Blog: Dr Helen Drury, Executive Director
The importance of aiming high
Posted: 12/01/19
Expecting that some children will struggle with mathematics quickly becomes a self-fulfilling prophecy.
A headteacher once took me to a Reception class and pointed out a little boy who was chatting with the teacher. She proudly told me how good he was at mathematics, and confidently predicted that, in the formal assessments that would be conducted seven years’ time (when the boy would be eleven), he would be exceeding national expectations in mathematics. Later in the same lesson, she drew my attention to another little boy, who she said was already struggling. ‘We’ll do what we can’, she explained, ‘but I can tell you right now that he’s going to need booster classes in Year 6 – it’s very unlikely he’ll meet national expectations’.
When I recount this story to secondary practitioners, there can be a tendency to fall into passing the buck – no wonder so many students are under-achieving at the start of secondary school: their primary teachers had such low expectations for them. But before putting the blame on the shoulders of primary colleagues, it’s worth just reflecting on the experience of that same little boy at secondary. Let’s say his headteacher’s prophecy comes true (and, of course, her thinking it makes it so very much more likely) and, despite ‘booster classes’ he arrives at secondary school below national expectations in mathematics.
Do his secondary teachers wonder:
– how many positive mathematics experiences he enjoyed in the early years?
– how equipped and empowered his primary school teachers were to provide him with the learning experiences he needed?
Or is the assumption made that he’s just one of those people who, for whatever reason, simply ‘isn’t good at mathematics’?
In fact, in a study of students who had been identified as “having a learning problem in mathematics”, roughly half “did not show any form of cognitive deficit”[1]. It is very likely that this boy was born with just as much potential to learn mathematics as his higher attaining peers. His under-attainment is very likely no reflection on his natural ability, but rather is the consequence of the limited quality of the opportunities he has been given to learn.
Even given a fairly standard offer of three hours of mathematics per week (and many schools dedicate more time to mathematics than this, plus intervention time on top) this boy will receive almost 600 hours of secondary mathematics education. Given 600 hours, surely his mathematics teachers can influence his learning outcomes? In a sense that time is wasted if it is decided right from the start that he does not have the potential to succeed in mathematics.
An important belief underlying a mastery approach is the belief that all students are capable of understanding and doing mathematics, given sufficient time. Students can achieve in and enjoy mathematics, whatever their socio-economic background or prior attainment, as long as they are given the appropriate learning experiences. Thinking that some students are ‘naturally good at mathematics’, and that others are not, fast becomes a self-fulfilling prophecy.
Whereas the UK seems to have become used to a tail of under achievement, other countries demonstrate that such a tail is far from inevitable. Many more children can succeed with mathematics than are doing so in the UK at the moment.
High-performing systems tend to structure their student progression and differentiation approaches around high expectations for all[2]. Countries with higher achievement tend also to have less variation in pupil achievement than others[3]. Increased variation in student achievement is associated with lower overall student achievement[4].
Professor Zhu Xiaohu of the Shanghai PISA Centre observed in 2013 that Shanghai:
“rank[s] world best in Maths and Science, not because of the performance of our top students, but because of the small gap between high and low performers. High quality is matched by high equality”[5].
Results from the TIMSS report in 2016 showed that in England, in contrast, the gap between the lowest performing and the highest performing children remains unacceptably wide even though England has risen to its highest point in these rankings for 20 years[6].
The OECD’s 2016 report, PISA 2015[7], states the proportions of students achieving different ‘levels’. At PISA level 2, students can use basic algorithms, formulae, procedures or conventions to solve problems involving whole numbers.
For example, they can convert an approximate price to a different currency and compare the total distance across two alternative routes. The report describes PISA level 2 as: “a baseline level of proficiency that is required to participate fully in modern society”.
“These low achievers can solve problems involving clear directions and requiring a single source of information, but cannot engage in more complex reasoning to solve the kinds of problems that are routinely faced by adults in their daily lives.”
Across the OECD, 23% of 15-year olds don’t even make it to this level. The UK was broadly in line with this, with 22% of students failing to achieve even PISA level 2. But in Singapore and China, half as many students are struggling with maths – just 10% fail to attain PISA level 2.
A significant reason for a smaller proportion of students falling behind in these higher performing jurisdictions is that their curricula, pedagogy and assessment are built around the belief that every student can succeed, given the appropriate time and teaching.
Success in mathematics is often used as an indicator of ‘innate’ intelligence, rather than something that everyone can achieve with effort. This attitude is more prevalent in some countries than others. When I wrote ‘How to teach mathematics for mastery’ in 2015-16, this seemed to be particularly common in the United States and United Kingdom. I wrote that many people believe that mathematical ability is a “gift” that some people have and others don’t, and that the assumption is often made that students’ capacity to learn is determined by an innate endowment of fixed intelligence[8].
It has been exciting to see this attitude beginning to shift over the past few years. I frequently meet teachers and school leaders who have genuinely high expectations of every learner they teach. Could we be seeing a national shift away from the ‘fixed’ theory of ability[9] that results in teachers and pupils believing that they are either good at mathematics or they are not? If so, we may start to see a resultant narrowing in the attainment gap that we otherwise risk assuming is inevitable.
This blog is based on an extract from ‘How to teach mathematics for mastery’ .
[1] Geary, D. C. (1994) Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association, p157.
[2] Reynolds, D. & Farrell, S. (1996) Worlds Apart? A Review of International Surveys of Educational Achievement Involving England. London: HMSO.
[3] Wilkinson, R., & Pickett, K., (2009) The spirit level: why more equal societies almost always do better. London: Allen Lane, The Penguin Press.
[4] Hanushek, E. A., & Woessman, L. (2010) The economics of international differences in educational achievement (Vol. 4925). Bonn: Forschungsinstitut zur Zukunft der Arbeit.
[5] National College for School Leadership (2013) Report on research into maths and science teaching in the Shanghai region. Research by National Leaders of Education and Subject Specialists in Shanghai and Ningbo, China 11-18 January 2013 (2013).
[6] Mullis, I. V. S., Martin, M. O., Foy, P., & Hooper, M. (2016). TIMSS 2015 International Results in Mathematics. Retrieved from Boston College, TIMSS & PIRLS International Study Center website: http://timssandpirls.bc.edu/timss2015/international-results/
[7] OECD (2016), PISA 2015 Results (Volume I): Excellence and Equity in Education, OECD Publishing, Paris.
DOI: http://dx.doi.org/10.1787/9789264266490-en
[8] Herrnstein, R.J. and Murray, C., (1994). The Bell Curve. Free Press.
[9] Dweck, C.S. (1999) Self-theories: Their role in motivation, personality and development. Philadelphia: Psychology Press.