##
**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.