Sharing Professional Practice

Well – it’s been a while, hasn’t it? The pressure of the immediate, Year 12 examinations, multiple administrative tasks, preparing PowerPoints for conferences, meetings with colleagues, students and parents…it must be term 4!!

A couple of posts ago I mentioned that there was a group of people in various schools here in Melbourne who were looking at what constituted ‘good work’ within their disciplines, within the profession and within professional teams. At a recent conference, I, and a couple of other teachers, presented on what we believed constituted good work in our chosen disciplines. We developed our theory of ‘good work’ around a quote from Mike Schmoker’s book: Results Now: How We Can Achieve Unprecedented Improvements in Teaching & Learning (ASCD 2006) : “Teaching is only as good as its impact on learning”. Our hypothesis was that students only authentically learn if they understand. We then investigated what understanding looked like in mathematics, history and the visual arts; how to develop those understandings and how we could tell if students had acquired them. I have been interested in the Understanding By Design curriculum framework for some time – its focus on developing and assessing understanding matches my own values in curriculum planning very nicely! Additionally, teaching and learning needs to be based around understandings – and not just ‘understanding how to’ goals but understandings that are actually big, transferrable ideas.

This is particularly true of the topic Quadratic Relationships, which we are studying at the moment in Y10. I know that a number of teachers everywhere like to teach quadratic factorisation with nifty little ‘tricks’ like multiplying the co-efficient of the squared term by the constant then looking for factors of the resulting number that add to the co-efficient of the x term. It is widely endorsed in various textbooks as well. This ‘works’ and students like following the template provided. (see a previous post on the use of ‘templating’ in mathematics education) BUT…has it added value to students’ understanding of factorisation? Can it be transferred to cubic factorisation, for instance? Or has this approach just confirmed in students’ minds that mathematics is just one set of unrelated rules after another…each new period bringing a new set of rules that define their experiences for 75 minutes?

The doctoral thesis of Dr Gaye Williams (and the focus of a previous post) – a mathematics lecturer at Deakin University – investigated the question:  ‘What factors are necessary in mathematics classrooms that lead to students becoming more creative thinkers?’One of her findings was that even in the classes of teachers who had been identified as ‘good teachers’ by their peers, their students and the school community in general, deep analytical thinking wasn’t evident.A teacher may be ‘first-rate’ in terms of their level of caring for their students, their knowledge of the discipline, their meticulous preparation, their desire to see their students learn and succeed, their knowledge of technologies etc. but does it necessarily follow that they are doing good work?

Are their students learning? Does this learning involve thinking and understanding?

Today, I received  my weekly email alert from the Curriculum Leadership Journal and was impressed by a series of articles from the NZ Ministry of Education in their Education Gazette on mathematics coaches – leading teachers in schools who are linked to a mathematics educator in the tertiary sector and given support in terms of alerting them to relevant articles, resources, new theories on pedagogy etc.These teachers then work closely with their peers giving demonstration lessons, informing their practice, coming into their classes and pair-teaching, providing feedback and so on. Great idea! These articles are here: Maths Help Multiplies, Tools For Understanding and An Equation for Confidence.

We can all become better educators when we engage in reflecting on our practice in the light of current pedagogical theories, looking critically at current approaches by using the measuring stick question “Does this add value to my students’ understanding”? and sharing our knowledge with colleagues. As we approach the time of the year when we look forward to the next and what we would like to do differently, consider rewriting curriculum that puts students’ understanding and ‘big picture’ ideas at its heart.


About Linda

I have been involved in secondary mathematics education in Victoria, Australia for over 25 years.
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