A mini-milestone for PISA in Focus

by Marilyn Achiron 
Editor, Directorate for Education and Skills

It seems like only yesterday…but it was, in fact, 50 months ago that we started our PISA in Focus series. Over these past four years we’ve mined PISA 2009 and PISA 2012 results to highlight some of the most important findings and stories from the triennial international survey of 15-year-old students – from the importance of early childhood education to the effect of family background on students’ education to whether or not doing homework is really beneficial (in general, PISA finds that yes, it really is…).

This month, PISA in Focus examines the impact of good teacher-student relations on both students’ well-being and performance. It’s not surprising that when students feel that their teachers are interested in them and support them they feel happier at school and often do better in school. What is surprising is that in several OECD countries, fewer than 60% of students attend schools whose principal reported that mathematics teachers in their schools believe that the social and emotional development of their students is as valued as the acquisition of mathematics skills. While long-term studies suggest that students’ results on the PISA test are correlated with how well they will do later on in life, good performance in standardised assessments like PISA can explain only so much. Success and well-being in life also depend on how well individuals have developed socially and emotionally, particularly throughout their crucial school years.

At this mini-milestone in our history, we’d like to thank you for your continued interest in PISA. In the coming months, we’ll be sharing more findings from PISA 2012 – even as we look ahead to December 2016, when PISA 2015 results will be announced and a new volume of stories will be open for the telling.

Links:
PISA 2012 Findings
PISA in Focus No.50: Do teacher-student relations affect students' well-being at school?
Full Set of PISA in Focus

Photo credit: © OECD

Got a math problem?

by Marilyn Achiron
Editor, Directorate for Education and Skills

Some 37% of students in the Netherlands reported that they often worry that mathematics classes will be difficult for them. In Argentina, 80% of students reported the same worry. What is the percentage-point difference between the two countries in the proportion of students who worry that mathematics classes will be difficult for them?*


While reading the above mathematics problem, did you:

1. start hyperventilating and repeat to yourself “I  can’t do this;
   I can’t do this; I can’t do this”
2. grab your mouse with the intent of clicking off this page
3. feel as though you have never encountered such a confusing
   jumble of words and numbers before
4. all of the above?

If you answered a, b, c or d, you’re in good company: on average, about one in three students feels anxious when confronted with a mathematics problem, and more than one in two students reported that they often worry that it will be difficult for them in mathematics classes. Those are alarming statistics – especially because PISA finds that greater anxiety towards mathematics is strongly related to lower scores in mathematics. As this month’s PISA in Focus reports, on average across OECD countries, mathematics anxiety is associated with a 34 score-point decline in mathematics performance – the equivalent of almost one year of school. In New Zealand, Norway and Poland, the decline associated with anxiety towards mathematics is even larger: at least 45 score points.

More worrying still, in almost all countries and economies that participated in PISA 2012, girls reported greater anxiety towards mathematics than boys. Only in Jordan, Qatar and the United Arab Emirates did boys report greater anxiety than girls.

PISA finds that students’ anxiety towards mathematics is not just about the subject, itself. Students are more anxious towards mathematics when their schoolmates get better marks than they do, on average. In Austria, Canada, the Czech Republic, France, Germany, Italy, Japan, Liechtenstein, the Netherlands and Slovenia, students who attend schools where the average student performs better than they do in mathematics tend to be considerably more anxious towards the subject than students who earn similar marks in mathematics, but attend schools where the average student performs as well as they do or worse.

So how can students learn to adopt a more Zen attitude towards mathematics? The answer may lie in their teachers. In 39 countries and economies, among students who performed equally well in mathematics, those students whose teachers consistently tell students how well they are doing in mathematics, give students feedback on their strengths and weaknesses in mathematics, and/or tell students what they need to do to improve in mathematics reported less anxiety towards math. Knowledge is power; and when staring down a mathematics problem, it can relieve stress too.

* There is a 43 percentage-point difference between the Netherlands (which has one of the smallest proportions of students who worry that mathematics classes will be difficult for them) and Argentina (which has one of the largest proportions of these students).

Links
PISA 2012 Findings
PISA in Focus No. 48: Does math make you anxious?
PISA in Focus No.48 (French version)
Full set of PISA in Focus
PISA 2012 Results: Ready to Learn (Volume III) : Students' Engagement, Drive and Self-Beliefs
Photo credit: The Scream / @Wikimédia

Maths education for innovative societies

by Stéphan Vincent-Lancrin
Senior Analyst and Project Leader, Directorate for Education and Skills

Mathematics is at the core of science, engineering and technology. Mathematic modelling of various phenomena underpins technology innovation. No wonder that mathematics education has always ranked high on the innovation policy agenda.

There is now ample evidence that preparing students for an innovative society goes well beyond preparing them for science-related professions. Given that a large share of professionals contributes in some way to innovation, the new educational imperative is to equip a critical mass of workers and citizens with the skills to thrive in innovative societies.

How can education systems meet this demand through mathematics education? First, they should improve students’ technical skills in mathematics. By technical skills, I mean the know-what (for example, the theorems) and the know-how (for example, the procedures to solve different types of problems). The 2012 results of the OECD Programme for International Student Assessment (PISA) show that many countries still have room for improvement. They also reveal that too many students still perceive mathematics as an educational stumbling block.

How could one possibly improve the learning outcomes in mathematics that are traditionally tested and, at the same time, develop other important skills for innovation, such as reasoning, understanding, posing (rather than just solving) problems, self-confidence, and even communication skills?

This is precisely the question that Zemira Mevarech and Bracha Kramarski address in a new OECD report entitled Critical Maths for Innovative Societies. Strong experimental and quasi-experimental research evidence points to one solution that teachers could easily adopt more systematically in their teaching: the explicit teaching of metacognitive strategies.

Meta-what? Let’s not be intimidated by scientific language. Metacognition simply means “thinking about” or “regulating” one’s thinking. While one often thinks about one’s thinking when learning, metacognitive pedagogies make students develop explicit (rather than implicit) learning and problem-solving strategies by making them systematically go through a series of questions about their learning.

