Real mathematicians are inquirers.
They have a curiosity of how something works mathematically, what they can do with their new understandings and then think about what they could discover next.
Not so often are children giving opportunities in maths where they can orchestrate what they want to discover nor take ownership of their learning. When we as teachers are constantly feeding them activities to do, they aren't being mathematicians; they are just having maths happening to them.
One strategy I have experimented with over the past few years is to present the class with the central idea. We discuss its meaning and then we brainstorm possible questions we could explore to become experts of its understanding.
Here is what we brainstormed for our unit into place value & number systems:
Doing this first in small groups before sharing as a class also served as an assessment tool. I was able to see where student's understanding of place values were at from their group discussions and by the type of questions they were generating.
I thought we came up with some really interesting questions to explore and these have now become the basis of our maths unit.
The next day we reexamine these questions, perhaps add some more ( as we will continue to do throughout the unit ) and think of what we should do to find out.
For example, to find out 'What are the advantages to a base 10 number system?' we thought we should:
- explore how the base 10 number system works
- compare it to other number systems (Roman numerals, Ancient Egyptian, Babylonian etc)
- discover why it is easy to multiply or divide by 10, 100, 1 000 etc
To find out 'Why does it need to extend infinitely in both directions?' we thought we should:
- find out just how far place values go in each direction: what comes after trillions or trillionths?
- why do we even need numbers like trillions? What about trillionths?!?
Looking at the scope & sequence, I already had in mind that we should be exploring:
° place value of whole and decimal numbers
° the idea that our number system extends infinitely in both directions
° comparing ancient number systems such as Roman numerals
° finding out why we can multiply / divide whole & decimal numbers easily by 10, 100, 1 000 etc
From brainstorming our own questions about our central idea, the students were able to create enquiry questions that covers the expectations of the scope & sequence, but they had the opportunity to think of what they feel they need to find out and the unit becomes much more student-centred. We keep our central idea with guiding questions displayed in our room and refer back to them often.
'What have we found out?'
'What should we do next?'
'How has this activity helped us to understand our central idea?'