Developing Critical Numeracy Across the Curriculum

Teacher Experiences

In 2008 a group of Tasmanian teachers took part in an Action Research project to explore how to bring "critical numeracy" into their classrooms.

Each group session explored a key topic such as percentage, average or graphing and how students of different development stages thought about these concepts. Teachers looked at articles from the news and critically analysed them, developing a sense of what critical thinking in numeracy might look like.

Following each session they designed a lesson around an article from the news and trialled it with their own classes or other classes in their school. They collected work from the students which they then shared in the next group session, unpacking what went on and why.

Not every lesson was successful, and many emergent learnings occurred. One of the important things teachers found was that they themselves were not well-versed in bringing critical numeracy thinking into their teaching and that it was a skill they needed to practice consciously. By having a collegial community of practice they could practice this with each other, as well as support each other in being able to make sense of what was happening in their lessons.

Some realised that they needed to take on "teacher roles" in the classroom that were different to their normal maths persona. So many of them actually trialled lessons with other classes before doing so in their own classes, in order to build up confidence and iron out issues.

Another key realisation was that one-off activities using contexts from the news might be useful to help students practice critical thinking, but it would be far more effective to integrate critical thinking in planning for whole topics. See an example of this in the average learning sequence designed by the teachers.

 

Teacher Experience


"In my first activity I created a worksheet which scaffolded students through some of the different stages of critical numeracy based on interpreting a graph about recycling. I had a few questions towards the end of the worksheet that I considered higher order critical thinking but despite the scaffolding there were few students who attempted them.

"When I discussed it in our action research group I found that Elsie had done the same activity but in a far more open-ended way. She drew out what students already knew about percentage, got her students to work in pairs to explore the graph and then had a discussion where she led the students into deeper meaning-making and analysing. The students then wrote a newspaper article to go with the graph, which seemed to me very creative (and not the sort of thing I would have considered for a maths lesson.)

"I realised how unreasonable it was for me to expect my students to move to critical thinking on their own. So while I had considered I had scaffolded through the worksheet, in fact they needed a different kind of scaffolding - one that enabled them to hear alternative views and take time to play with the alternative meanings in order to reach a higher order understanding."
 

Questions and Issues

How do we make better connections?

"There is an issue of teaching foundation skills in their own 'box'. Students can't see when it is important to recruit these understandings to apply to other contexts. How can we help make better connections for students between the context, the mathematical idea and the maths tools?" 

How do we know students' thinking?

"It is important to have a sense of likely student misconceptions from the research - it gives me a sense that my students are normal. But I also need to find out exactly what they are thinking about - help them to articulate their "alternate" views and explore the merits of them. I wonder what alternate views I might be holding?"

Assessing

"How do we assess this sort of thinking? How might we change our assessment to value critical thinking in maths? How might students assess their own abilities to critically reflect?"

Authoritative knowledge

"Students may see information coming from particular sources such as a newspaper as 'authoritative knowledge' so it is important to help students see that it is okay to question such knowledge."

Changing teacher roles

"I have come to realise I have been quite a procedural maths teacher - students follow the rules of maths to complete maths worksheets individually. I found I had to adopt a new style of teaching - allowing for discussions or more group work so students could develop conceptual and contextual understandings."

Choosing and designing activities

"How can we develop an eye to see the potential of contexts in building critical thinking? What are contexts that we are comfortable with and which we think the students will relate to? How can we use creative activities which enable students to demonstrate their critical thinking?"

Meta-cognition

"How do we develop our own capacity for critical thinking? How do we make the Four Resource Model thinking a natural part of our thinking processes? Practice, Practice Practice? How do we know we are doing it well? How do we model it for students and help make visible the different aspects?

Tangents and emergent learning

"When I am teaching something new it is hard to know what is on track and off track. I realise I need to give myself and the class some scope to explore the tangents because very interesting things can happen, but at the same time I need to be focussed on my intent for the lesson."