Initiated by the Hungarian mathematician George Polya, these strategies have had several developers and promoters. For example, the teaching method developed by Mevarech and Kramarski, called IMPROVE, asks students to answer four types of questions when exposed to new content knowledge or when solving a problem: comprehension questions (e.g. what is the problem about?); connection questions (e.g. how does this problem relate to problems I have already solved? Please explain your reasoning); strategic questions (e.g. what kinds of strategies are appropriate for solving the problem, and why? Please explain your reasoning), and reflection questions (e.g. does the solution make sense? can the problem be solved in a different way?). These questions and their related processes then gradually become a habit of mind. Rigorous research shows that using this pedagogy, and others like it,  yields positive results on a variety of outcomes and skills that matter in innovative societies.

First, compared to traditional pedagogies, these methods lead to better learning outcomes in arithmetic, algebra and geometry, and their effectiveness increases in co-operative learning settings and when they also address learners’ emotional responses.

Second, they do not enhance only traditional learning outcomes, but also other skills for innovation. Metacognitive pedagogies help students to articulate their thinking, actively use the “mathematics language”, be more curious as they relate their learning to their interests, provide elaborated explanations, and also be involved in conflict resolutions and mutual learning. Students thus become better at mathematical reasoning, and better at regulating their emotions when confronted with mathematical problems. Students who have been taught using these pedagogies show less anxiety towards mathematics, for example.

Metacognitive pedagogies work for students in primary, secondary and tertiary education, as well as in teacher training; and some longitudinal studies show that they have a lasting effect and lead to much better retention of knowledge.

A noteworthy finding for policy makers is that metacognitive strategies are effective both for traditional and for complex, unfamiliar and non-routine math problems. Because they can be more authentic, more open, and more related to real life, these kinds of problems may arguably better prepare students to exert their creative and critical minds. An example of such a problem is the following: “several supermarkets advertised that they are the cheapest supermarket in town. Please collect information and find out which of the advertisements is correct.” Students then have to design and implement a strategy to come up with a reasoned answer. These kinds of problems may have several solutions, depending on how students interpret the problem: the students may go for a different basket of goods, or take into account qualitative differences in a different way – as we do in real life.

Some mathematics educators believe that complex, unfamiliar and non-routine problems are not “real maths” problems; but the good news is that, whatever the type of problem they prefer, metacognitive strategies will still improve their students’ learning outcomes.

Would metacognitive pedagogies have positive effects if mainstreamed in mathematics education (and possibly other disciplines)? Singapore is the only country where metacognitive strategies are now one explicit dimension of the mathematics curriculum. That means they are taught in teacher training and teachers are obliged to use them. This might partly explain why Singapore is consistently one of the top performers in mathematics, in both the PISA and the Trends in International Mathematics and Science Study (TIMSS) tests.

Many educators and policy makers call for more evidence to support improvement of educational practices and reform education systems before adopting education reforms. For once, we have strong evidence. So why wait any longer to promote the use of metacognitive pedagogies in the classroom?

Links:
Critical Maths for Innovative Societies The Role of Metacognitive Pedagogies
PISA 2012 Results: Creative Problem Solving (Volume V)
PISA 2012 Results: What Students Know and Can Do (Volume I)
Measuring Innovation in Education: A New Perspective
Art for Art’s Sake? The Impact of Arts Education
The Nature of Learning: Using Research to Inspire Practice 
Centre for Educational Research and Innovation (CERI)
OECD Insights: Want to improve your problem solving skills? Try metacognition
Photo credit: © Aakash Nihalani (“Sum Times”)

Spread the wealth, reap the benefits

by Marilyn Achiron, 
Editor, Directorate for Education and Skills

Quick: Who has more up-to-date textbooks: students in wealthier schools or students in poorer schools? Actually, it depends where you live. As this month’s PISA in Focus explains, not only are some countries better than others in allocating their educational resources more equitably across schools, but students in these countries generally perform better in mathematics.

PISA 2012 asked school principals to report whether teacher shortages, or shortages or inadequacy of physical infrastructure or instructional materials, like textbooks, hindered their school’s ability to provide instruction. PISA found that while disadvantaged schools benefit from investments in smaller classes, they are also more likely to suffer from teacher shortages and inadequate instructional materials than advantaged schools. In general, schools with more socio-economically disadvantaged students tend to have less adequate resources than schools with more advantaged students.

It may come as a surprise, but according to PISA data, the United States is the second least-equitable OECD country, after Mexico, in the allocation of educational resources. One in four disadvantaged students in the United States attends a school whose principal reported that a shortage or inadequacy of science laboratory equipment hindered – to some extent or a lot – the school’s capacity to provide instruction. Meanwhile, only around one in seven advantaged students in the United States attends such a school. The differences between advantaged and disadvantaged schools are even starker among Latin American countries, including the OECD countries Chile and Mexico. For example, fewer than one in two disadvantaged students, but more than three in four advantaged students, in Mexico attend schools that have adequate instructional materials.

Apart from making a huge difference to individual students, inequity in resource allocation has an impact on a country’s overall performance in PISA. After taking into account countries’ relative wealth, 19% of the variation in mathematics performance across all the countries and economies that participated in PISA 2012 can be explained by differences in principals’ responses to questions about the adequacy of science laboratory equipment, instructional materials, computers for instruction, Internet connectivity, computer software for instruction, and library materials. At least 30% of the variation in mathematics performance across OECD countries can be explained by how equitably resources are allocated across all schools.

PISA has consistently found that, when it comes to education, money isn’t everything, and that beyond a certain minimum level of expenditure per student, how the money is spent is more important than how much money is spent. When money is translated into such tangibles as up-to-date textbooks, reliable Internet access, and a school library full of books, spreading the wealth evenly across all schools, regardless of their socio-economic profile, gives all students, not just those in the wealthiest schools, the nourishment they need to succeed.

