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Inside Teaching : August 2010
www.atra.edu.au | firstname.lastname@example.org CURRICULUM & ASSESSMENT 31 Information from NAPLAN tests can support teachers and school leaders in planning for the learning of individual students and for improvement across the whole school. thelma PeRso explains how to to do exactly that in numeracy. The National Assessment Program for Literacy and Numeracy (NAPLAN) tests, which have now been administered by the Australian Curriculum, Assessment and Reporting Authority (ACARA) in 2008, 2009 and this year, provide information on student performance across language conventions, writing, reading and numeracy. One of the effects of assessments like NAPLAN is that they prompt teachers to refect on what is being tested and consider what their students are doing, and the thinking behind their actions, and that can be a powerful tool to guide teaching. I’m going to concentrate here on the uses of NAPLAN to guide the teaching of mathematics for numeracy attainment by students, but what follows would also apply to literacy, and reading and writing in particular. According to the report of the National Numeracy Review, commissioned by the Human Capital Working Group of the Council of Australian Governments, there are three dimensions of numeracy that need to be explicitly taught through relevant experiences in schools: mathematical, strategic and contextual. Mathematical numeracy is about mathematical content; having number, measurement and spatial sense that derives from deeply understanding mathematical ideas and concepts, and knowing procedures and skills needed to apply these. For example, students know that the average –ormean–of16,18and24 cannot possibly be 17 because they deeply understand that average is a measure of the ‘centredness’ of a set of numbers; they know that 36 ÷ 0.3 can’t possibly be a number less than 36 but must be approximately 3 lots of 36; they know that a whole number minus 1/2 and then 1/3 will leave a small fraction remaining because they can visualise the amounts involved. Strategic numeracy and contextual numeracy are about using mathematical sense to decide whether mathematics will assist in a situation and whether results obtained through subsequently applying mathematics make sense in a particular context. It includes having a disposition and attitude of confdence, to choose and use mathematics when and where it’s helpful to do so and to reason about those choices. Strategic and contextual numeracy would appear to be dependent on mathematical numeracy, since you frst need to have some deep knowledge about mathematics in order to be able to apply it strategically to a range of contexts. Clearly, you need to learn the tools of mathematics before you can apply them. Consequently, in the early years of schooling the learning will focus on the tools, for example, understanding numbers and how they work, understanding operations and calculation. As students move through the early years into the middle years the curriculum emphasis will increasingly focus on application; independent choices about which tools to apply, how to apply them and how to critique their effectiveness. As students move through the year levels, numeracy lessons change from being lessons about mathematics to being lessons enabled through mathematics. As teachers, we need to be aware of the numeracy ‘toolkits’