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.
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.
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.
So what is Authentic Inquiry Maths?
Mathematics is a language that helps people understand the world in which they live.
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.