Changing Students Relationship with Math

Jo Boaler Forward by Carol Dweck Mathematical Mindsets—Unleashing Students’POTENTIAL Through Creative Math, Inspiring Messages and INNOVATIVE TEACHING

I finally read Jo Boaler’s book Mathematical Mindsets. I’ve had it in my ‘to read pile’ for a couple of years now even though it was highly recommended to me by more than one educator. Carol Dweck wrote the Foreword and she shares, “Boaler is one of those rare and remarkable educators who not only know the secret of great teaching but also know how to give that gift to others.”

The book was indeed a treasure for me to read and an important reminder on the mathematical pathways we need to purposefully create for each of our students. Boaler reminded this reader, “Mathematics more than any other subject, has the power to crush students’ spirts…When students get the idea they cannot do math, they often maintain a negative relationship with mathematics throughout the rest of their lives” (p. x).

I want to enhance the experiences our students have with mathematics, and even more importantly frame their mindset so they embrace these opportunities rather than shying away from them. There are too many takeaways from the book to list here as you can see from the tabs in my personalized copy, but here are a few reminders that are just incredibly critical for all of to remember.

First, math is not just about numbers. It’s so much more than that. Mathematics is a mindset. “The new evidence from brain research tells us that everyone, with the right teaching and messages, can be successful in math…” (p. 4). In other words, how we teach and the messages we convey to our students while we are teaching matters...a lot. Starting with changing the way students feel about mistakes. “When we teach students that mistakes are positive, it has an incredibly liberating effect on them” (p. 15).

Boaler shared a teacher’s example of how she helped her students understand that mistakes are a way for the brain to make connections, learn, and growth...literally. Students were asked to take a perfectly smooth piece of paper, smash into a ball based on the frustrations they have when they make a mistake in math, smooth the paper back out, and draw colored lines where creases were created. She likened the scattered colored lines to the growth that occurs in the brain when a mistake was made. The students were then required to keep this piece of “brain art” into their math notebooks as a reminder of what happens to the neurons and dendrites in their brain when they make a mistake...they grow and connect.  One student’s brain art said, “Biggest mistake you can make is being afraid to make one” (p. 17). There is so much truth in this statement.

Next, Boaler reminds us a mathematical mindset is not a passive activity. Students must see their role as active participants, trying to understand and make sense of numbers and the patterns they create in the world around them. This productive struggle “number sense and mathematical mindsets develop together, and learning about ways to develop one helps the development of the other” (p. 36). Teaching students their disequilibrium of what they know and what they don’t know yet will be a constant theme while learning, but risk-taking and collaboration with others will be valued.

Moving away from redundant math facts and mindless homework “practice” into engaging relevant tasks that give students multiple opportunities to show what they know starts with how teachers facilitate student’s learning. Rather than walking the reader through an abstract explanation of math instruction, in chapter five she provides five examples from schools across the country who purposefully planned rich mathematical tasks and the impact it had on student motivation and engagement. Boaler states, “These are all cases that I have personally witness among groups of people and that have given me important insights into the nature of the teaching and tasks that bring about such learning opportunities” (p. 58).

The case studies demonstrate how teachers create mathematical excitement and offer critical insights into students discovering the openness of numbers, the power of visualization, making connections, and moving beyond memorization and speed of computation. I know this will be the go-to chapter for teachers because Boaler also shared how to strategically design tasks that create and encourage excitement about mathematics including thinking about how to...

1. Encouraging multiple methods, pathways, and representations...more than one way.
2. Encourage inquiry...What if?
3. Ask before modeling...curiosity is a great motivator.
4. Use visuals...make it tangible.
5. Make it low floor and high ceiling...think accessibility for each student.
6. Can students convince and reason to a partner or group...be skeptical.

Then, Boaler also bravely addresses equity. “All subjects extend to difficult levels; the reason so many people think math is the most difficult is the inaccessible way it is taught. We need to change the thinking around this if we are to open mathematics to many more people” (p. 96). Developing a mathematical mindset should be an opportunity provided to each student. To make math equitable Boaler recommends…

1. Offering high-level content to all students.
2. Changing mindsets on who can achieve in mathematics.
3. Encouraging students to go deeper with their thinking and reasoning.
4. Moving out of isolation into a collaborative setting.
5. Providing more positive framing and encouragement to girls and students of color, and
6. Forget homework…enough said.

Finally, there are times when I read a book and I am so overwhelmed with the ideas and content, but this was not the case with Mathematical Mindsets. I felt a sense of relief when I read the final chapter because Boaler provided a pathway on where to start to support all students developing an appreciation for mathematics. “In this chapter I will provide a set of teaching ideas, drawing from throughout the book, that can help you create and maintain a growth mindset mathematics classroom” (p. 171).

As Boaler’s subtitle states, “unleashing students’ potential through creative math, inspiring messages and innovative teaching” is an opportunity we should all prioritize for our students as learners now and as they continue to learn.