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When mathematicians perform their calculations, they use symbols such as numerals, plus and minus signs, brackets and the radical sign – that’s the language of mathematics. To teach and learn mathematics, however, it is particularly important to be able to communicate well in words, not only in symbols.
Words are essential when it comes to understanding what the mathematical symbols mean. This is something that is experienced particularly often by children at school who have problems understanding language – either because their home language is not spoken at their school, or because they are unfamiliar with the higher-level, more academic language used in the classroom.
The role played by language in maths lessons
When learning about fractions, for example, pupils have to understand terms like a quarter or an eighth, and need to know what simplifying and extending means. "Our empirical studies show that students with limited language proficiency also struggle with developing a conceptual understanding of the mathematical concepts. They are simply unable to participate in the classroom processes of explaining and discussing meanings", says Professor Susanne Prediger, who runs the Institute for Development and Research in Mathematics Education (IEEM) at TU Dortmund University.
Working with linguists and experts in language didactics in the MuM – Mathematics Learning in Multilingual Classrooms project (only in German), she has been exploring since 2009 how subject-specific and language-specific aspects are interconnected when it comes to teaching and learning mathematics. "We collaborate with linguists, and more recently especially with Angelika Redder (only in German) from Hamburg University. This is a great experience because the interdisciplinary exchange of perspectives on the students’ learning processes helps us gain a deep understanding of the role of language."
Benefits of multilingualism
These joint studies have also shown that multilingualism need not always pose an obstacle in maths lessons. Those who speak several languages can also derive benefits from this. "Our quantitative research shows that students who mix and combine their languages have stronger learning gains than the students who speak only German", reports the maths education expert. In addition, the researchers analyse video recordings of remedial maths lessons to discover the extent to which multilingual pupils learn mathematics more intensively if they utilise all their languages. "These students seem to deepen their conceptual understanding by adopting different perspectives", notes Susanne Prediger. "Flexible speaking seems to promote flexible thinking." She goes on to say that pupils able to describe a fraction in different ways are also more likely to understand the abstract concept behind it.
New approaches to classroom learning
The empirical basic research concerned with precisely describing the linguistic problems involved in learning mathematics is just one part of the MuM research project. The researchers also develop new approaches to mathematics teaching at secondary level. The idea is to help pupils with language difficulties improve their ability to speak and understand German while at the same time increasing their understanding of mathematics. These approaches have already found their way into the classroom via continuing education programmes for teachers and via lesson modules made available on online platforms.
With a view to mobilising those linguistic resources that pupils bring with them from home and taking greater advantage of these resources during learning at school, the researchers want to go one step further. They are working on classroom learning approaches that would allow pupils in future to use not only German in maths lessons, but also their various home languages such as Turkish, Russian or Farsi. "This is a bit more difficult", explains Prediger, "but we are optimistic that we can handle as many as seven different languages in the classroom. This is the major challenge in the next MuM project."
Institute for Development and Research in Mathematics Education (IEEM) at TU Dortmund University
The researchers at the IEEM develop and explore theoretical approaches to and practical suggestions for mathematics lessons. The IEEM is involved in international collaborations as well as in inter-university and interdisciplinary research projects.www.mathematik.tu-dortmund.de > IEEM