The Book: Mathematical Mindsets: Unleashing Students’ POTENTIAL through Creative Math, Inspiring Messages, and INNOVATIVE TEACHING by Jo Boaler. And yes, it is a great companion to Carol Dweck’s seminal Mindset: The New Psychology of Success. (Dweck even wrote the preface.)
Boar’s explicit goal in the book is to, “[G]ive math teachers, leaders, and parents a range of teaching ideas that will enable students to see mathematics as an open, growth, learning subject and themselves as powerful agents in the learning process.”
To that end she balances insights into different teacher and student dispositions toward math with detailed means of how to create a classroom based on growing intelligence rather than showing intelligence. To that end, she wants students to be in “disequilibrium” with math challenges. That’s because disequilibrium comes from not being able to address new problems with current thinking. So, to “get” something, a student needs to adapt their learning models.
But to move through disequilibrium to intellectual growth, students need engaging lessons which include providing multiple pathways to solutions, inquiry opportunities, visual components, and low floors and high ceilings. Engaging lessons also ask the problem before teaching the method.
The book provides plenty of problems to pose to students that meet all of her criteria and can be expanded to cover multiple standards.
Beyond disposition and technique, Boaler provides research based arguments for ensuring equity that include offering high quality content to all, change ideas about who can succeed in math, encourage underrepresented groups to pursue STEM content, and eliminate or change the nature of homework.
Boaler seems to like to flip things around. Math teachers face the classic, “When am I ever going to use this?” all the time. I figured out a few years ago that students are usually satisfied if I can show how anybody ever uses it. But, next year, thanks to this book, I’ll also try to get students facing any problem to ask themselves: “Can I use math to solve this?”
Jo Boaler is also the cofounder, along with Cathy Williams of youcubed at Stanford University. Youcubed offers resources, ideas, and articles for teachers, students, and parents who seek to make math and open, growth-oriented subject. Youcubed offers self-paced online courses on how to learn math – one course for teachers, another for everyone.
I’ll be signing up for the course as soon as school gets underway. In the meantime I’ll be making a poster this quote that will be our foundation for algebra this year:
“We want to see patterns in the world and understand the rhythms of the universe.” Jo Boaler
The Blog: Kalid Azad, who aims to give readers a “lasting, intuitive understanding of math,” writes the fantastic blog Better Explained – Learn Right, not Rote.
Direct applications for teachers include his ADEPT method: 1) Start with an Analogy to tell what it’s like, 2) Use Diagrams to help visualize it, 3) Provide Examples to help experience it, 4) Talk in Plain English, and 5) Get Technical with formal details. Much of the what he writes about, like Euler’s formula, “imaginary” numbers, and e go well beyond what we cover in my 8th grade algebra class. But it’s still beneficial – by understanding e better, I’ll better explain interest rates and exponential functions. Plus, I like math and it’s refreshing to have my own skills and understanding challenged more than they been have since graduate school in the early ’80s.
To develop intuition, Azad has three tips: 1) Find the central theme of a concept, 2) Explain a fact or property using the theme; 3) Explore related properties using the same theme; and three morals: 1) Search for insights and apply them, 2) Develop mental toughness, and 3) It’s ok to be visual.
Better Explained is clean and easy to navigate. Searching for a particular topic like interest rates is easy, but if you’re browsing for fun, try starting at the Intuition Cheatsheet.