Jo Boaler - Mathematical Mindsets - Chapters 4/5

WHAT

CHAPTER 4

- Children have a natural mathematical curiosity
- The best thing we can do for young students is to get them to play with numbers
- Children should see maths as conceptual, growth subject that they can make sense of, not just a series of short questions that don't relate to anything.
- Number sense is about understanding numbers, what they represent and the relationships between them.
- Putting pressure on students through timed tests has been shown to cause anxiety.
- It is recommended to use strategies or memorisation. Strategies have been shown to be more effective.
- There is a bit of a myth about maths practice. Mindless repetitive practise doesn't produce results. Practising the same problems in different forms is preferable.
- When problems are represented in their simplest form then students are not given the opportunity to think and are often confused by slight variations (e.g a hexagon)
- Homework does not help students improve as mathematicians.
- Number talk is an effective pedagogical method for teaching number sense. This involves posing an abstract problem and encouraging students to share how they solved the problem.

CHAPTER 5

Rich math mathematical tasks

- Teachers are the most important resource for students. We create the environments, give positive messages and set engaging tasks.
Ways to create rich tasks -
1. Open the task to encourage multiple methods, pathways and representations
2. Make it an inquiry task
3. Ask the problem before teaching the method
4. Add a visual component
5. Low floor, high ceiling
6. Add the requirement to convince and reason

SO WHAT/NOW WHAT

We are going to be focusing on multiplication and division early next Term. Previously I would have used time activities and repeated practise. I will still include elements of memorisation, but I will have a greater focus using visual aspects and showing questions in multiple ways. Using a thinkboard and the Piccollage app on the Ipad will be a great way to do this.

When planning RIch tasks I will refer to the ideas from chapter 5. One of the ones that stands out to me is to create the task and then teach the method. This will get students interested first and actively trying to seek out ways to solve the problem. Once the method has been taught, they are more likely to want to use it as they will see a purpose for it.