Language-responsive mathematics teaching
Language matters for mathematics learning, in particular for developing conceptual understanding of mathematical concepts (Moschkovich, 1999; Prediger, 2022). That is why mathematics instruction should also enhance the language needed for mathematics learning.
For enhancing students’ conceptual understanding of mathematical concepts, the most important part of the academic language is what has been termed meaning-related thinking language (Pöhler & Prediger, 2015; Prediger, 2022). It involves the discourse practices of explaining meanings and describing mathematical structures as well as the phrases to articulate them. Such meaning-related phrases are, e.g., “grouping into pairs”, “part of a whole” or “depends on”.
In a language-responsive mathematics classroom, experienced mathematics teachers master the following tasks of teaching (Prediger, 2019):
We have translated one example for a language-responsive teaching unit to English:
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Korntreff, Stefan & Prediger, Susanne (2022). Describing relationships generally with variables and expressions. Language-responsive instructional material for grades 7–10. Open Educational Resources. Freely available under sima.dzlm.de/um/8-002.
If you understand German, you can learn more about the general approach in several films: sima.dzlm.de/filme
Multi-language-responsive mathematics teaching
Multi-language-responsive mathematics teaching also serves the goal to enhance students’ conceptual understanding of mathematical concepts by attending to meaning-related language.
For this purpose, we exploit students’ multilingual resources with five practices that meet the tasks of language-responsive teaching in particular ways.
We can demonstrate our appreciation of language diversity by valuing the linguistic diversity the students bring and permitting the use of multiple languages in pair and group work. This can empower students to engage in more intense communication, which is important at a general education level. Encouraging communication in multiple languages supports students in building bridges from everyday life into mathematics and back.
Beyond these pedagogical and communicative purposes, we can also exploit the power of multiple languages for mathematics learning itself, i.e., for epistemic purposes. Our approach is to identify mathematical potentials, establish and develop language comparisons of the literal meanings of terms and then initiate discussions about meanings through language comparisons. In this 22-minute film, we explain these different practices.
These films also contain scenes from mathematics classrooms showing the idea: When students break down terms for mathematical concepts from other languages into their literal meanings, then, different aspects of meaning can sometimes emerge. When this happens a more multifaceted view of the whole concept becomes available than if the concept is discussed in only one language. This can encourage students to explain the meanings of concepts in the first place, and to connect several meanings to each other. Consequently, the language comparisons provide great opportunities to initiate thinking and talking about mathematics by unpacking terms from multiple languages.
To do this, however, we first need to introduce students to the idea of translating not just by overall sense, but literally. This makes language reflection possible. Later, we can build on this by eliciting further technical terms and their literal translations from multilingual students. This positions these students as knowers and valuable contributors to classroom discussions.
You can experiment with the approach with the following teaching material
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Uribe, Ángela, Prediger, Susanne, Platen, Yasmin, Ferrari, Eugenia, Lekaus, Silke, Meaney, Tamsin, Revina, Shintia, & Schüler-Meyer, Alexander (2025). Unpacking mathematical concepts in multiple languages: Examples triangle, perimeter and even numbers. Multiple-language-responsive teaching material. German Center for Mathematics Teacher Education. Open Educational Resource under sima.dzlm.de/um/multiple-languages and multilingualmath.nl
The teaching material contains reflections on three mathematical concepts:
The concept of Triangle is used to introduce the practice of language comparison in a conceptually simple case: Tri-ángulo (Spanisch for “three-angle”),
Drei-eck (German for “three-vertex”), Tre-kant (Danish for “three-side”); each refers to different components of the triangle. By discussing differences, students become aware that unpacking words can be mathematically interesting.
Area and perimeter provide the second example, and focuses on conceptually challenging students to clearly distinguish between them. Omtrek (Netherlands for “around-track”) speaks nicely and is easy to distinguish from Emvadón (Greek “go into something“).
Odd and even is the third example: The different terms for odd and even in multiple languages refer to two models of division: gerade Zahl (German for “levelled-out number”) uses the idea of partitive division, while çift sayılar (Turkish for “couple number”) refers to quotitive division.
Even when the area/perimeter or odd/even are taught separately, we suggest to start with the triangle example to sensitze students for language reflections on literal meanings.
For the perimeter example, a second 8-minute film provides insights into classrooms.
Further materials
On the project website Multilingualmath.nl, you can find further materials for classrooms and professional development.
Project background
The approach was initially developed in the project “MuM-Multi” (BMBF grant to S. Prediger & A. Redder) with S. Prediger, T. Kuzu, A. Uribe & A. Schüler-Meyer.
It was further explored, consolidated in the project “Exploiting the Power of Multiple Languages for Mathematics Learning” (grant Erasmus+-Project Nr: 2021-1-NL01-KA220-SCH-000024585 to A. Schüler-Meyer, S. Prediger & T. Meaney) with A. Schüler-Meyer, A. Uribe, S. Prediger, S. Lekaus, E. Ferrari, S. Revina, and T. Meaney.