Links:
PISA 2012 Findings
PISA in Focus No. 44: How is equity in resource allocation related to student performance?
PISA in Focus No. 44 (French version)
Photo credit: Teenager students outside protecting their heads from a rain of books / @Shutterstock

Why policy makers should care about motivating students

by Marilyn Achiron
Editor, Directorate for Education and Skills

What’s in it for me? Positive answers to that ubiquitous (and often crass) question may actually make a fundamental difference in how students learn. As this month’s PISA in Focus explains, students who are highly motivated to learn mathematics because they believe it will help them later on score better in mathematics – by the equivalent of half a year of schooling – than students who are not highly motivated.

Most students recognise that learning mathematics is important for their future studies and careers. Indeed, 75% of students agree or strongly agree that making an effort in mathematics is worth it because it will help them in the work that they want to do later on; 78% agree or strongly agree that learning mathematics can improve their career prospects; 66% agree or strongly agree that they need mathematics for what they want to study later on; and 70% agree or strongly agree that learning many things in mathematics will help them get a job.

Results from PISA 2012 show that, on average across OECD countries, the difference in mathematics performance between students who reported higher levels of motivation to learn mathematics and those with lower levels of motivation is 18 score points, or the equivalent of roughly half a year of schooling; in Korea, Norway and Chinese Taipei, the difference is greater than 30 score points. The results also reveal that motivation is particularly strongly associated with performance among the highest-achieving students. On average across OECD countries, the difference in PISA scores associated with instrumental motivation is 21 points among top performers while it is only 11 points among low achievers. In Belgium, France, Hungary and the Slovak Republic, the score difference, related to motivation, between high and low performers is larger than 20 points.

Perhaps surprisingly, students’ motivation is also associated with certain education policies – particularly those related to sorting or grouping students into different schools or programmes, such as general versus vocational programmes. PISA examined different ways of grouping students between schools and found that students’ motivation is lower in those school systems that offer a larger number of distinct education programmes; where larger proportions of students attend vocational or pre-vocational rather than academic programmes; where students are grouped or selected for these programmes at a younger age; where a large proportion of students attends academically selective schools; and where a large proportion of students attends schools that transfer students with low achievement, behavioural problems or special learning needs to another school.

While creating homogeneous student populations through grouping may allow teachers to tailor instruction to the specific needs of each group, selecting and sorting students generally reinforces socio-economic disparities, results in differences in opportunities to learn, and consequently, de-motivates large numbers of students who do not feel they are being given equal opportunities to succeed. Indeed, selecting students in these ways implies that only some students can achieve at high levels, and thus runs the risk of de-motivating the very students who would benefit the most if their parents, their teachers and their schools held high expectations for them. If students can’t find a good answer to the question why should I bother studying? then all of us have failed.

Links:
PISA 2012 Findings
Pisa in Focus No. 39: Are grouping and selecting students for different schools related to students’ motivation to learn?
PISA 2012 Results: Ready to Learn: Students' Engagement, Drive and Self-Beliefs
Photo credit: College math student /@Shutterstock

Our mothers were right: Hard work and perseverance do pay off

by Marilyn Achiron
Editor, Directorate for Education and Skills

How many times have you heard successful people, in all walks of life, credit their triumphs to hard work and perseverance? Now PISA adds to the chorus with some hard evidence: when students believe that working hard will make a difference in their studies, they score significantly higher in mathematics.

This month’s PISA in Focus examines how students’ perseverance and belief that hard work yields positive results are clearly linked to better performance. Students who reported, through the PISA student questionnaire, that they continue to work on tasks until everything is perfect, remain interested in the tasks they start, do not give up easily when confronted with a problem, and, when confronted with a problem, do more than is expected of them, have higher scores in mathematics than students who reported lower levels of perseverance. In as many as 25 countries and economies, students who have greater perseverance score at least 20 points higher in mathematics than students who reported lower levels of perseverance; and in Finland, Iceland, Korea, New Zealand, Norway and Chinese Taipei, this difference is larger than 30 score points.

Similarly, students who strongly agreed with the statement “If I put in enough effort, I can succeed in mathematics” perform better in mathematics than students who did not agree by an average of 32 score points. The score-point difference in mathematics performance that is associated with this self-belief is 50 points or more in Iceland, Korea, Norway and Chinese Taipei – well over the equivalent of a full school year.

The relationship between students’ perceived control over their success in mathematics and their performance in mathematics appears to be particularly strong among the highest-achieving students. Among these students in OECD countries, those who strongly agreed that they can succeed in mathematics if they put in enough effort have a performance advantage of 36 score points over students who did not agree with that statement; among the lowest-achieving students, the difference is only 24 score points. In 24 countries and economies, this difference is 15 score points or more, and it is particularly large – 30 score points or more – in Hungary, the Slovak Republic, Sweden and Turkey.

Students’ perseverance and drive to learn are not immutable; they can be nurtured with the right kind of guidance and teaching. For example, PISA results reveal that teachers’ use of cognitive-activation strategies, such as giving students problems that require them to think for an extended time, presenting problems for which there is no immediately obvious way of arriving at a solution, and helping students to learn from their mistakes, is associated with students’ drive. And students who reported that their mathematics teachers use teacher-directed instruction (such as when teachers set clear goals for learning) and formative assessments (when teachers give students feedback on their strengths and weaknesses in mathematics) also reported particularly high levels of perseverance and openness to problem solving.

Yet, the use of such strategies among teachers is not widespread: only 53% of students across OECD countries reported that their teachers often present them with problems that require them to think for an extended time, and 47% reported that their teachers often present problems for which there is no immediately obvious way of arriving at a solution. On average across OECD countries, only 17% of students reported that their teacher assigns projects that require at least one week to complete.

What this suggests is that many more students need to be given the chance – and encouragement – to show that they are capable of putting in the hard work – and doing so over a longer time – so  that they, too, can ultimately add their voices to the growing chorus.

