Rethinking How We Teach Maths

In this blog I will discuss the professional development I am currently taking on mathematical mindsets from Jo Boaler at Stanford University. Lesson 1 gave us a brief introduction to the ideas of the course, we will begin this blog at Lesson 2. Follow along with this series to read about Lessons 3 and 4.

Setting up a Mathematical Mindset Class

The focus in Lesson 2 was on how we engage students to understand 4 key points:

1. Maths is an open and visual subject

2. Everyone’s brains can grow and change

3. Maths is not about speed

4. Struggle and mistakes are good, that's when brains are more active and strengthening pathways

Why should we focus on these 4 points?

Photo Credits: Jo Boaler, Mathematical Mindsets, Stanford University

Jo focuses on how it is far easier for the mind to compress concepts rather than methods. She introduced the idea that big understandings fire the synapses in our brains and then convert it into compressible learning.

Continuing the lesson, Jo worked us through a series of visuals and activities. I saw clear connections to the first 3 points, ‘maths is an open and visual subject, everyone’s brains can grow and change, maths is not about speed’. 

Visualisation

In the example below the goal is to look at a collection of dots quickly and count (without counting) the number of dots.

Photo Credits: https://davidwees.com/content/math-talk/

Using this image as an example, we would quickly see the dots and explain how many dots we saw and how we visualised it. In Jo’s clip with students, they discussed how they visualized the number and realized there are multiple strategies to find the collection.

We then looked at numbers 1-36 represented as dots. As students, we were asked to look for patterns in the dot sequences. What patterns do you see?

Photo Credits: Jo Boaler, Mathematical Mindsets, Stanford University

I can see clear connections with multiplication. Number 2 is represented by 2 dots, the number 4 is represented as two sets of these 2 dots next to each other. The number 8 is 2 sets of the number 4. The number 16 is 2 sets of the number 8 or 4 sets of the number 4. It is the same for the 3, 6, 9. I found 12 interesting because they used the 3 sets of 4 and not 4 sets of 3, however the 3 sets of 4 are shaped in a triangle representing the patterns of 3. 

Methods of Teaching

Finally, we were briefly introduced to how to teach mathematical methods. Jo compared 3 ways of teaching.

Photo Credits: Jo Boaler, Mathematical Mindsets, Stanford University

Jo concluded that the 3rd method had the greatest impact on student learning. She believes that they are more engaged and receptive to the methods being taught.

What are my takeaways?

I really enjoyed this lesson. The emphasis on the four key objectives: maths is an open and visual subject, everyone’s brains can grow and change, maths is not about speed, struggle and mistakes are good, that's when brains are more active and strengthening pathways, was evident throughout the lessons and clips of her teaching.

The clips of the teaching felt genuine. In lesson 1 the videos seemed staged and came across as a marketing campaign, however in lesson 2 I believed I was watching a real teacher conducting a real lesson. The students were engaged and passionate when sharing. The ideas expressed by the students were being reviewed by their peers and then alternative solutions were offered. The 4 key objectives for this lesson came across as the driver behind this lesson. At the end of this lesson I was inspired to focus on growth mindset and giving students chances to learn through exploration of mathematical concepts.

Where to next?

What I hope to see is a focus on how the 4 principles that were well-presented and inspiring fit within a national curriculum. Specifically how do you allow enough time to explore challenging problems prior to teaching methods and still meet all the expectations of the curriculum. I would like to know what planning documentation looks like. How do we focus on maths as an open and visual subject, maths not being about speed, struggle and mistakes being good within our planning? In New Zealand, when looking at Number, we look at Number strategies, Number knowledge, Equations and Expressions and Patterns and Relationships. I am interested in how we plan the approach presented by Jo Boaler within our curriculum while also addressing these areas in Number. 

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