Everyone seems to be having a summit these days so I thought…why not teachers of mathematics?
Today marked the start of our ‘meeting week’, a week without students in which staff meet to reflect and review on the academic year about to end and to plan for the one ahead. All teachers of secondary mathematics in our school met today to look at algebra across these year levels.
Our goals were:
- To develop a common understanding of the purpose of algebraic processes and thinking
- To develop a common language to be used
- To explore and compare personal beliefs regarding the teaching of certain aspects of algebraic thinking and processes
- To reflect on these and compare them to available research
- To develop a coherent thread of algebraic thinking and processes from Y7 to Y12 as much as possible
There were specific ‘rules’ for the environment in which this was to happen:
- One of professional respect
- One of respectful challenge, rather than mutual endorsement. Expect to justify what you say in terms of how it contributes to improved student learning. All voices need to be heard.
- One that accepts that you will not always get what you want but one of continuous capacity building; of each teacher and of the faculty
- Where we consider ‘our’ students rather than just ‘my’ students
Teachers worked within small groups of 4 or 5. We started by articulating the meaning for the common algebraic processes of expand, factorise, simplify and solve. This brought out a few misconceptions and helped to build a common understanding of the language we use.
Participants were then asked to think about what algebraic thinking involved and looked like. Then everyone was asked to respond to the following – with respect to expansion, factorisation, simplification and solving.
- What mistakes are typically made by students when expanding?
- How do you/ would you teach expanding?
- How does the way you currently teach expanding relate to how it is taught at other levels?
- How could you develop your teaching of expansion to deliberately address algebraic thinking?
Following this, teachers compared approaches as to how they would teach students to factorise a particular quadratic trinomial, solve an equation involving two algebraic fractions, complete the square etc. The catch cry became “think back, think forward”..ie. how does this process relate to what students already know and how will it link to what they will experience in the future?
We briefly looked at how the CAS calculators can be better used to develop algebraic thinking by allowing students to experiment, get answers, look for patterns, generalise, predict.
A really collaborative, open discussion that I think will set the scene for professional dialogue to come.