Data on performance in maths
Itâs not all bad. I like a few platitudes, so letâs go for âWe could be betterâ. In this book, I am suggesting one source of ideas â the outliers â on how to help things get better. Low achievers need attention for their own sakes, but I believe that what we learn from teaching them successfully can be a way of improving our overall statistics in surveys such as those PISA results.
Since this is a book about maths, here are some numbers.
There is some data around that supports my opening paragraph. For example, the 2010 Sheffield Reportâs evidence on levels of achievement in maths showed that 22% of 16- to 19-year-olds in England are functionally innumerate. This is a problem that has been in existence for at least 20 years. A 2011 report from the Conservative Party, âA World-class Mathematics Education for All Our Young Peopleâ, stated that âmuch greater attention needs to be paid to those students (nearly half of each cohort) who currently are deemed to âfailâ mathematics at age 16â. The 2017 National Numeracy booklet âA New Approach to Making the UK Numerateâ stated that âGovernment statistics suggest that 17 million adults â 49% of the working-age population of England â have the numeracy level that we expect of primary school childrenâ. This is relatively consistent data but at least itâs not worse. But, then, itâs certainly not better. Of course, âwhat we expect of primary school childrenâ doesnât have much mathematical precision in the minds of many people (but see Appendix 1). Further evidence that the situation is not so good for older learners in the UK was that we were the worst-performing of the 17 OECD countries in the âNumeracy/Knowledgeâ component of Adult Financial Literacy (2016).
According to the Nuffield Foundation UK report âUnderstanding Mathematics Anxietyâ (2019), the proportion of adults with functional maths skills equivalent to a General Certificate of Secondary Education (GCSE) grade C (the passing grade) fell from 26% in 2003 to 22% in 2011. In contrast, functional literacy skills were steadily increasing, and 57% of working-age adults gained the equivalent level. The PISA data released in 2019 suggests that maths for 15-year-old UK students is improving and pushing us up the international rankings. Of course, it may be more complicated than that but it is encouraging.
In terms of students re-taking the UK national maths examination (GCSE) for 16-year-old students, results for maths show that of the 155,000 entries in 2018â2019, 37.2% achieved a lower point score for this re-take than for the previous attempt and 36.5% made progress, according to Julia Belgutay (Times Educational Supplement, 21 October 2019). In terms of pass rates, the data is stark: âFewer than a quarter of maths entries from candidates aged 17 and over across the UK resulted in a pass at grade 4 (equivalent to C) or better, with the pass rate dropping from 23.7 per cent in 2018 to just 22.3 per cent this summer, according to data from the Joint Council for Qualifications publishedâ on 13 November 2019. (https://webcache.googleusercontent.com/search?q=cache:FWX-ZzalL4UJ:https://www.tes.com/news/gcse-results-english-and-maths-resits-pass-rates-drop+&cd=1&hl=en&ct=clnk&gl=uk). We seem to have a cohort of learners for whom the current system is not working. I am suggesting, again, that maybe we could do even better on the PISA rankings if we could reach this cohort.
When we seek international data, the key source is PISA. It tests students at age 15. New results on their 2018 international assessments were released in December 2019. The UKâs ranking in maths had remained stable from 2006 to 2015, around the OECD average. A sample of the positions in the 2015 survey has Shanghai (1), Singapore (2), Hong Kong (4), Switzerland (9), New Zealand (16), the UK (27), Ireland (28) and the US (35).
In the 2019 results for maths, the UK was 18th, up from 27th in 2015. This represented a âparticular improvementâ, according to an analysis by the National Foundation for Educational Research. The education director of the OECD said that these were âpositive signalsâ which demonstrated âmodest improvementsâ.
And since Iâm with this recent PISA, Iâll include this statistic: Boys scored lower than girls in mathematics by 12 score points, which is wider than the average gender gap across OECD countries (5 score points).
The TIMSS (Trends in International Mathematics and Science Study) provides data on the mathematics and science achievement of 10-year-old students from the US compared with that of students in other countries. The 2015 results put Singapore at 1, Hong Kong at 2, Ireland at 9, England at 10 and the US at 14.
It seems to me that sometimes statistics are out there to be abused, especially by politicians. For example, in England, there is our national examination for maths for students who are 16 (and then older if they need to re-take after failing the first time). I love â although maybe thatâs not the right word for such depressing content â this observation from Professor Alan Smithers, director of the Centre of Education and Employment at Buckingham University:
What is happening is that this year (2019) the exams are harder, and the Office of Qualifications and Examinations Regulation [Ofqual] has wanted to keep the grade pattern comparable with previous years, so it has had to lower the number of marks required to get a pass grade. These grades will lead to us fooling ourselves into assuming that young people are doing much better than they actually are. Ofqual are creating an illusion.
Education ministers are in a winâwin situation. They make exams harder, thinking that this is enough to raise standards, so thatâs a win. Then, if results are (inevitably it seems) lower, they lower the pass mark and â âHey presto!â â standards have risen. Thatâs a win, too. We should include a cynical component when we teach statistics.
Later, I will talk about the âcurse of knowledgeâ, defined as âa cognitive bias that happens when an individual, communicating with other individuals, unknowingly assumes that they have the background knowledge to understandâ (taken from a 1...