Learning by heart may not be best for your mind

by Alfonso Echazarra

Analyst, Directorate for Education and Skills



PISA 2012 Released Mathematics Item (Proficiency Level 6)

Some of the greatest geniuses had remarkable memories. Mozart, according to legend, sat and listened to Allegri’s “Miserere”, then transcribed the piece of music, entirely from memory, later in the day. Kim Peek, the savant who was the inspiration for the blockbuster film, Rain Man, memorised as many as 12 000 books. But unlike Mozart, who composed more than 600 works during his brief life, Peek was unable to distinguish between the relevant and the irrelevant, or discover hidden meanings and metaphors in the texts he had committed to memory.

What do these stories have to do with learning mathematics? Or, put another way: in light of these stories, how would you encourage students to learn mathematics? By understanding what mathematics concepts, procedures and formulae mean and applying them to a lot of different maths problems set in a lot of different contexts? Or by learning them by heart and applying them to a lot of similar maths problems? Sooner or later, the method matters. Students who avoid making an effort to understand mathematics concepts may succeed in some school environments; but a lack of deep, critical and creative thinking may seriously penalise these students later in life when confronted with real, complex problems. As Albert Einstein provocatively said: “Any fool can know; the point is to understand”.

A similar message is relayed in this month’s PISA in Focus and a new OECD paper on education, “How teachers teach and students learn: Successful strategies for school”. The analyses show that students who mainly use memorisation when they study do well on easy questions. For example, “CHARTS Q1”, a multiple-choice question from the PISA 2012 test, refers to a simple bar chart and is considered one of the easiest questions in the mathematics assessment. Some 87% of students answered this question correctly. Students who reported that they use some type of memorisation strategy when they study mathematics, such as learning by heart, recalling work already done or going through examples again and again, had about the same success rate on this easy item as students who reported using other learning strategies.

But complex problems are a different matter; they require more than a good memory. For the most challenging question from the PISA 2012 mathematics test, “REVOLVING DOOR Q2”, students who reported using mainly memorisation strategies were much less likely than students using other strategies, such as connecting ideas or working out exactly what is important to learn, to answer correctly. Answering “REVOLVING DOOR Q2” correctly requires substantial geometric reasoning and creativity, involves multiple steps, and draws heavily on students’ ability to translate a real situation into a mathematical problem. Only 3% of participants answered this question correctly.

The findings also show that, contrary to received wisdom, East Asian students are not necessarily the ones who use memorisation strategies the most. Memorisation is used almost everywhere, but fewer 15-year-olds in Hong Kong-China, Japan, Korea, Macao-China, Shanghai-China, Chinese Taipei and Viet Nam reported using it than students in, let’s say, English-speaking countries to whom they are often compared. For instance, 5% of students in Viet Nam, 12% of students in Japan and 17% of students in Korea reported that they learn as much as they can by heart when they study mathematics, compared to 26% of students in Canada, 28% in Ireland, 29% in the United States, 35% in Australia and New Zealand, and 37% in the United Kingdom.

In some situations, memorisation is useful, even necessary. It can give students enough concrete facts on which to reflect; it can limit anxiety by reducing mathematics to a set of simple facts, rules and procedures; and it can help to develop fluency with numbers early in a child’s development, before the child is asked to tackle more complex problems. But to perform at the very top, 15-year-olds need to learn mathematics in a more reflective, ambitious and creative way – one that involves exploring alternative ways of finding solutions, making connections, adopting different perspectives and looking for meaning. So yes, you can use your memory; just use it strategically, lest Einstein call you a fool.

