# Is it possible to learn mathematics by language

#### Alexandra Merkert

### Learning in language-sensitive math lessons

#### In mathematics lessons, not only mathematical problems, but also linguistic challenges play a decisive role. For a successful math lesson, it is important to also take these language barriers into account.

Since the results of the PISA study it has been known that language skills are an important prerequisite for learning and school success in all subjects (OECD 2007). This has been confirmed by empirical studies for mathematics lessons that were long considered to be “language-poor” (Gürsoy et al. 2013). The American educational researcher Clara Lee Brown even understands mathematics as a language of its own, which the pupils first have to acquire, mostly alongside other languages (Brown 2005).

However, not only students who are in the process of acquiring a second language benefit from language tuition in mathematics. Even learners who are experienced in using the German language can fail in class due to linguistic hurdles. This is due to the fact that everyday language skills are often insufficient to easily cope with the language requirements of the lesson.

In the subject of mathematics, too, it seems necessary to have a certain linguistic register, for which the term “educational language” was introduced in German-speaking countries (Gogolin 2006). Susanne Prediger, mathematics didactician at TU Dortmund University, systematizes the role of language not only as a learning medium, but also as a learning goal, learning obstacle and learning requirement (Prediger 2013). In the area of mathematics didactics, not only signs and symbols, but also everyday, educational and technical language must be taken into account (Prediger / Wessel 2011).

Learning with language-sensitive math problems

In the course of a task, the structure of which is based on the mathematical modeling model according to Blum and Leiss (Blum / Leiss 2005), the students are encouraged to describe the problem and explain the solution strategy (M1 + Fig. 1). Mathematical modeling is about grasping and understanding the problem situation in order to assign and apply a mathematical method by simplifying or structuring. The result found must then be interpreted and checked as well as presented and explained. The illustration of the task is deliberately kept simple, taking into account the “coherence principle” (Mayer / Fiorella 2014, p. 280), according to which the learning material should not be enriched with unnecessary elements just to make it appear more interesting.

The representation of the different available waffle cones is intended to help the students to create a mental representation from the information presented, which is why text and image are placed in local proximity to each other. In the context of the assignment, the pupils should also be informed that the solution and the result can be presented in several ways, for example by means of an invoice, a table, a drawing or in words.

The spectrum of representations can range from the naming of a single number to a breakdown of the strategy in the form of an explanation, a drawing or a table. While the application of a bundling strategy can become apparent through drawings, for example, some students already show all possible solutions and the underlying principle in complex tables.

Start a questioning conversation

When starting to work on a word problem, learners are often faced with many questions. But how can you put these questions adequately into words so that teachers can provide targeted help? In order to break through the speechlessness and the students ...

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