Authentic Inquiry Maths - Revisited

This was my very first post, written over a year ago.

Time to revisit and see if it still holds true...

Authentic Inquiry Maths

Did you ever read a book called “The Number Devil”  by Hans Magnus Enzensberger? If you ever see a copy of it, grab it and have a look. In chapter one, Robert, the hero of the story, meets the Number Devil. The Number Devil explains to Robert that knowing a little bit of arithmetic, such as addition and subtraction, is quite useful for when the batteries of your calculator run out but really it has little to do with mathematics.

How often do teachers fail to grasp the distinction? How often do we overstate the importance of the “skills” that we fail to recognize the importance of their application? It’s like a football team that focuses so much energy on their training sessions that they forget to turn up to play their game.

I had some parents come to me with a few questions last week about the importance of skills and learning multiplications facts. I agreed - yes, that's important - but it's also important to know why we do something.

The place of skills training

Make no mistake – a good level of competence and fluency with operational skills is useful in producing fast and accurate calculations.

Make no mistake – the skills are not an end in themselves.

TRAIN for the GAME

Just like a sports coach, I believe that students need to train to develop skills.

By “TRAIN” I mean:

Tedious Repetitive Activities Involving Number

Just as in a sporting context, what we do in training is useful. A football coach will drill players over and over until they get mastery of the skill.

But this is not the end of the process. There are no trophies for the team that trains the best or has the best drilled skills session. The skills need to be employed and articulated in the game context.

Yes, I still agree that all players need to learn skills. It'd probably also important to know that great players keep practicing when they get home. 

By “GAME” I now refer to:

Genuine Application of Mathematical Experience

Children have a great capacity for learning and replicating very sophisticated processes and operations. Does this necessarily imply understanding? I’d be inclined to say no – I can’t really observe understanding until I see how students apply their knowledge or skills to a real-world problem.

Just as the coach wants to see his players apply their ball skills in the game, I want to see my students apply their maths skills in the real world.

We're heading into grand final season for all our winter sports here in Oz. Now the players get to really demonstrate their abilities. It's too late to start learning how to kick the ball - all of that should have happened at training.

So what is Authentic Inquiry Maths?

Mathematics is a language that helps people understand the world in which they live.

That previous statement could almost have been lifted straight from "Making the PYP Happen" - "

"In the PYP, mathematics is viewed primarily as a vehicle to support inquiry, providing a global language

through which we make sense of the world around us." (pg 81)

When we get students who are keen to apply their knowledge and skills to make sense of the world around them, then we see authentic inquiry learning happening.

To get to this point, there are a few things that I feel are central to authentic inquiry in general and maths in specific:

1. Inquiry is in response to a provocation or problem drawn from real-life experience.

2. The provocation may be chosen or decided by the teacher but the direction and focus of the inquiry is determined by the student.

3. Inquiry is an open-ended process that follows a cycle – good inquiry leads to further provocations and problems to investigate.

4. Collaboration is central to effective inquiry to ensure multiple perspectives and relevance to a diverse audience.

5. An inquiry moves the student from the known into the unknown. It needs to challenge the student to question his or her own understanding.

6. An inquiry is transdisciplinary. In maths, this means a shift in thinking away from “pure maths” to a focus on “real maths”.

On this framework I intend to develop my own exploration into the world of maths and maths education. As a teacher and learner, I aim to follow my own advice – to TRAIN for the GAME.

Yep - I'm still thinking about it, trying to make sense of the world around me, still learning...