Many Year 6 teachers were this week piloting a new classroom task: formal testing of 11-year-olds' mental maths. Using the School Curriculum and Assessment Authority's sample test materials, teachers have been presenting children with a precisely timed set of oral questions which require fast, written answers.
We both agree with the aims behind these tests: to improve and assess children's mental numerical skills. We also recognise the need for a change in the classroom culture, so that what the children call "fast arithmetic" becomes part of the daily maths routine. However, the tests in their current form are unlikely to help achieve this objective, and could prove counterproductive.
We have two key concerns - timing and presentation - and we hope our comments will be taken into account when next year's tests are drawn up.
The tests are divided into three sections. Each question in the first group must be answered in five seconds, the second in 10 seconds, and the third in 15 seconds. It is not necessary to be a teacher to appreciate that five seconds is a very short time in which to answer questions such as, "Change 9.5 metres into centimetres", or "What is 3.2 multiplied by 100?" The panic factor alone militates against a correct answer. However, we are not arguing against timed questions, nor even against the five-second limit. Our concern focuses on the purpose of the time limit.
There are some number facts that all 11-year-olds should have on instant recall. These include number bonds to 10, the addition of 10 to any two-digit number, and most of the tables facts. Thus, it is reasonable to ask a child to give a "quick-fire" response to questions such as "Six and four?", "73 and 10?" or "Seven fives?" The very short time limit is entirely appropriate here, and we would not consider it to be "panic-inducing". Children are well used to rapid-fire tables or number-bond tests.
However, there are a whole range of "second-order" calculations where children should be able to give a fast, efficient answer without getting a pain in their stomachs. Many of the 10-second questions in the sample test fall into this category. Good examples are: "A train journey starts at 7.40. It lasts for 45 minutes. At what time does it finish?"; or "Colin has Pounds 6.50. He wants to buy a computer game which costs Pounds 19.25. How much more money does he need?". If a child can give the correct answer within a short time, without being unduly stressed, then they are confident and efficient operators. Imposing a five- or 10-second time limit produces a panic which means that few children are able to process the information necessary to produce the answer.
We feel the time limits should take into account the purpose behind the testing. There could be a limited number of "quick-fire" numerical-fact questions with a five-second time limit. Then there should be some quick arithmetic calculation questions with a short, but not unreasonable time limit. One minute per question, including the reading of it, would seem acceptable. We would then get a reasonable assessment of the children's mental numerical fluency rather than of their character when under pressure.
Presentation is also an issue. Currently, all the questions are presented orally, and SCAA suggests that schools use the taped delivery provided. There are several problems with presenting every question in this format. Accent, tone and expression are important if children from Devon to Newcastle are to be expected to hear, make sense of and process the questions within the time limit. It also restricts the type of questions asked. But, most important, it takes no account of the fact that these children are living in the late 1990s and will be operating, mathematically speaking, in the year 2000 and beyond.
Today's universe, to a great extent, is iconic. Information is conveyed through visual signs, which children are skilled at decoding. It is surely sensible to recognise that often we are required to respond, numerically, to something we see rather than something we hear.
We suggest that the mental arithmetic tests draw upon a variety of visual signifiers, such as "special offer" signs, road signs and video symbols. Some of the questions could be presented in oral form, some visually, and some in a mixture. For example, "Look at this poster. How many tickets can you buy with Pounds 2?" with a poster showing school disco tickets at 45p each.
We firmly believe that mental arithmetic, or what we prefer to call numerical fluency, matters. Teachers throughout primary school and beyond should teach these skills in an active and stimulating fashion to all children. The National Numeracy Project, with its careful and detailed framework, is providing teachers with the strategies and the support they require to help them to do this. However, we need to get the tests right, or we are in danger of scuppering the ship just as it about to set sail in the right direction.
If over-ambitious timing and one-dimensional presentation lead children to perform badly, teachers may condemn the aims behind the tests as unrealistic and simplistic.
Ruth Merttens is professor of primary maths at the University of North London, and Sue Price is deputy head at Moretonhampstead Primary School, Devon, where Ruth teaches one morning a week