# Mathematical Curiosity

Curiosity –  Can you think of a time when you or your kids were mathematically curious?  When it comes to math it seems that we focus on knowledge not on curiosity.

Jo Boaler’s course interviewed several speakers who have a passion for math, people who have what she calls an ‘inquiry relationship’ with math.

Computer scientist, educator and robotics designer, Sebastian Thrun, spoke about having an intuition. I marvelled when Sebastian Thrun explained how he looks at a math problem and develops an intuitive understanding of the solution. In fact he states that we should not move further with the problem until we have an intuitive understanding.  Then he takes a further two weeks to fully solve the problem mathematically. I marvelled because the intuitive understanding of the solution comes first.

Take a look at the qualities identified in an inquiry relationship:

###### Image from How to Learn Math by Jo Boaler.
• being curious
• making connections
• not worrying about uncertainty or making mistakes
• using intuition
• exciting inquiry – you can solve any problem

As an educator I can only say:  “Help me develop these qualities in the young learners in my classroom!”  In fact help me live my life that way.  It would be ever engaging.

My question is: “How do I give students who do not have the inquiry relationship  – this curiosity,  sense of intuition, and connection that makes math come alive?”

Today my online grade 3 students shared their solutions and processes for solving a math question related to patterns. Afterwards we talked about the things that we do as mathematicians to solve a problem. As a collaborative group, I was pleased with the ideas these grade threes identified. However I need to go further to guide my students to as they make the inquiry relationship their own.

At first they may not see how all this happens but as parents and teachers, model and talk about curiosity, courage, intuition and connections  – students will see what an inquiry relationship looks like.  By identifying attitudes, thought process, a willingness to take risks, and communicating that math is an engaging challenge and fun, I think we can guide students to develop this passion and connection.

There is more.  Intuition and curiosity are linked to understanding and confidence. Jo Boaler describes these qualities as a double helix.

Understanding and Intuition

Confidence and Curiosity

These attributes are iterative, a child must develop the understanding to gain intuition and intuition carries understanding further.  Confidence grows as curiosity is satisfied and curiosity depends on the confidence to explore.

Cultivating those qualities in a math classroom means that as a teacher I  promote, model and identify those qualities as we engage in a mathematical world.

# Teacher Language Matters

As I listened to examples of number talks in the math classroom, this stands out, teacher language matters.

“I think I heard you say.”

“How did you know you should have…..”

“Where do you think your mistake came from?”

“So you are saying…”

“How did you figure that out?”

“Do we see it another way?”

“How do we see this one?”

The teacher’s language conveys that effort, thinking processes  and grappling with the ideas are what matters. Students have the freedom to explore the ideas.  Relational equity develops as each student’s contribution is valued and analysed in an effort to come to a common conclusion.

And there is more … students see that math is a beautiful, creative and connected subject.