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Mathematics Education and Language Diversity

Richard Barwell, et al., editors
Publication Date: 
Number of Pages: 
New ICMI Study Series
[Reviewed by
Annie Selden
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This ICMI Study Volume has 15 chapters authored by 47 contributors from 22 countries including Brazil, South Africa, Germany, Denmark, Cameroon, Tanzania, Russia, USA, and Canada. Each ICMI Study volume is written after an ICMI Study Conference — this one was in Brazil in 2011. The conference itself had 91 participants from 27 countries, which resulted in a published conference proceedings, different from this volume. According to the introductory chapter, this ICMI volume “brings together the combined thinking of over 5 years of work by colleagues from many parts of the world”.

From this volume, one can learn a variety of interesting facts about language that can lead to teaching and learning problems. For example, Chapter 2 considers how the grammatical structure of a language can facilitate or impede mathematical expression. Different languages can treat numbers variously as nouns, verbs, or adjectives. Thus, mathematical expressions and numbers can be easier to deal with in some languages than others. While in English, number words can serve as nouns or adjectives, in the Maori language, numbers are verb-like. Sometimes counting depends on what is being counted, so things classified differently may not be added together easily, as is the case with some languages of Papua New Guinea.

Furthermore, how well a language’s number system fits with today’s dominant base-ten written notation depends on the regularity of the system. For example, Yoruba has a primary base of 20 with secondary bases of 10 and 5, and uses subtraction more than addition, making for multiple representations of large numbers. [On a personal note, one of the Yoruba professors we knew in Nigeria, whose PhD education was in UK, claimed that he did all his mathematics in English, as Yoruba was not suited for doing mathematics.]

The presence or absence of particular logical connectives can also impede or facilitate reasoning. The Kpelle people of Liberia have words for both the “inclusive or” and the “exclusive or” and perform better on tests of logical disjunction than English-speaking US college students, but less well on tests of implication. No practical suggestions are given, however, on what to do about such differences in grammatical structure if one happens to be teaching some students whose native language has a grammatical structure very different from the language of instruction.

On the other hand, Chapter13 on language and new media and multimodality reports research with Canadian pupils of Grades 2 and 4 that includes examples of mathematical problems teachers might try in their own classrooms. For example, these pupils were asked to explore optimization problems in the context of area and perimeter, a relationship well-known to create problems even for US pre-service teachers. The pupils were asked: (1) If you put 16 tables in a rectangular array, which arrangements fits the fewest chairs all around? (2) What are the dimensions of the biggest rectangular pen that can be created with 20 meters of fencing? The Grade 2 pupils first investigated the story in which 2, the 3, 4, 6, and 12 children share 12 cookies and used linking cubes to model their solutions. They also used their imaginations to illustrate various arrays of everyday objects — for example a 1 × 12 array might be a snake or a caterpillar. After that, they pupils considered the tables and chairs problem.

Other chapters warn of taking a “deficit model” of students whose native language differs from the language of instruction, consider the challenges and opportunities of second language learners in undergraduate mathematics and teacher education, or consider the multilingual contexts of indigenous populations in Latin America. One doesn’t need to read the entire volume — one can just select one or more chapters of interest.

Annie Selden is Adjunct Professor of Mathematics at New Mexico State University and Professor Emerita of Mathematics from Tennessee Technological University. She regularly teaches graduate courses in mathematics and mathematics education. In 2002, she was recipient of the Association for Women in Mathematics 12th Annual Louise Hay Award for Contributions to Mathematics Education. She remains active in mathematics education research and curriculum development. 

See the table of contents in the publisher's webpage.