Pupils are no better at aspects of basic maths today than they were in the 1970s, despite rising exam results, a major new study from King's College London has found.
The proportion of pupils who understand algebra, ratios and fractions at the age of 14 has fallen since the 1970s, while the proportion who struggle with even the simplest concepts has increased. The findings are in contrast to the number of pupils gaining grade C or above in maths GCSE, which has risen every year since the exam was introduced.
Researchers say the data, based on samples of 7,000 pupils, raises questions about how schools currently prepare children for exams. During 2008 and 2009, pupils were given test questions first used in a research project in 1976 and 1977 to compare how performance had changed.
Jeremy Hodgen, professor of maths education at King's and the principal investigator on the four-year project, told a conference in London that there were wide-ranging problems in maths education. The research revealed that pupils were not given enough time to develop understanding, but instead were moved through a system that encourages them to plug numbers into formulae, giving the illusion of understanding.
"The biggest problem is that students don't understand mathematics well enough," Professor Hodgen said. "The second issue is the slow rate of growth in understanding. It is clear that learning maths, in terms of understanding maths, takes time.
"The third issue is that this data suggests we need to ban early entry to GCSE. It is a mad policy to encourage students to take GCSE to test aspects of ... reasoning when we know students haven't attained understanding."
Problems arise when pupils are asked to tackle non-routine problems, Professor Hodgen said. For example, pupils were asked: "If six-tenths is 0.6, what is eleven-tenths?" The most common answer was 0.11, instead of 1.1.
The research also looked at how fast pupils learned across key stage 3. There was a bigger gain in knowledge between Year 7 and Year 8 than between Year 8 and Year 9, showing that attainment slowed as pupils grew older.
Robert Coe, a professor at Durham University's School of Education and a member of the research team, said the proposed changes to the national curriculum would have little effect on improving understanding of maths if the main driver in schools remains the number of pupils reaching grade C.
"Key stage 3 scores and GCSE scores are going up, but for many years my colleagues and I have been saying these are not real changes," Professor Coe said.
The test questions
My car can go 41.8 miles on each gallon of petrol on a motorway. How many miles can I expect to travel on 8.37 gallons?
41.8 + 8.37
41.8 EUR 8.37
41.8 - 8.37
8.37 + 41.8 8.37 - 41.8
8.37 EUR 41.8
Correct calculation: 8.37 x 41.8
In 1976-77, 54 per cent of pupils answered correctly.
In the new study, 33 per cent answered correctly.
e + f = 8
e + f + g = ...
In both 1976-77 and the new study, 37 per cent of pupils gave the correct answer.
Number crunch: The proportion of pupils who understand algebra, ratios and fractions at the age of 14 has dropped since the 1970s.
The biggest problem is that students don't understand maths well enough.