Developing a "critical numeracy" equivalent to the 4 Resource model of Critical Literacy

I have been working on a project which is looking at developing "critical numeracy" across the curriculum. One aspect has been working with teachers in an Action Research project which has explored the issues of creating critical numerate thinking classrooms (of which there have been many).

The other aspect is updating (and re-visioning) the website Numeracy in the News which provides good articles for students and teachers to bring critical thinking. The newspaper article provides a context for maths ideas and terminology which are often used in confusing, misleading or controversial ways. They are a way of engaging students in critical thinking or debate and deeper thinking of both the numeracy ideas and the context itself.

But developing "critical thinking" in numeracy is problematic....

The notion of "critical thinking" can have different meanings and intents based on whether one is bringing a postmodern consciousness versus a modernist consciousness. The Four Resource model (developed by Luke and Freebody) develops an approach to Critical Literacy which clearly comes from a postmodernist perspective. Both science and maths teaching cultures seem heavily situated in a modernist culture. For example, Conceptual Challenge Theory, used as constructivist practice in science teaching, asks students "Is your concept intelligible, plausible and useful?" in order to convert them from their "misconceptions" to the "right" conception. So underlying this "critical thinking" process is an assumption that:

• there are "truths" and "right" conceptions,
• it is based on a limited notion of scientific inquiry (primarily seen as an empirical lens) without bringing in any sense of critique of the science lens,
• the teacher owns the process of leading students through.

A postmodern/integral approach to it would value a metaphor of curriculum as conversation - where everyone, including the teacher would be treating the subject as something to inquire into, and understandings can be enriched by using different lenses. The teacher would also make visible the critical thinking strategies. So rather than scaffolded worksheets where the teacher might have in mind a larger vision of the thinking process and from that write directed, linear questions whose origins are invisible to the students, they would be helping students also see key thinking strategies and help empower them in using these.

Now most of you are thinking "Hey, that is not rocket science." But what I have found in this project working with teachers is that making the big underpinning thinking strategies visible is not simple - mainly because of an unfamiliarity of using such generic thinking strategies, most of which seem irrelevant to the business of coming to know a maths idea. Maths teachers often become trapped in quite procedural ways of knowing maths and it is hard to break out of that box. So teachers might be happy to ask students "Is it true?" but find it hard to get into the more "critical theory" based questions - "Are there different meanings? What are the value systems here? What are the purposes? Who might be silenced? How does it position me? What am I going to believe? What decisions are likely to come from this?"

But should these type of quesitons be part of critical numeracy? Why do we want to have critical numeracy anyway? Perhaps to help students develop discernment - so they can make balanced decisions about social, environmental , political or health issues.... So critical numeracy becomes one lens that students can apply, along with ethical, scientific, socio-cultural, spiritual lenses. So is it OK for critical numeracy to just ask questions "What does it mean? Is it true?" or should it ask more? And if it asks more, can it ask them in such a way that it is easily accessed for people who have been encultured in a modernist discipline area?

And can the model itself act as a transformational tool for teachers in helping them to emerge from the modernist box?

So my trick has been to create a numeracy equivalent to the 4 Resource model for Critical Literacy which is being used in our schools. I wonder whether this can provide a bridge between disciplines? I have integrated ideas from Conceptual Challenge Theory and the Harvard Project Zero Visible Thinking project.

However, it is too easy to fall in love with a model that you have invented. I want to now apply holistic, postmodern and integral lenses to it. And it is very clear that this model privileges the "mental" ways of knowing. How does it integrate heart, mind and soul to develop not just reasoned discernment, but wise discernment?

What are your thoughts?