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”)

What Spanish schools can learn from Spanish schools

by Andreas Schleicher
Acting Director and Special Advisor on Education Policy to the Secretary-General

I arrived in Madrid in the morning of 1 April, coming from Singapore. I met with Singapore’s school principals and policy makers the day before to review the results from our new PISA problem-solving skills assessment. Singapore’s education system has at times been criticised for encouraging rote learning at the expense of creative skills development. Those critics should have a second look.

The PISA results show that 15-year-old Singaporeans are quick learners, highly inquisitive and able to solve unstructured problems in unfamiliar contexts. Indeed, no education system outperforms Singapore on this problem-solving test. The Spanish results on the same test, which I presented later in the day in Madrid, were a lot more troubling.  As shown in previous PISA assessments, Spanish students face challenges in math and science. However, there is bigger concern regarding their problem-solving skills. Spanish students performed significantly worse on tasks requiring creative problem-solving skills. The issue is not simply concerning poor kids in poor neighbourhoods, but is an issue that touches children from many regions of Spain. What’s more, these results do not correlate with the amount of money going into Spanish schools.

This is troubling because the dilemma for educators is that routine cognitive skills, the kind of things that are easy to teach and easy to test, are also the skills that are easiest to digitise, automate and outsource. There is no question that state-of-the-art knowledge in a discipline will always remain essential. Innovative or creative people generally have specialised skills in a field of knowledge or a practice. As much as ‘learning to learn’ skills are important, educational success is no longer about reproducing content knowledge, but about extrapolating from what we know and applying that knowledge creatively.

Is that beyond what can be achieved in the Spanish education system? The PISA results show that school curricula – and teachers – make a difference in imparting creative problem-solving skills. Engagement with, and at, school is relatively high in Spain, and I witnessed this first hand at the Santa María La Blanca school, just half an hour by car from where I had presented the disappointing PISA results in the morning. Comparatively speaking, I was amazed at how much the school in Spain had in common with schools in Singapore. Structurally, there was nothing spectacular about the building. The school’s teachers hadn’t had more extensive training. Nor did the students come from more advantaged backgrounds. It was all about the learning environments and about learner ownership. The lessons weren’t one-size-fits all, but I witnessed students designing their own learning experiences on constant reviews and revisions of their learning goals. These students were able to explain to an outsider, like myself, what they were learning, how they were learning and why it mattered.

These students were experiencing the most rewarding kind of learning achievement: knowledge as a product of hard work versus knowledge as inherited intelligence or luck. The teachers I met embraced diversity through differentiated instructional practices, realising that ordinary students have extraordinary talents. Each students’ learning path is planned jointly, facilitated by the latest digital technology. And, as always, behind a great school is a great principal. Someone who supports teachers to make innovations in pedagogy, to improve their own performance and that of their colleagues. It is a team effort in constructing stronger pedagogical practice.

The PISA results show that school autonomy is still rare in Spain. Additionally, schools exercise even less autonomy than they actually have. However, Santa María La Blanca has moved beyond the paradigms of standardisation and compliance and enables their teachers to be inventive. The teachers are no longer looking upwards to bureaucracy, but look outwards to the next teacher and the next school to create a network of innovation.

If all Spaniards knew what some Spanish schools know, students would probably match their peers in the world’s top performing education systems. Having the belief in being able to achieve at high levels, and the ability and willingness to do what it takes, would equip Spanish students with the attributes to enable them to lead full lives, meet challenges and make the most of available opportunities along the way.

Perhaps there is not much we can find in Singapore that we can’t see somewhere in Spain too. But, what makes Singapore different is that it has made success systemic. They have aligned policies and practices across all aspects of the system to encourage ingenuity and entrepreneurship, made policies and practices coherent over sustained periods of time, and seen innovative practices that are consistently implemented.  In this way, Spain still has a long educational path ahead.