Links:
PISA
Pisa in Focus No. 37: Do students have the drive to succeed?
PISA 2012 Results: Ready to Learn: Students' Engagement, Drive and Self-Beliefs
Photo credit: Sisyphus, Simple Drawing and Modern Representation of famous Greek mythology character /@shutterstock

Working to change the mindset for math

by Marilyn Achiron
Editor, Directorate for Education and Skills

What is it about math that strikes fear and trembling in students and adults alike? Perhaps the fault is not in the math, but in ourselves – in how we teach and learn it. Jo Boaler certainly thinks so. She calls mathematics literacy the issue of the 21st century. Even as more companies are looking for people who can use advanced reasoning skills to solve problems, students spend most of their time in math class learning how to compute, she says. Boaler, a British-born professor of mathematics education at the Stanford Graduate School of Education and author of several books on teaching and learning mathematics, brings the latest thinking in psychology, particularly the work of Carol Dweck, and neuroscience to bear on her argument that students would be better served if teachers took a multi-dimensional approach to math (including problem solving, reasoning and communicating) rather than a one-dimensional approach (teaching how to perform various mathematical processes). Indeed, given the emerging evidence she cites of how the former type of teaching results in high student performance, “it’s a no-brainer”, she says.

But the brain, itself, provides some of the all-important evidence for advocating multi-dimensional learning of mathematics. “With recent findings about brain plasticity, we are learning that the brain is more flexible than once thought; and that brain structure changes after training,” Boaler said during a recent visit to OECD headquarters in Paris. “That means that all students can achieve.” Not only that, she says: brain activity increases when students make mistakes in the process of learning: “When you make a mistake, your synapses fire; this doesn’t happen when you get the answer right,” Boaler noted.  “Mistakes are the most useful thing a kid can make.”

So, if the evidence is so concrete and overwhelming, why aren’t we seeing wholesale changes in the way mathematics is taught and learned? “Kids who do well on procedural tests might not do as well on different kinds of problems,” Boaler said. “Teachers and parents don’t know the evidence; it’s a communication issue as well. And some of the problem is about ‘who should achieve’: some people don’t have equity in mind.”

It comes down to teachers’ attitudes, too. “Some teachers embrace change, some are much more conservative about change,” Boaler said. She finds a “huge willingness” among elementary and middle school teachers in the United States to alter the way they teach mathematics, and more resistance among high school teachers. “Good math teaching is good teaching,” she said. Right now, “math is taught as a ‘right or wrong’ subject, which conveys the message that either you can or you can’t do it. This is a stereotyped message about who can achieve; and it has all the ingredients for failure and inequity -- which is what you see in mathematics performance. A lot has to do with beliefs among teachers. One belief that the best teachers have is that all of their students can achieve.”

Change is happening, albeit slowly. In the United States, for example, the new Common Core curriculum puts greater emphasis on problem solving. (Results from the PISA 2012 assessment of problem solving will be released on 1 April.) “People are seeing results of problem-solving tests and they are freaking out,” Boaler said. “Industry wants change. Mathematics performance has to do with confidence: if students feel they can’t do it, that’s a huge barrier; it’s a damaging mindset to have, for both high- and low-performing students. But when you promote learning as a process, great things happen. ”

Boaler has started a movement to change the way math is taught in schools, which can be seen at www.youcubed.org.

Links:
Jo Boaler
Stanford Graduate School of Education
What's Math Got to do With It? written by Jo Boaler
Carol Dweck
Common Core
Results from PISA 2012
Photo Credit: Concept illustration of a human brain made from crumpled paper with numbers and equations on it / @Shutterstock

What do your parents do for a living? (and should it matter?)

by Marilyn Achiron
Editor, Directorate for Education and Skills

Does where you come from really tell you anything about where you’re going? When it comes to parents’ occupations and students’ performance, the answer is a qualified ‘yes’ – but it also depends on where, geographically, you go to school.

Intrigued? PISA is unveiling a web-based, interactive tool (occupations@pisa2012) that allows anyone to explore and compare the relationship between student performance in reading, mathematics and science and parents’ occupations in PISA-participating countries and economies.

The tool is based on results from PISA 2012. Among many other questions concerning students’ backgrounds, PISA asked participating students what their parents did for a living. Their responses were then coded into an internationally comparable classification that allows for identifying individuals working in similar industries, on similar tasks, with the same types of responsibilities. As this month’s PISA in Focus reveals, students whose parents work in professional occupations generally outperform other students in mathematics, while students whose parents work in elementary occupations tend to underachieve compared to their peers.

PISA shows that in the United States and the United Kingdom, where professionals are among the highest-paid in the world, students whose parents work as professionals do not perform as well in mathematics as children of professionals in other countries – nor do they perform as well as the children in Shanghai-China and Singapore whose parents work in manual occupations.

Results also show that, while France and New Zealand perform around the OECD average in mathematics, the performance gap between the children of skilled workers and those of unskilled workers is among the largest observed in participating countries and economies. By contrast, the relative high performance of Finland, Hong-Kong and Korea stems from the fact that the difference in mathematics performance between children of skilled and unskilled workers is relatively small. You’ll also see that Germany is not among PISA’s strongest performers overall because, while the children of professionals in Germany are among the world’s best performers in mathematics, students whose parents work in manual occupations perform very poorly, and these families make up a large share of the country’s total population.

This all boils down to a relatively simple message: if school systems want all of their students to succeed in school, they should give the children of factory workers and cleaners the same education opportunities that the children of doctors and lawyers enjoy.

Links:
Occupations@pisa2012
PISA 2012 Results
PISA in Focus No. 36: Do parents' occupations have an impact on student performance?
Photo Credit: Small Boy with Businessman Looking at Board with Mathematics Formulas / @Shutterstock

 

Mathematics for the 21st century

By Charles Fadel
Founder and Chairman, Center for Curriculum Redesign

Why are mathematics taught? 
From Aristotle, Plato, Al-Khawarizmi, and Al-Kindi, to John Allen Paulos (Temple U.), Paul Ernest, (U. of Exeter), and Eleanor Robson (U. of Oxford), maths thinkers have stated three types of reasons: emotional, cognitive and practical. 

