Boaler prompts us to think deeply about the characteristics and actions of real math teachers and mathematicians young and old, novice and professional with a number of lists, lists I'll return to as I design, adapt, and apply learning tasks and endeavors with my fifth grade students. The ideas below are directly culled from Boaler's book. I've written an oversimplification of her ideas, hence you should read her book, but these lists will get me started when it comes to embedding her rich research and ideas into my practice.
You are a Mathematician when. .
- You are comfortable being wrong.
- You try out seemingly wild ideas.
- You are open to different math teaching and learning experiences.
- You play with ideas without judging them.
- You are willing to go against traditional ideas.
- You keep going even when the work or problem is difficult.
You Teach Math Well when you
- "open up the task so there are multiple methods, pathways, and representations."
- "include inquiry opportunities."
- "Ask the problem before teaching the method."
- "Add a visual component and ask students how they see the mathematics."
- "Extend the task to make it lower floor and higher ceiling." (wide breadth and accessible to many)
- "Ask students to convince and reason; be skeptical."
You engage students when. . .
- "the task is challenging but accessible"
- the task is seen as a puzzle.
- includes visual thinking tasks that brings about understanding
- students have a chance to develop their own way of seeing the problem and solution
- the classroom environment allows students to be unafraid of making mistakes and proposing their own ideas
- students respect each others' thinking
- students use their own ideas
- students collaborate
- groups represent diverse skill, ability, perspectives
Positive math activities often include these steps:
- posing a question
- going from the real world to a math model
- performing a calculation
- returning from the model to the real world to see if the question was answered or problem solved.