Links:
PISA in Focus No. 61: Is memorisation a good strategy for learning mathematics? by Alfonso Echazarra
PISA á la loupe No. 61: La mémorisation : Une stratégie payante pour l’apprentissage des mathématiques?
How teachers teach and students learn: Successful strategies for school.
PISA Try the Test: Explore PISA 2012 Mathematics, problem solving and financial literacy test question
Source: PISA 2012 Released Mathematics Items

Is international academic migration stimulating scientific research and innovation?

by Dirk Van Damme
Head of the Innovation and Measuring Division, Directorate for Education and Skills

Higher education and academic research are among the most rapidly globalising systems. Today, around 5 million students study and do research in a country other than their own, attracted by the quality of overseas universities and willing to complement their education portfolio with international experience. Employers generally value the impact international education has on the skills and mind-set of graduates, and see international experience as indispensable for future global leaders.

But in an age when governments are increasingly concerned about rising levels of migration and are making their migration policies more stringent, international student mobility is also being scrutinised. Some countries impose stricter visa requirements or limitations on the time for international students to stay in the country. Others make it more difficult for graduates to stay and work in the country where they have studied. The prospect of losing the economic returns from international students and the income provided by fee-paying students does not seem to dissuade some governments from imposing stricter regulations on international students.

The recent Education Indicators in Focus brief looks in more detail at the international mobility of master’s and doctoral students. The mobility of doctoral students is of special concern because of its relevance to research policy. The chart above illustrates the close relationship between the number of international doctoral students in a country and the country’s commitment to research, as measured by spending on R&D in tertiary education. Countries with a large share of international doctoral students are also countries that invest a lot in research.

The chart does not suggest any causality. In fact, there are two ways to interpret the relationship. Countries with relatively high levels of investment in university research are probably well-integrated in global research networks. International collaboration naturally leads to an exchange of researchers. Favourable research climates, high levels of investment and the prospect of collaborating with researchers working at the cutting edge in their fields offer attractive opportunities for young doctoral researchers.

The global research landscape is diversifying. Next to the academic centres in the United States and the United Kingdom, new strongholds of global academic research are emerging in countries such as Switzerland, the Netherlands and Sweden. These countries have opened up their universities for international researchers, and now 30%, 40% or even more than 50% of the doctoral students in these countries are of foreign origin.

But it could very well be that the causality also works in the other direction. Higher numbers of international researchers probably contribute to the global competiveness of academic research by strengthening integration in research networks or by facilitating international knowledge transfer. We can find support for this hypothesis in comparing our data on the percentage of international doctoral students with OECD data on the share of publications in the top 10% academic journals. The strong country-level correlation between both sets of data suggests that doctoral students have a positive impact on the quantity and quality of scientific research in the host country. In turn, this could prompt governments to increase their R&D spending on universities. Indirectly, international students then contribute to the innovation process and the development of a research-intensive knowledge economy in the host country.

The case of Switzerland is telling. A small country in the heart of Europe that is now fiercely debating migration policy, Switzerland has opened up its universities to international researchers and doctoral students, while at the same time increasing its R&D investment. Anyone who looks at international rankings has noticed that Switzerland is rising rapidly up the global academic hierarchy. Sweden and the Netherlands are close behind. This is no coincidence.

Current debates about international student mobility tend to overemphasise the benefits for the individual student or the financial returns for the host institution or host country. But it is also important to look into the wider benefits of academic migration. Laboratories and research centres at the frontier of their fields cannot do without strong integration in global networks and without international researchers. Progress in scientific research happens by sharing and confronting ideas, questioning established wisdom and looking at the world from different perspectives. International exchange and mobility of doctoral researchers is absolutely critical to this. Countries that curtail academic mobility risk paying a high price.

Links:
The internationalisation of doctoral and master's studies, Education Indicators in Focus, issue No. 39, by Gabriele Marconi.
L’internationalisation des études de doctorat et de master, Les indicateurs de l'éducation à la loupe, issue No. 39 (French Version).

Graph sources: OECD Education Database, http://stats.oecd.org/, (accessed 21 January 2016), and OECD (2015a), Education at a Glance 2015: OECD Indicators, OECD Publishing, Paris, http://dx.doi.org/10.1787/eag-2015-en, Table B1.2.