Extending mathematical understanding

Why is it that so many students struggle with mathematics?  It’s one of the questions I’ve been pondering after reading the work of  MIT mathematician, Dr Seymour Papert.  For me, Papert is becoming a modern John Dewey and his assessment of why children struggle is persuasive:

I think part of the trouble with learning mathematics at school is that it’s not like mathematics in the real world. In the real world, there are engineers, who use mathematics to make bridges or make machines. There are scientists, who use mathematics to make theories, to make explanations of how atoms work, and how the universe started. There are bankers, who use mathematics to make money — or so they hope.

But children, what can they make with mathematics? Not much. They sit in class and they write numbers on pieces of paper. That’s not making anything very exciting. So we’ve tried to find ways that children can use mathematics to make something — something interesting, so that the children’s relationship to mathematics is more like the engineer’s, or the scientist’s, or the banker’s, or all the important people who use mathematics constructively to construct something.

We know that providing students with a solid foundation in literacy and numeracy sets them up for life-long learning.  We also know that the gap between the performance of Australian students and their East Asia counterparts is widening and has been for the past twelve years.  According to the report released by the Grattan Institute, Australian students are on average two years behind Shanghai students in maths and at least one year behind students from Singapore and South Korea.  As a system, we can learn from other systems such as Ontario Canada, which has made significant investment in improving literacy and numeracy.  As Michael Fullan continues to remind us whenever he visits, they have focused relentlessly on literacy and numeracy and it has become the work of school principals, lead teachers, teachers and even parents.

I invited Tim Hardy, Team Leader in System Learning to share the context of our K-12 numeracy strategy.  My thanks to Tim for his guest post below.

In 2008, COAG released its National Numeracy Review Report (NNRR), and for many, the issues highlighted are not surprising.

“While the overall levels of numeracy / mathematics achievement in Australia are quite good by international standards, there is an unacceptable proportion of Australian students (particularly but certainly not only amongst Indigenous students) who are not achieving acceptable standards of proficiency. Many students also lack confidence in the subject, do not see personal relevance in it and are unlikely to continue its study voluntarily.” (National Numeracy Review Report 2008 xii)

With the moral imperative well established, ‘Numeracy Now’, an initiative of our system, came about as a strategic response to the fifteen recommendations from the NNRR to ‘improve numeracy outcomes for all’. The recommendations specifically reflect the issues that were identified from the available research and include directions for teaching standards, school expectations and system organisation.

An example of these recommendations include: the development of pedagogical content knowledge of teachers; that mathematics be taught in context and ‘beyond the mathematics classroom’; the use of diagnostic tools such as interviews for mathematical assessment; systemic assessment programs to provide a research base to inform pedagogy; that an emphasis be on developing conceptual understandings rather than routine procedural tasks; specialist teachers regularly working shoulder to shoulder with classroom teachers; needs of cultural and minority groupings be identified and understood; and the building of leadership capability

An initial priority of our strategy was the development of instructional leadership capability within our schools. In collaboration with our academic partner, Dr Ann Gervasoni from the Australian Catholic University, over one hundred leaders including primary and secondary principals, lead teachers and system leaders have completed the Leading Mathematics Learning and Teaching program. The focus of the learning includes: the Mathematical Assessment Interview; identification of the most vulnerable learners; creating productive learning environments; developing pedagogical content knowledge of teachers; researched based teaching strategies; tracking and monitoring of student progress and implementation planning.

While the NNRR specifically recommends that the focus needs to be on the early years of schooling, our strategy has included secondary schools, initiating an authentic K-12 structure. The collaboration between primary and secondary teachers, specialists, lead teachers and principals has been profound, creating a shared understanding about quality teaching and learning with a collective responsibility for all learners.

In conjunction with the leadership program, the Extending Mathematical Understanding (EMU) – Specialist Teacher Intervention program, facilitated by Dr Ann Gervasoni, trains nominated teachers from each school to teach a daily intervention program for the most mathematically vulnerable Year 1 and Year 7 students.  The aim of this program is to equip teachers with the knowledge and skills to provide accelerated intervention that promotes students learning and a  positive and confident disposition. To further build on our system capability, we have a teaching educator currently training to become an accredited professional learning leader in order to facilitate the accredited EMU intervention program. The ‘behind-the-screen’ facility to observe teachers facilitating an EMU group, is a feature of the program.

Schools showing parents how to support children with maths at home.

The most important outcomes of the initiative are:  all Year one students assessed with ongoing tracking and monitoring; the most vulnerable students are identified in Year 1; a decline in vulnerable students in the second and third year of the project and that leaders are equipped to lead implementation plans based on credible data. An encouraging observation by our academic partner Ann Gervasoni is that of teachers applying their new knowledge into innovative practice to include the effective use of digital technologies e.g. teachers using iPads with a clear mathematical purpose, students using digital manipulatives to develop conceptual understanding, recording their thinking, with the ability to share beyond the classroom.

Parents of participating schools have expressed appreciation for the opportunity to learn about what is happening at school and importantly how best to support their children at home when it comes to mathematics.

Tim’s summary of our strategy reflects a fundamental principle from which we work – moving from an ‘I think’ mentality of teaching to ‘We learn’.  This approach uses the best research and data as a base line.  We focus on what works, why it works for each student and how we can continually extend teachers, students and even parents in their mathematical understanding.


3 thoughts on “Extending mathematical understanding

  1. I love the EMU program and I can see students getting so much more out of maths than they did before, Even students who did well at traditional maths are able to extend their thinking and have lots of strategies in their kit bag. When I was at school we were taught algorithms so if we were adding 97, 98 and 99 you had to start with writing the numbers into columns and adding up the units, carrying the tens etc. With EMU kids have a number of strategies they can pick from, and the kids are teaching me! Well Done!

  2. After completing the Leading Mathematics Learning and Teaching program in 2011, I was able to make sense of what I instinctively knew about the learning of mathematics ie that it is complex, yet with the development of mathematical understanding rather than a focus on procedure, it becomes exciting and achievable for all students.
    The focus on meaningful mathematical experiences encourages and enhances mathematical understanding and conceptual development that is easily transferable to a range of problem solving situations. Mathematics is no longer limited to ‘school maths’ but as indicated in the blog is in the context of real life occupations and experiences.
    Parents (and sometimes teachers) often say they are no good at maths. I now challenge this comment. When I ask them to reflect on the mathematics they do in their everyday life they quickly agree that to survive in society without mathematical knowledge is near impossible. We all calculate, estimate, count, shop, budget, manage financial affairs, use timetables, plan holidays etc without even consciously acknowledging the mathematics involved. What these people are really saying is – ‘I’m no good at school maths.’
    Through the work we now do in the Numeracy Now initiative of Leading Mathematics Learning and Teaching, we have moved mathematics out of the traditional school parameters of procedural practice to find answers to pass tests (school maths), to mathematical experiences that develop deep conceptual understandings.
    In doing so we are giving all students the opportunity to be ‘good at maths’, believe they are ‘good at maths’ and to pass those all important tests as well.
    All students CAN become numerate life-long learners and it is our moral imperative as teacher to ensure this.

  3. It’s inspiring to read about the way school communities in Parramatta are reimagining the learning and teaching of mathematics and creating highly effective learning environments. Well done everyone.

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