Practice at “Guesstimating” Can Speed Up Math Ability

A person’s math ability can range from simple arithmetic to calculus and abstract set theory. But there’s one math skill we all share: A primitive ability to estimate and compare quantities without counting, like when choosing a checkout line at the grocery store. Practicing this kind of estimating may actually improve our ability to do the kinds of symbolic math we learn in school, according to new research published in Psychological Science, a journal of the Association for Psychological Science.
Previous studies have suggested a connection between the approximate number system, involved in estimating, and mathematical ability. Psychological scientists Elizabeth Brannon and Joonkoo Park of Duke University devised a series of experiments to test this association.
The researchers enrolled 26 adult volunteers and had them complete 10 training sessions designed to hone their approximate number skills. On each of these training sessions, the participants practiced adding and subtracting large quantities of dots without counting them.
They were briefly shown two arrays of 9 to 36 dots on a computer screen and then asked whether a third set of dots was larger or smaller than the sum of the first two sets, or whether it matched the sum.
“It’s not about counting, it’s about rough estimates,” explains Park, a postdoctoral researcher at Duke.
As participants improved at the game, the automated sessions became more difficult by making the quantities they had to judge closer to each other.
Before the first training session and after the last one, their symbolic math ability was tested with a set of two- and three-digit addition and subtraction problems, sort of like a third-grader’s homework. They solved as many of these problems as they could in 10 minutes. Another group of control participants took the math tests without the approximate number training.
Those who had received the 10 training sessions on approximate arithmetic showed more improvement in their math test scores compared to the control group.
In a second set of experiments, participants were divided into three groups to isolate whether there had been some sort of placebo effect in the first experiment that made the approximate arithmetic group perform better. One group added and subtracted quantities as before, a second performed a repetitive and fast-paced rank-ordering with Arabic digits, and the third answered multiple choice questions that tapped their general knowledge (e.g., “which city is the capital of France?”)
Again, the people who were given the approximate arithmetic training showed significantly more improvement in the math test compared to either control group.
“We are conducting additional studies to try and figure out what’s driving the effect, and we are particularly excited about the possibility that games designed to hone approximate number sense in preschoolers might facilitate math learning,” Park said.
Park and Brannon can’t yet isolate the mechanism behind their effect, but the research does suggest that there is an important causal link between approximate number sense and symbolic math ability.
“We think this might be the seeds — the building blocks — of mathematical thinking,” Brannon said.

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Press release available on the APS website.
This research was supported by a James McDonnell Scholar Award, a grant from the Eunice Kennedy Shriver National Institute of Child Health and Human Development, and a Duke Fundamental and Translational Neuroscience Postdoctoral Fellowship.
The APS journal Psychological Science is the highest ranked empirical journal in psychology. For a copy of the article “Training the Approximate Number System Improves Math Proficiency” and access to other Psychological Science research findings, please contact Anna Mikulak at 202-293-9300 or amikulak@psychologicalscience.org.

This year the International Mathematical Olympiad, the world championship of secondary school mathematics, was held in Colombia. The results of the British team were unusually good, and they were ranked 9th best in the world.

The six students obtained 2 gold medals, 3 silver medals and 1 bronze. The British result was markedly stronger than that of any other EU country, and in Europe was second only to that of Russia.

The contestant Andrew Carlotti now has the strongest medal record of any British competitor, overtaking both Simon Norton and the late John Rickard.

France finished above Germany for the first time since reunification, and the nations of the Far East are becoming stronger at this event, just as those of central and eastern Europe are mostly not doing so well.

The British report is here.

British participation is organised by the United Kingdom Mathematics Trust.

Is ATM against “formal written methods”?

From a letter published by the Association of Teachers of Mathematics (ATM) in The Guardian, 29 July 2013:

The Association of Teachers of Mathematics is dismayed at the programmes of study for mathematics just published […] The curriculum as presented will result in more attention spent on developing technical competence in outdated written methods for arithmetic at the expense of developing secure foundations for progression through mathematical concepts and skills. […] Appendix 1, entitled formal written methods for multiplication and division, but including addition and subtraction as well as multiplication and division, is a complete travesty and needs to be removed.

See the original letter at The Guardian

Schools ask pupils to sit GCSE maths exams twice

From The Independent:

Thousands of teenagers are being put in for multiple GCSE maths exams in the hope they will get crucial C grade passes in at least one of them.

The practice is exposed by the exams regulator Ofqual today as it reveals that 15 per cent of candidates sitting GCSEs  – around 90,000 candidates – were last year submitted for maths exams with more than one board. Ofqual officials believe there will be a repeat this year because the pressures that drove schools to do it  – including boosting performances in league tables – are still there.