Setting aside the emotional and cognitive reasons, let’s discuss the implications of the practical reasons. Mathematical understanding is crucial for high performance in our personal, public, and work lives. At home, we may want to understand the results of a medical test, or rekindle our child's love of math. As citizens, we may want to judge the rise in carbon-dioxide levels in the air, or the proportion of tax dollars that should go to health, education, or war. At work, we may need to estimate the money, time, and employees for a large project. Finally, mathematics underlies our science, technology, and engineering.  OECD countries spend $236 billion per year on mathematics education yet most countries report shortages in Science, Technology, Engineering and Maths (STEM) talent.

How is the breadth of mathematical application reflected in PISA? 
There are four contexts assessed: personal (self, family and peer groups), societal (one's community), occupational (the general world of work) and scientific (application to science and related issues and topics). These contexts are outstanding choices. Furthermore, by weighting them equally, PISA ameliorates the misconception that mathematics is useful only in the scientific context.

How do we make maths relevant for all occupations, and for new occupations?
The synthesis of research by the OECD and the Royal Society highlights the need to rebalance traditional mathematics (geometry, algebra and calculus) with new branches (statistics and probabilities, applied maths and discrete maths) which are relevant for a wide swath of occupations.  

The OECD Global Science Forum Report on Mathematics in Industry describes the needs for different types of mathematics: statistics & probabilities; complex systems; computational maths. Additionally, the Royal Society’s ACME 2011 “Mathematics in the workplace and higher education” highlights requirements such as: mathematical modelling (e.g. energy requirement of a water company; cost of sandwich); use of software and coping with problems (e.g. oil extraction; dispersion of sewage); costing (allocation; dispute management) (e.g. Contract cleaning of hospital; management of railway); performance and ratios (e.g. Insurance ratios; glycemic index); risk (e.g. clinical governance; insurance); and quality/SPC control (e.g. furniture; machine downtime; deviation of rails).

How are maths used in personal and societal contexts?
Again, personal and societal uses highlight the need to rebalance traditional mathematics (geometry, algebra and calculus) with new branches (statistics and probabilities, complex systems) and deepening the understanding of basic arithmetic (number sense and proportionality).

John Allen Paulos, Mathematician at Temple University, and Author of “A Mathematician reads the newspaper“ has stated: “Gullible citizens are a demagogue’s dream… almost every political issue has a quantitative aspect”.

In PISA, Personal uses, mostly arithmetic and spatial, encompass: personal finance, proportional reasoning, understanding technical documents (plans, charts, etc.), mental maths (percentages, four operations, mental calculating including estimating, etc.), estimation (measures/references/distances such as navigation, etc.), basic geometry (billiards, parking, etc.), and spatial reasoning.

Societal uses - related to data, logic, scale, chance, relationships – are defined in PISA as: structured logical arguments, understanding data (statistical), chance/risk/uncertainty (probabilities), visualization and presenting data, magnitude of numbers (budgets, taxes, etc.), rate of change (exponential, logarithmic, S-curve, etc.), understanding systems and scale (ecology, etc.) including identifying relations between objects.

How can we achieve a more numerate society?
Shockingly perhaps, none of this is particularly new!  A 1982 US National Science Foundation report stated: 
“more emphasis on estimation, mental maths…
“less emphasis on paper/pencil execution…”
“content in… algebra, geometry, pre-calculus and trigonometry need to be… streamlined to make room for important new topics.”
“discrete mathematics, statistics/probabilities and computer science must be introduced”.

The Center for Curriculum Redesign’s Stockholm Declaration has stated:
“We call for a far deeper and reconceptualized understanding of mathematics by the entire population as a critical right, requiring:

• a new vision of mathematics education that anticipates needs and reinforces the role of mathematics in society, economies, and individuals, and strengthens gender equity,
• changes to existing Mathematics standards as presently conceived, through a significant rethinking of what branches, topics, concepts and subjects should be taught in Mathematics for human, economic, social and career development…”

Humanity has a very large stake in making these goals happen, and to do so very soon.

Links:
“What should students learn for the 21st Century?™: The Center for Curriculum Redesign
PISA 2012 Results
Image Source: Charles Fadel, Center for Curriculum Redesign

The high cost of truancy

by Marilyn Achiron
Editor, Directorate for Education and Skills

Resisting authority may be some teenagers’ sport of preference, but they’re hobbling themselves if they think that skipping school is cool. Results from PISA 2012 show that playing truant is related to significantly poorer performance in mathematics, which has repercussions on students’ futures, and on the performance of their school and school system. But all parents and teachers have the means to reduce the incidence of truancy.

This month’s PISA in Focus examines the cost of student truancy. Across OECD countries, 18% of students skipped at least one class and 15% skipped at least an entire day of school without authorisation in the two weeks prior to the PISA test. On average across OECD countries, skipping classes is associated with a 32-point lower score in mathematics and skipping days of school is associated with a 52-point lower score. In Japan, Korea and Chinese Taipei, the score-point difference associated with having skipped classes is larger than 80 points, and in Hungary, Japan, Korea, New Zealand, Shanghai-China and Chinese Taipei, the score-point difference associated with having skipped days of school is also larger than 80-score points.

Schools, too, pay for truancy in the form of poorer performance. In Croatia, Japan, Korea, the Netherlands, New Zealand, Slovenia, Chinese Taipei and Viet Nam, a 10 percentage-point increase in the proportion of students who skip classes or days of school corresponds to a decline in the school’s average mathematics performance of between 10 and 34 score points, after accounting for the socio-economic status and demographic background of students and schools and various other school characteristics.

And student truancy is negatively related to a school system’s overall performance. Among OECD countries, after accounting for per capita GDP, school systems with larger percentages of students who play truant tend to score lower in mathematics. After accounting for differences in the level of economic development, measured by per capita GDP, 16% of the variation in mathematics performance across OECD countries can be explained by differences in the proportions of students who skip school. By contrast, in most high-performing school systems, such as Hong Kong-China, Japan, Korea and Shanghai-China, virtually no student skips classes or days of school.

In most countries, there is very little difference in the incidence of truancy between advantaged and disadvantaged students. Across OECD countries, for example, 19% of disadvantaged students reported that they had skipped classes, compared with 17% of advantaged students, on average; and 18% of disadvantaged students reported that they had skipped days of school, compared with 12% of advantaged students. That means that the problem of truancy cuts across all types of families and schools – and so does the solution.

