Developing Critical Numeracy Across the Curriculum

Thinking Strategies


Harvard Project Zero
Visible Thinking

Explains why it is important to make thinking visible

Develops thinking ideals

Provides easy to use thinking routines

Shares teacher experiences in using thinking strategies

Making the Four Resource Model for Critical Numeracy explicit

The Four Resource Model for Critical Numeracy can act as a checklist for both students and teachers in asking "What sort of thinking have we been doing?", "Do we need to explore other types of thinking?", "What happens if we ask analysing questions now?"

It is a simple model that students can use to make their thinking visible - and one that they can use in literacy as well as numeracy.

One teacher in The Action Research Project for Critical Numeracy said:

"We were having a great whole class discussion which I thought was going quite deep.  Later when I looked at the Critical Numeracy Model I realised that a lot of our discussion was around meaning-making - with some questions that related to analysing. I realised how important it was for me to practice critical thinking in all the quadrants myself. I tend to only consider a few aspects and this is now stretching me."

Thinking routines which support the Critical Numeracy Model

Thinking routines are regular thinking strategies you might use over time with which students become familiar. Students can use them in cross curriculum contexts. They are designed to be simple, memorable and to extend thinking beyond habitual limited patterns. Below we suggest thinking routines from the Harvard Project Zero Visible Thinking website, as well as some others which can support development of critical numeracy:

I see, I think, I wonder

Think, pair, share

3 Things I know, 2 questions, 1 analogy

Connect, extend, challenge

What makes you say that?

Generate, sort, connect, elaborate

Thinking Routines which can support the development of Critical Numeracy

Futures Wheel


Does it fit?

Creative Hunt

Options Explosions

Question starts             Claim, support, question

Stop, Look, Listen        True for who?

Step Inside: what does the person perceive, know, care about?

Tug for truth                Circle of viewpoint

de Bono's 6 hats

Developing student meta-cognition

During and after activities students can be asked to reflect on their thinking using such questions as:

  • What surprised, intrigued, inspired or challenged you?
  • How have your ideas or values changed as a result of this thinking process?
  • What questions or strategies did you find most useful in developing your thinking?
  • If you were to do this activity again how might you do it differently and why?
  • What strategies might you use in the future to further develop your thinking skills?
  • What mathematics would you like to know more about as a result of this investigation?

Useful Research and Links

Developing communities of Thinking - Dr Yoram Harpaz - homepage