On Mathematical Mindsets

I was finally able to finish Jo Boaler’s Mathematical Mindsets, thanks to the seven hours of flight to KL and back. 🙂 As I wrote in my previous book blog post on Mindset by Carol Dweck, Mathematical Mindsets was the first book I began reading this year but I ended up finishing Mindset first.

Jo defines the mathematical mindset as one in which “students see mathematics as a set of ideas and relationships, and their role as one of thinking about ideas and making sense of them.” She then goes on to say that, although young children may begin to develop (what Carol calls) a growth mindset in mathematics early in life through games and puzzles, this quickly changes to a fixed mindset when they enter school, where they are forced to memorize number facts and follow a single, procedural pathway through timed tests and homework, in which they mindlessly apply a decontextualized mathematical procedure again and again. This in turn privileges students who memorize facts and procedures easily, deceiving them into believing that they are mathematically “gifted” (a myth that a fixed mindset apparently perpetuates), and, conversely, causing those who don’t memorize easily to believe that they are dumb in math or, worse, that they are dumb, period.

In lieu of these bad pedagogical practices, Jo offers evidence-based alternatives. For instance, instead of timed tests, which (can) cause lifelong and possibly debilitating math anxiety, and which give the impression that the essence of mathematics is being fast, she recommends the use of conceptual mathematical activities without time pressure (see e.g., the activities in her Fluency Without Fear web article). Jo also believes that homework that involves mindless practice of disconnected procedures should be replaced with reflective activities, if not eradicated altogether. And instead of “tracking,” in which students get placed into ranked sections, with the lowest performing students being placed in the bottom section, Jo recommends teaching heterogeneous classes instead, using strategies such as open-ended tasks, a choice of tasks, individualized pathways (using, e.g., SMILE cards), or the complex instruction model of Elizabeth Cohen and Rachel Lotan.

What I liked about this book is that it references many research studies (Jo’s as well as others’) and mathematics pedagogies. What I didn’t like about it is that ideas are repeated in the same form again and again and again (get the idea?) throughout the book, bloating it. Jo also tends to toot her own horn (e.g., “In an award-winning research study… I…”), when she obviously doesn’t have to. But I understand how difficult it is for academics to write popular books, so I take my hat off to Jo Boaler (and Carol Dweck) for making their results accessible to those of us who are not experts in their fields.

Possible books for next month’s book blog post:

  • Pernille Ripp’s Passionate Learners: How to Engage and Empower Your Students (2016);
  • Kevin Carey’s The End of College: Creating the Future of Learning and the University of Everywhere (2016); or
  • Greg Toppo’s The Game Believes in You: How Digital Play Makes Our Kids Smarter (2015)

Till then!


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