In 8 of the 11 countries and economies with available data, students whose parents regularly eat the main meal with them are less likely to have skipped classes or days of school. And students who reported that they have good relations with their teachers are five percentage points less likely to have arrived late for school, on average across OECD countries, and four percentage points less likely to have skipped classes or days of school during the two weeks prior to the PISA test. In other words: parents and teachers can nurture student engagement with and at school – and by doing so, discourage students’ impulse to skip school – by being more engaged themselves with their children and students.

Links:
PISA in Focus No. 35: Who are the school truants?
PISA 2012 results
Ready to Learn: Students' Engagement, Drive and Self-Beliefs (Volume III)
What Makes Schools Successful? Resources, Policies and Practices (Volume IV)

Photo credit: Erasing desk  / @Shutterstock

Japan finds inspiration in its PISA results

by Miki Tadakazu
Analyst, Directorate for Education and Skills

PISA 2012 showed mixed results for Japan. While Japanese students maintained their strong performance in mathematics, reading and science, the assessment found that 15-year-olds in Japan take less pleasure in learning mathematics and have less interest and motivation in doing so than the average student across OECD countries although Japanese students’ interest and motivation have improved since 2003. The Japanese government is using these findings to improve both the way students learn and what they learn.

Up until 2002, Japanese primary and secondary students attended school six days per week. Saturday schooling was eliminated that year in an effort to let students have a wide variety of activities and experiences outside of school. But after that reform was adopted, educators realised that inequities in schooling began to develop. In particular, while advantaged students benefited from Saturday studies at the privately owned and managed educational institutions known as juku, disadvantaged students usually did not have access to these opportunities. Many parents reported that they wanted their children to attend school on Saturday morning.

Late last year the government made it clear that individual local education boards could opt to have learning activities on Saturdays to meet their students’ learning needs. The aim of this reform is to conduct high-quality learning activities on Saturday in cooperation with parents, local communities and economic communities. Each school can provide diverse learning opportunities such as classes that fall within their curriculum, extra-curricular activities and non-profit organisations’ coordinating activities, based on their students’ needs.

On 14 December, using PISA mathematics items, the Minister of Education, Culture, Sports, Science and Technology, Hakubun Shimomura took the initiative to experimentally teach mathematics during Saturday learning activities in a public elementary school located in Itabashi City in Tokyo. The goal was to ensure the effectiveness of Saturday learning activities in school by increasing students’ diverse learning opportunities and improving their pleasure, interest and motivation to learn. During his learning session, he not only taught how to solve equations, but also dissected them and showed students how they encounter these kinds of problems in everyday real life situations.

Students who took the session said, “I got tense but enjoyed myself,” and “I hope my score will improve if I join Saturday learning sessions.” Minister Shimomura gathered from this session that Japanese students could enjoy a wide variety of learning activities, which could further develop their pleasure, motivation and interest to learn. 

Among other ways of using this additional time in school, the “period of integrated study”, mandatory in the Japanese curriculum, will be used. During this study time, the focus is on learning through observation, experiments, field study, investigation and problem solving. The idea, then, is that on Saturdays, parents and members of the local community are more available to offer their specific knowledge and skills to students, skills that are used in daily life and that may also inspire students to take a greater interested in weekday course work.

Providing learning activities on Saturdays is not intended to add more time for students to absorb and reproduce established knowledge. Rather, the aim is to offer learning activities that challenge students to apply what they have learned in school to real-life problems and that help them acquire the kinds of “soft” skills – communication, collaboration and imagination – that are considered essential for the 21st century.

Links:
PISA 2012 Results
PISA 2012 Country-Specific overview on Japan
OECD Programme for International Student Assessment
Strong Performers and Successful Reformers in Education - Lessons from PISA for Japan
Photo credit: Ministry of Education, Japan

What we learn from the PISA 2012 results

by Andreas Schleicher
Deputy Director for Education and Skills and Special Advisor on Education Policy to the OECD's Secretary General

 

International comparisons are never easy and they aren’t perfect. But PISA shows what is possible in education, and it helps countries see themselves in the mirror of the education opportunities and results delivered by the world’s leaders in education. Even those who claim that the relative standing of countries in PISA mainly reflects social and cultural factors must now concede that improvement in education is possible. In mathematics, countries like Brazil, Mexico, Tunisia and Turkey rose from the bottom; Italy, Portugal and the Russian Federation advanced to the OECD average or close to it; Germany and Poland rose from average to good; and Shanghai-China and Singapore have moved from good to great. Indeed, of the 65 participating countries, 40 saw improvement in at least one of PISA’s three subject areas. These countries did not change their culture, or the composition of their populations, nor did they fire their teachers; they changed their education policies and practices.

We focused this year’s PISA assessment on mathematics. Each year, OECD countries invest over 200 billion euro in math education in schools; but poor math skills still severely limit people’s access to better-paying and more-rewarding jobs and, at the aggregate level, inequality in the distribution of math skills closely relates to how wealth is shared within nations.

This PISA 2012 assessment came at a time when countries were still grappling with the aftermath of the economic crisis - a period that has brought home the urgency of equipping more people with better skills to collaborate, compete and connect in ways that drive our economies forward, foster employment and reduce social inequality.

A large part of the challenge in education lies in addressing underperformance. Across countries, almost one in four 15-year-olds did not even reach Level 2, the PISA baseline level of proficiency in mathematics, where students have to do little more than employ basic algorithms or procedures involving whole numbers. But in Canada, Korea, Shanghai-China and Singapore, it is one in ten or fewer. According to one estimate, if all 15-year-olds in the OECD area attained at least PISA Level 2 in math, they would contribute USD 200 trillion in additional economic output over their working lives. While such estimates are never wholly certain, they do suggest that the benefits of improvement dwarf any conceivable cost. Part of the issue lies with students living in social disadvantage, and many school systems amplify that disadvantage. According to PISA, advantaged and disadvantaged schools show particularly wide differences in levels of teacher shortages. Attracting the most talented teachers and school leaders to the most challenging classrooms will therefore be key to making headway. Indeed, PISA finds that higher-performing countries allocate educational resources more equitably among advantaged and disadvantaged schools.

