NAPLAN tests are with us whether we like them or not (I don’t). And every year teachers in Year 3 and Year 5 spend too much of their valuable maths session time preparing for the test items in Terms 1 and 2. The pressure is huge. Both teachers and parents want their students to demonstrate that they are progressing well on their learning trajectory. And every year we get the results quite late and feel good or bad depending on whether our class scored above or below the rest of the state.

We have been analysing the NAPLAN Numeracy results for primary students in NSW over the last 10 years and find the proportion of questions always includes too many items that test the stage above and too few questions that test the stage below. We argue that to be a valuable data source the proportion of items should be more from the stage below. As a nation, have the students entering Stage 2 achieved the appropriate standard for Stage 1? As a nation, have the students entering Stage 3 achieved the appropriate standard for Stage 2?

The answers to these two questions really matter. Over the last 20 years Australian students have not demonstrated a high enough level of achievement on international tests. Too few secondary students are selecting mathematics and too few students entering tertiary education have the required mathematical skills. Primary schools are the first port of call for all students of mathematics. Are we teaching mathematics as well as we can? Do our maths sessions provide our students with the best environment in which they can learn Mathematics?

In 2016, the NAPLAN numeracy tests will match the proportion of items in the test from each sub-strand with the sub-stand content in the Australian Curriculum: Mathematics. How will the test creators determine this proportion? e.g. there are 2 substrands for Geometry (Shape/Location & Transformation and even a third, Geometric Reasoning, from Grade 3 onwards) and 2 substrands for Statistics & Probability (Chance/Data Representation & Interpretation). Does this mean the each get an identical number of items? And does that mean that one content descriptor is equivalent in value to another? In Grade 4, for example, one Measurement content descriptor says “Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (ACMMG084)”. Yet this covers 4 separate substrands in Measurement, all of which use separate instruments of measurement. Another issue is how do you write a pen and paper test item for something as practical as measuring a real-life object? The Grade 4 content descriptor for Chance, “Describe possible everyday events and order their chances of occurring (ACMSP092)”, requires just one train of thought and more easily transfers to a multiple choice test item.

The next problem is whether each test item is meant for most students, say a core item, or is it to test achievement at a deeper level that perhaps only low block students can succeed in answering? For example, the 2012 Grade 3 NAPLAN test items for numeracy included only 9 items out of 35 that matched core Stage 1 (Stage Below) content descriptors. If we were successful, we’d expect about 80% of our students to successfully demonstrate their understanding of a core Stage Below question. We think it is more important to know if your students demonstrated achievement at core Stage Below questions than non-core questions. Another way to look at this is to say that in Grade 3 2012, only 26% of NAPLAN Numeracy questions enabled your students to demonstrate achievement of core Stage 1 maths. So 74% of questions were potentially too difficult for most students. What’s the point of knowing this?

The Year 5 paper in 2012 included 25 items out of 40 that tested core Stage 1 or Stage 2 content descriptors, still not ideal but much more effective than the Grade 3 paper.

This dilemma also transfers to programming. How do you know as a teacher what proportion of your time to plan for each substrand in Mathematics? Here at Maths Matters Resources we have very strong feelings about this dilemma and give specific advice for how to solve it. Basically about half your time should be planned for Number & Algebra, and half for Measurement & Geometry and Probability. The content for the second half is not insignificant. Number & Algebra should not take up the majority of your time as a teacher. It is not more important than that second half. And Statistics (Data) covers all substrands in Mathematics and potentially could be part of any maths session. We include sample term overviews in The Maths Session – Programming. In the same section, we also include a document called Reflecting on your Term Overviews. And of course just because you decide to focus on Multiplication in Grade 3 doesn’t mean everything is planned for the Grade 3 content descriptor. Some of your students may still be at Grade 2 or Grade 4 levels and above in their progress along the learning trajectory.

We will be fascinated to see the structure for this year’s Numeracy test items for Grades 3 and 5. Our hope is that about half the test items will relate to Number & Algebra and that some of these include Data items. And our hope is also that a large proportion of questions relate to core Stage Below content. Our hope is also that we get a fast turn-around on feedback from the NAPLAN papers to help teachers adjust their programs to match specific student needs.