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?

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”)

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