A belief that all students can achieve at a high level and a willingness to engage all stakeholders in education – including students, through such channels as seeking student feedback on teaching practices – are other hallmarks of successful school systems. New results from PISA also show that students whose parents have high expectations for them tend to have more perseverance, greater intrinsic motivation to learn math, and more confidence in their own ability to solve math problems.

But the challenges of school systems are not just about poor kids in poor neighbourhoods, but about many kids in many neighbourhoods. Only 2% of American students reach the highest level of math performance, demonstrating that they can conceptualise, generalise and use math based on their investigations and apply their knowledge in novel contexts. That compares with an OECD average of 3%, and proportions of up to 31% in Shanghai-China. The world economy will pay an ever-rising premium on excellence, and a number of countries have shown how the share of top performers in school can be raised significantly, including in high performers, such as Hong Kong-China and Korea, and low performers, such as Italy, Portugal and the Russian Federation. It is important that raising excellence and improving equity are not seen as conflicting policy objectives. Indeed, of the 13 countries that significantly improved their math performance since 2003, three also show improvements in equity in education, and another nine improved their performance while maintaining an already high level of equity.

Of course, raising outcomes is easier said than done. The status quo has many protectors, and countries need to be bold in thinking and in execution to effect real changes. Obviously, we can’t copy and paste school systems wholesale. But PISA has revealed an encouraging number of features shared by the world’s most successful school systems.

Everybody agrees education is important. But the test comes when education is weighed against other priorities. How do countries pay their teachers, compared to other highly skilled workers? Would you want your child to be a teacher rather than a lawyer? How do the media talk about teachers? What we’ve learned from PISA is that the leaders in high performing systems have convinced their citizens to make choices that value education, their future, more than consumption today.

But placing a high value on education is just part of the equation. Another part is the belief that all children can achieve. The fact that students in some countries consistently believe that achievement is mainly a product of hard work, rather than inherited intelligence, suggests that education and its social context can make a difference in instilling the values that foster success in education.
In the past, different students were taught in similar ways. Today’s top school systems embrace diversity with differentiated instructional practices; they realise that ordinary students have extraordinary talents and they personalise educational experiences. High-performing school systems also share clear and ambitious standards across the board. Everyone knows what is required to get a given qualification. This remains one of the most powerful system-level predictors in PISA.

And nowhere does the quality of a school system exceed the quality of its teachers. Top school systems pay attention to how they select and train their staff. They watch how they improve the performance of teachers who are struggling and how to structure teachers’ pay. They provide an environment in which teachers work together to frame good practice. And when deciding where to invest, they prioritise the quality of teachers over the size of classes. Not least, they provide intelligent pathways for teachers to grow in their careers.

High performers have also moved on from administrative control and accountability to professional forms of accountability and work organisation. They support their teachers in developing innovations in pedagogy, in improving their own performance and that of their colleagues, and in pursuing professional development that leads to stronger education practice. The goal of the past was standardisation and compliance; now, top performers enable teachers to be inventive. In the past, the policy focus was on providing education; in today’s top school systems, it’s on outcomes, shifting from looking upwards in the bureaucracy towards looking outwards to the next teacher, the next school, about creating networks of innovation.

Perhaps the most important outcome of world-class school systems is that they deliver high-quality education across the entire school system so that every student benefits. Overall, Finland did not come out quite as impressively as in previous assessments; but what makes Finland still special is that only 6% of the performance variation among students lies between schools. In other words: every school succeeds.

Last but not least, high-performing systems tend to align policies and practices across all aspects of the system, they make them coherent over sustained periods of time, and they see that they are consistently implemented.

Of course, there is no single combination of policies and practices that will work for everyone, everywhere. Every country has room for improvement, even the top performers. That’s why the OECD produces this triennial report on the state of education across the globe: to share evidence of the best policies and practices and to offer our timely and targeted support to help countries provide the best education possible for all of their students. With high levels of youth unemployment, rising inequality, a significant gender gap, and an urgent need to boost growth in many countries, we have no time to lose.

Links:
PISA 2012 Results
OECD Programme for International Student Assessment
Press release: Asian countries top OECD's latest PISA survey on state of global education
Follow:
PISA on twitter: @OECD_Edu @SchleicherEdu @OECDLive #OECDPISA
Facebook PISA  for Parents

How did the smartest kids in the world get that way?

by Marilyn Achiron
Editor, Directorate for Education and Skills

Last week, students, teachers and parents in New York State were stunned to learn that not even one in three third-through-eighth graders passed the new, state-wide English and math exams – tests aligned with the effort now underway in the United States to foster deep analytical and problem-solving skills and introduce more rigorous standards, known as the Common Core, into the country’s education system. While most US states have adopted the Common Core, disappointing first results are dampening enthusiasm for the reform: some states have already stopped rolling out the new exams, citing cost concerns.

I can think of one person who probably isn’t surprised by either the test scores or the resultant sulky foot-dragging to implement reforms: journalist and author Amanda Ripley.  In her new book, The Smartest Kids in the World: And How They Got That Way, published today in the United States by Simon and Schuster, Ripley sets the scene for what is turning out to be a battle for the soul of US education. Using PISA 2009 results as the backbone of her story, Ripley sets out to find out why it is that American students are falling behind their contemporaries in countries that aren’t as wealthy or innovative as the United States. “PISA could not tell me how those countries got so smart, or what life was like for kids in those countries, day in and day out, compared to life in America,” she acknowledges. So with three American teenagers as her guides, she explores the human dimension of PISA results: what school is really like for students in Finland, Korea (two PISA top performers) and Poland (a rapidly improving PISA participant).

