Tonight our school district sponsored a webinar for parents about mathematical mindsets. The main speaker was Jo Boaler, from Stanford University, who is arguably most famous for establishing the YouCubed online math community and for reigniting and popularizing (within education at least) the ideas of growth and fixed mindsets, which were originally coined and researched by Carol Dweck in the 1970s.

This post is a little different from my usual, as it is a reflection and the beginnings of my processing the information shared tonight. Inspired by the webinar, though, you can expect several more specific posts that you’ll see coming in the next few weeks and months.

The webinar was divided into four different parts. First was information, principles of practice, and research presented by Jo Boaler. This research was followed by taking audience questions. Third, she moved into specific recommendations (some of which will be reviewed in forthcoming articles) to parents. Finally a second presenter — Yolanda Beckles from The Knowledge Shop — presented as a parent who works specifically with parents and families on “raising STEM kids.”

Here I want to summarize what I got from the research portion of the evening. Again, look for more details and reviews in future posts as I process and revisit this information more over time.

The research/informational presentation fell into two main themes: five mathematical mindsets for high math achievement, and fixed views of math vs number flexibility. While I attempted to write down the statement of the principles as accurately as I could, the summaries/descriptions/commentaries are my own.

Boaler’s five mathematical mindsets for learners:

Neither intelligence nor ability is “fixed” or “preprogrammed.” Our brains learn constantly. The neurons form new pathways, build new connections, strengthen old connections. We are always learning as long as our brains are alive. Learning is something our brains naturally do.*Our brains are constantly growing and changing.*. I think what was meant here is that it is the time of the most brain growth. If there is no struggle, then it is likely we already knew the material and our brain is not growing. It might be strengthening already-strong connections, but there is only so much stronger they can become. Building new pathways and connections, and building the initial stages of that myelin sheath (which is what makes established connections stronger and also more efficient) are the results of actual learning and building understanding.*The best time for our brains are when we are struggling and making mistakes*Brain chemistry is a crazy thing. We’ve been learning that the same chemicals associated with negative emotions and stress can block learning and brain growth. Yet the brain chemicals associated with positive and calm emotions not only leave our brains open to learning but are released when we learn something new. Learning actually makes us happy!**Let go of limits: what you believe about yourself changes what your brain can learn.**. We are designed for multiple inputs. Our brains process information in many different centers, and creating connections between those processing centers for different ideas builds more and deeper understanding of any topic, not just mathematics. We can take advantage of this in math, though, by presenting information numerically, graphically, in pictures, in words, using models, and more. Often, presenting mathematical ideas in a variety of ways is essential in teaching neurodiverse populations. (I write here of both “diagnosable” neurodiversity and also the wide natural diversity in how each our brains prefer to receive, process, and communicate information.) More than this necessity for finding a way to communicate with each of us, multiple presentations allows everyone to create neural pathways and build stronger**The most powerful brains are interconnected***and more useful*understanding of ideas.(Yes, Boaler is British and says “maths” instead of the American “math.”) Early in her public career, Boaler became one of the most known researchers studying the impact of timed tests on students, particularly with respect to math anxiety. It is now widely recognized that an emphasis on speed in math class can hinder learning. Not only is it anxiety-inducing for many people, but speed also prefers surface-level rote memorization over deeper understanding. As Boaler quoted tonight, this type of speed-based learning creates “easy come, easy go connections.” However, we in the teaching field are recognizing that there has been a bit of an overcorrection. Many have equated the ideas of speed with fluency, and thus education has slipped a little from its focus on fluency. Fluency is still important, and a lack of fluency can make later math more difficult. I’ll save more on this for a future post, but for a quick preview, you can see a little more in my post on learning multiplication facts.*Being good at maths does not mean being fast.*

Boaler then went on to share about mindsets of “fixed mathematics” vs “flexible numeracy.” While this seems a callback to her oft-criticized adaptations of Dweck’s fixed vs growth mindset work, I appreciate that this changes the focus to the activity and the mathematical approach.

Students or their parents or teachers might be practicing a “fixed mathematics” mindset if they believe there is “one correct way” or only one appropriate method to solve a mathematical problem. This mindset may be in play if students consistently * rely* on rote memorization of either facts or counting patterns.

“Flexible numeracy,” in contrast, is expressed by an ability to perform mathematical operations in multiple ways, use ideas of numeracy to estimate (or as Boaler now says “to ish”) or to find alternative means of calculation, and to use multiple ways of modeling mathematics. Flexible numeracy is associated with “high achieving” mathematics students in both Boaler’s and her predecessor’s research, while “fixed mathematics” skills are associated with “low achieving” math students in that same research.

I think there are few teachers who would be surprised by this connection (besides the few who still believe rote learning and timed testing are valuable — a diminishing perspective, thank goodness). However, I am curious to explore what implications this research has not only on mathematical growth through early numeracy, but also in more challenging situations such as dyscalculia, trauma, traumatic brain injury and more. One of the more common criticisms I’ve seen of Boaler’s work is that it underplays the role of a variety of types of diversity, sometimes oversimplifying the messages. I’m not sure how much research I’ll find on these themes, but I’ll definitely be looking out for it. And when I find it, I’ll share it with you.

Besides, those curiosities, I have a lot of thoughts and reactions to the information from tonight. I hope to make these helpful to you, so watch this space!

**You’ve Got This!**