use to solve them.
- Students, not teachers, determine the method.
- Diagrams or pictures or manipulatives can be used to increase understanding.
- They are accessible to a wide range of student abilities i.e. low floor, high ceiling point of entry

- Create an environment where all students can be successful in mathematics
- Look at alternate methods of assessment

The book and appendix is packed with strategies, methods and handouts that can be used to create a growth mindset in the elementary and junior high school mathematics classrooms. In addition to the book, many excellent ideas can also be found at www.youcubed.org.

Book review by Lorraine Day Lanoue

It is Thursday after school and you have brought in Catherine’s parents to talk to them about her poor performance in math. “I was never any good at math, either” says her mom, with a sign. “Yeah,” says her dad. “She comes by it honestly. I struggled with math too. It must be genetic.”

Are weak math skills really genetic? How do you help a family like this? If these are questions you grapple with, the Jo Boaler’s book Mathematical Mindsets is for you. Subtitled Unleashing Students Potential Though Creative Math, Inspiring Messages and Innovative Teaching, this 291 page volume is full of practical and research based advice for teachers. Most importantly, it will shift your view on the subject of math, helping you see it as a creative and flexible subject.

Many of us in the teaching profession have heard of Carol Dweck’s concept of a growth mindset. Jo Boaler argues nowhere is a fixed mindset more prevalent and disabling that in our math classrooms. A focus on speed, accuracy and procedural knowledge has left many students feeling they just are not math people. Boaler then goes on to document how that fixed mindset is fostered and what we can do to create classrooms where mistakes are valued, students work together while learning from each other, and all can be successful.

Initially the concept of mistakes being valuable was a hard one for me to swallow. But Boaler elaborates how recent brain scanning technologies have allowed us to see the brain in action, revealing we learn more from making mistakes than from just regurgitating correct answers. She is also not focused on 2 + 2 = 5 types of mistakes, but rather having students get a mental workout through grappling with rich, engaging tasks. For example, have primary students work in pairs with 10 (or a different sum) items. One partner hides some of the items under a cup. The other has to figure out how many are hidden based on what number of items are still left visible. There are various strategies students can use in this game, and I can see how it would provide a mental workout even if a student wasn’t getting all the answers right. Being set up as a game, I could see weaker students trying harder on this task than if they were given a similar pencil and paper set of addition or subtraction tasks. Boaler states “Worksheets that repeat the same idea over and over turn students away from math, are unnecessary, and do not prepare them to use the idea in different situations.” (pg 42.) She also states “students need to feel really comfortable offering different ideas and not being afraid of being wrong.” (pg 19) Employers no longer need employees who can calculate, rather they need creative problem solvers who can tackle novel problems in innovative ways.

We also need to ensure a wider range of our students are prepared for the jobs of the future, and as a teacher interested in social justice topics, I was happy to see Boaler included a chapter on Mathematics and the Path to Equity. She explores how streaming practices often lead to girls and students of colour being left behind in our math classrooms, blocking them from rewarding STEM careers. She shares exciting research studies that show how changing how we teach leads to more students being successful. For many of us, differentiation brings to mind having to prepare multiple worksheets or tasks and lots of extra work. But Boaler shares a different vision, where diverse groups of students work on challenging problems that are easy to access yet have a high enough ceiling to stretch even the most capable. With defined group roles to keep all students accountable, stronger students share their strategies and provide scaffolding to help weaker students grow their own understandings.

As busy people with limited time to read, many of us educators are looking for something we can use immediately in our classrooms. This book provides an extensive appendix of photocopiable homework reflection questions, self-assessments, feedback forms, group work roles and classroom activities.

Another appendix outlines the seven key messages students need to hear in math class:

- Everyone can learn math to the hightest levels
- Mistakes are valuable
- Questions are really important
- Math is about creativity and making sense
- Math is about connections and communicating
- Math class is about learning not performing
- Depth is more important that speed

For anyone who would like to explore these ideas but who does not have time to read, Jo Boaler is co-founder of YouCubed, a website dedicated to these ideas. It includes videos, links to research and a bank of searchable classroom tasks at all grade levels. If you go on Youtube and search Jo Boaler Number Sense there is a great 3 minute video clip by Boaler. She also offers an excellent online video-based course for teachers through Stanford University which covers much of the same content in further depth. If your new year’s resolution was to improve your teaching of math, Jo Boaler’s excellent work is a great place for you to start.