She follows 15-year-old Kim from rural Oklahoma to Pietarsaari, Finland, where the American exchange student learns first-hand what the Finnish word sisu (roughly translated: strength in the face of great odds, and then some) really means; she follows 18-year-old Eric, a high school graduate who also completed the demanding International Baccalaureate Diploma Programme, from suburban Minnesota to Korea, where he planned to spend a year experiencing the “pressure-cooker” of that country’s education system; and she follows Tom, 17, a voracious reader from Gettysburg, Pennsylvania, to Poland (“[he wanted] to live somewhere where people knew the names Dostoyevsky and Nabokov”) to discover how one country could come so far so fast.

In lively, accessible prose, Ripley paints a warts-and-all picture of both the “education superpowers” and the failing American education system, and discovers the solution to the “mystery” of effective education. It involves rigor (“The problem with rigorous education was that it was hard”), learning how to learn – and recover – from failure (“’Success,’ as Winston Churchill once said, ‘is going from failure to failure without losing your enthusiasm’”), and parents who are involved in their children’s education, not so much by being active in parent-teacher associations or coaching a sports team, but by reading to their young children every day and talking with their older children about their day or about what’s going on in the world. “They let their children make mistakes and then get right back to work. They teach them good habits and give them autonomy,” Ripley observes.

Regular readers of the educationtoday blog, PISA in Focus, or the PISA initial reports will be familiar with most of the data and some of the conclusions in The Smartest Kids in the World. But Ripley’s book looks at the data from a new perspective: that of the students who are the beneficiaries -- or victims -- of their countries’ education systems. Those stunned parents and teachers in New York State and elsewhere would do well to read this book first if they are inclined to blame their children’s/students’ poor results on a new test.

Links:   
OECD PISA for Parents
Videos on Finland and Korea as part of the Strong Performers, Successful Reformers video series
 Photo credit: Evaluation symbol  / @Shutterstock

A Curriculum for the Next Billion

by Charles Leadbeater
Author of Learning from the Extremes and Innovation in Education: Lessons from Pioneers Around the World, published by Bloomsbury with the support of the The Qatar Foundation’s WISE initiative.

Today, global companies are fascinated by the prospect of what the World Economic Forum calls ‘the next billion’ – the future consumers of the developing world whose income is rising from around $2 a day to between $5 and $7 a day. Most of these people are recently arrived in rapidly expanding cities, often living in the poorest areas: every month about 5 million people in the developing world move to cities.

If we were to look at these families as parents and learners, what kind of education will they be looking for? Or to put it another way, if we were to design a curriculum with ‘the next billion’ what would they want?

Having spent much of the last three years visiting a wide variety of education projects in cities across the developing world, it strikes me that the first thing that people want is facility with a global language, usually English, but also in some places Spanish and, in others, Mandarin. They want a language that will give them access to people and jobs linked to global networks and trade – a business hotel, a job in retail, manning a phone in a call centre – rather than confining them to ply their trade in purely local markets.

Next they want a mastery of basic mathematics, the ability to understand numbers and do fairly basic sums, like working out discounts or more complex applications like planning a production schedule. Maths is foundational to much else that people need, and want. to learn.

The third ingredient is digital literacy. People need to be able to work competently and capably with computers, and not just the basics of the Microsoft world of Word and Excel, but increasingly the world of the web and social media, apps and programming. They need to be comfortable with having to learn, and learn again, as technology changes.

None of that, however, is worth very much unless they are skilled at working together with other people. So the fourth thing their education needs to give them is a well-grounded experience in social skills so they know how to respond to customers and work well with their colleagues, to find collaborative solutions to problems. Some of those skills are social and relational, based on empathy and sympathy. But others are more about collaborative self-government, which is why it is so important that education provides children with ample, structured, challenging opportunities to work together, in groups, on projects which they can make their own. As social media spreads so it will open up ever more opportunities for people to find one another and come together to achieve common goals. Citizens will need to learn how to make the most of these technologies, for better government, richer culture and more successful businesses.

All of this needs to be married to entrepreneurial and creative capacity, by which I mean the ability to spot an opportunity, mobilise support to take it, learn how to take risks and recover from setbacks. Most of the ‘next billion’ will find themselves working in small entrepreneurial companies. Studies of the urban poor show that many have to hold down two or three jobs to survive. Their education needs to help them become micro-entrepreneurs, adaptive and resilient, fleet of foot. Learning to juggle work if, not balls, is a key skill.

The slim core skills set out above might provide the starting point for thinking about the kinds of skills all young people might need in the years ahead, in the developed and the developing world.

Yet that is only at best half the story. Setting out what people should learn is just the starting point. How they learn is almost as important. Effective learning needs to be a structured, well-designed, highly engaging activity which challenges and stretches young people as well as supporting them and building their confidence. It needs to pull people to it, by the laws of attraction. Too much of the time at school it is the other way around: people are pushed into learning they do not really understand and cannot make meaningful.

To be motivating learning needs to be intrinsically satisfying and to offer at least the distant prospect of a pay-off: a better job; a practical skill; a useful way of thinking.

Achieving that will mean that learning will have to become more connected to, if not located in, the real world of work and production. The most impressive and attractive places to learn in future, in the developed and developing world, will give young people ample opportunities to design and make, produce and sell things, with their hands and their heads. They should go to school to learn by working and having fun. They should study by making and building rather than sitting and listening.

Too often education is seen as a pristine preparation for a later career. Work is held at bay for as long as possible. I doubt we can afford that distinction in the future in which education increasingly seems to be losing touch with the real world that young people live in – and the real world seems increasingly unwilling to give them the jobs they crave. We need learning to give young people a real sense of what creative, satisfying, productive work can be, so they can take those standards and expectations into their later working life.

All innovators succeed by challenging ingrained conventional wisdom. Breaking down the barriers between work and learning will be one of the chief opportunities for educational innovators in the decades to come, especially if they want to meet the needs of the next billion parents and children entering formal education.


Links:
Innovation in Education: Lessons from Pioneers around the World
See also: OECD Skills Strategy

Visit our interactive portal on skills: http://skills.oecd.org
Languages in a Global World: Learning for Better Cultural Understanding

Photo credit: Population of our World in Colour / Shutterstock