Links:
PISA 2012 Results, Volume V
Country note Spain (Problem Solving)
Country note Singapore (Problem Solving)
Photo credit: School girl drawing sketches with marker /@Shutterstock

Creativity in schools: what countries do (or could do)

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

Are we really serious when we say that schools should nurture creativity and other skills for innovation? An increasing number of countries see fostering of creativity and critical thinking as the next educational challenge: traditional good grades may no longer suffice to equip the workforce with the skills needed to fuel innovation-driven economic growth.

The recent international OECD-CCE-Singapore workshop gave 30 education decision-makers from 12 countries the opportunity to share the lessons from Asian educational initiatives aiming to foster pupils’ creativity and critical thinking. While most of these initiatives build on project-based, research-based, and other active pedagogies, some start to use design thinking methods to scaffold the learning of innovation skills.

Singapore and Korea are two good examples of countries emphasising creativity, critical thinking and character building in their curricula. Since 2009, Korea expects its schools to foster creativity as part of quality subject-based learning – but also to devote almost 10% of overall school time to projects and other transversal activities that foster creativity. As for Singapore, their “Desired Outcomes of Education” include critical and inventive thinking as well as social and emotional competences. At the end of secondary school, among other things students are expected to be “resilient in the face of adversity”, “innovative and enterprising” as well as “able to think critically and communicate persuasively”.

A visit at Haig Girls’ School in Singapore showed that this is more than just words. Creativity and innovation are at the heart of the project of this elementary school. Teachers have developed common criteria to monitor their students’ progress in “critical thinking” and in “creative and inventive thinking”. Students also assess themselves and their peers by answering questions such as “I am able to brainstorm multiple ways to reach a solution” (critical thinking) or “I am able to connect ideas in an interesting and creative manner to create a unique idea” (creative thinking).

Among its multiple projects, the school also asks pupils to engage in genuine innovation activities. After a long collective brainstorming, a small group of pupils has imagined and prototyped an inventive way of closing an umbrella—a useful invention in a country where it rains almost every other day. Why use two hands to fold your umbrella and risk one of them getting wet when you could do it with just the one hand holding the handle? To keep you dry and speed up the closing process, the girls have replaced the press-stud on the small band that is generally rolled around the fabric to fasten the umbrella tight with a magnet. The magnet is heavy enough to make the band twist around the pole before adhering to the magnetic frame and keeping the fabric tight. Ingenious, no?

Including creativity and other skills for innovation in national curricula is a helpful starting point for them to be taken seriously in school. The next step is to also formally assess these skills. Singapore and Korea have thus changed their national exams and assessments to incentivise teachers and students to pay due attention to them in their teaching and learning.

Prototype tool for assessing pupils’ creativity in schools

Could we develop simple formative assessment tools to help teachers and students to pay more attention to habits of minds conducive to creativity in the school context? A recent OECD working paper,  “Progression in student creativity in school”, reveals how assessment helps specify and clarify what creativity really means, especially as there are many different views about what it is. A prototype tool for assessing pupils’ creativity in school maps the dispositions of creative habits of minds along 5 dimensions: inquisitive; persistent; imaginative; collaborative; disciplined (each dimension including 3 sub-dispositions). The findings of two field trials in English schools show that the assessment tool led teachers to be more precise and confident in developing their pupils’ creativity, and learners to be better able to understand what creativity entails and to record evidence of their progress. Such tools are an important step to raise daily awareness of skills in thinking and creativity and see them materialise in school learning.

While the journey ahead is still long, it is encouraging to see countries taking action and starting to share the tools and lessons that will eventually make all students and teachers reach the promised land.

Links:
For further information on CERI Innovation Strategy for Education and Training, please visit our webpage: www.oecd.org/edu/innovation
The following working papers should be of interest:
• Progression in student creativity in school: first steps towards new forms of formative assessment by Bill Lucas, Guy Claxton and Ellen Spencer
• Assessment and Innovation in Education by Janet Looney
• Bringing about curriculum Innovation by Kiira Kärkkäinen
View our video of Howard Gardner discussing creativity and 21st Century education as well as his interview.
Summary reports and presentations on education for innovation can also be found in our conference webpage.
Diagram: Lucas, Claxton and Spencer (2013)
Photo credit: Shutterstock / Girl with umbrella