Since my initial post on this topic, ACARA have added a note to their website to explain the changes. The main change to the NAPLAN numeracy assessment involves moving from two papers consisting of 32 questions each, one of which was a non-calculator paper, to a single paper with 48 questions. This single paper has a non-calculator section that only contains *eight* questions.

According to ACARA:

“…the test continues to cover all sub-domains of numeracy, allowing students to demonstrate performance across a range of numeracy skills. The reduction will not affect either the reliability or validity of the test.

Students in Years 7 and 9 will continue to answer calculator and non-calculator questions, and the number of questions requiring mental calculation (without the aid of a calculator) remains the same as in previous years – there is no reduction in the number of questions of this type.”

You may ask how it is possible that there has been no reduction in the number of ‘mental calculation’ questions when we have gone down from a 32 question non-calculator paper to just 8 questions. Well, there is some logic to this. A proportion of the questions on the non-calculator paper involved things like mentally rotating shapes, constructing expressions or reading graphs. A calculator would be of no benefit for these questions. However, it seemed unlikely to me that these items would constitute 24 of the 32 questions.

So I did a check. I looked at the 2016 Year 7 non-calculator paper. I was able to identify 18* questions out of 32 that involved some form of calculation that a student could complete with a calculator if it were available. That’s more than eight. It also represents 28% of the total whereas 8 questions out of 48 represents 17%.

Personally, I don’t think *28%* *of questions* requiring a mental or pen-and-paper calculation is enough, particularly given the widespread concern about Australia’s continued decline in international assessments such as TIMSS and PISA and specifically in the science and maths subject areas.

Arguing – as I am sure the maths subject associations would – that there is no need for students to be able to do manual calculations in an age of calculators misses a number of key points. Maths is not purely functional – it’s not just about getting a result. The functional argument is like arguing that we shouldn’t teach children how to draw because we have cameras. As well as consolidating knowledge of maths facts, mental arithmetic is likely to support all sorts of activities such as proportional reasoning, factorisation and so on that lead into higher levels of maths. Even if we did accept the functional argument, a calculator user with no mental arithmetic will struggle to spot when he or she has made an error.

It’s worth pointing out that the suite of NAPLAN papers consists of five assessments. Only *one *of these is a numeracy assessment, with the other four assessing different aspects of literacy. Now, the numeracy element is going to be reduced in size and contain a smaller proportion of non-calculator questions.

**Questions 2, 3, 9, 11, 13, 14, 17, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 31*

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There’s another effect to consider : reducing the number of numeracy questions will, I believe, increase the measurement error. This probably doesn’t impact on whole school numeracy data (because the errors should cancel out), but I would be concerned it makes NAPLAN less reliable for tracking individual student achievement and growth.