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Inside Teaching : August 2010
Inside Teaching | August 2010 CURRICULUM & ASSESSMENT 36 Now, you might accuse me of basing my argument merely on one example, so let’s look at another one, Question 25 from the same 2008 Year 7 NAPLAN numeracy test paper. It’s clear that large proportions of Year 7 students don’t understand the concept of fraction, or at the very least are unable to visualise fractional amounts, leaving aside the literacy level required in order to understand the context and syntax of this question. The fact that 48 per cent of students selected 3/7 indicates that they merely added the two numerators and the two denominators, and that’s a great concern. The 17.2 per cent who selected 4/7 did know to subsequently subtract their result from 1 – correctly determining that two steps were needed – but they still do not understand the relationship between the numerator and denominator of a fraction. Neither do they understand the concept of fraction since they were unable to visualise the quantities they were dealing with. If they were, they would have known that if they added 2/3 and 1/4 of the same total quantity they would be left with a very small quantity from the whole amount. In other words, if they deeply understood that fraction is about quantities of a whole and used that information to visualise the situation, they would know that of the four options, the solution could only possibly be a small fraction and since only one of the four options, 1/12, is small, then this must be the correct one. It’s clear from these results that fractions are still being taught in many classrooms as algorithms and procedures, rarely with discussion or visualisation and rarely embedded in real- world contexts that support the development of deep understandings of mathematical concepts. For students to get these questions correct on NAPLAN tests these approaches are essential. What next? Every teacher of mathematics might proftably undertake an analysis similar to the one I’ve undertaken here using their own data, and might proftably share it with colleagues. It’s worth looking at the results of individual students, variations in results between student sub-groups in your classes and student responses to questions from different strands. It’s also worth refecting on your current teaching of mathematics for numeracy attainment and discussing that with your colleagues. A key focus of that refection and discussion should be to question whether your students are being taught a deep understanding of mathematics concepts and the capacity, confdence and disposition to use them, or merely a set of methods and procedures. IT’S CLEAR FROM THESE RESULTS THAT FRACTIONS ARE STILL BEING TAUGHT IN MANY CLASSROOMS AS ALGORITHMS AND PROCEDURES, R ARELY WITH DISCUSSION OR VISUALISATION AND RARELY EMBEDDED IN REAL-WORLD CONTExTS THAT SUPPORT THE DEVELOPMENT OF DEEP UNDERSTANDINGS OF MATHEMATICAL CONCEPTS.