# Strategies to provide scaffolding when teaching mathematical concepts

Effective teachers ensure that all students understand what they are meant to be doing and are actively involved throughout the session. This means that students need to not only recognise the individual words in a problem or an instruction, but also to understand how the words work together to convey a specific, precise mathematical meaning. While some words and phrases have completely different meanings in mathematics from those in everyday English (these can be recognised and taught), other problems are less obvious. The syntax of mathematical discourse, especially in relation to prepositions, word order, and the implications of the context, can be a barrier to ELLs working with word problems.

The conditional and comparative terms used in contexts involving logic have no equivalent in some languages, and the meaning of terms such as “unlikely”, “likely”, and “probable” will be unclear to some students. When teaching probability, it is essential that students understand these terms. Explicitly teach the terms in a real-life context and then make links to the mathematical concepts.

Students need to learn ways to explain and justify a concept. Some ways to build this ability include:

• providing multiple opportunities for ELLs to notice and then use the new mathematical language (Ellis, 1991)
• rephrasing and helping students to notice the differences in phrasing
• using guided questioning
• using “wait time” after asking a question so that students have an opportunity to translate the question, if necessary, and to form an answer
• building on what students say, that is, amplifying not simplifying (rather than using only basic language for ELLs, it is essential to model more sophisticated or complex language use)
• beginning with oral tasks and then moving to written responses. The oral task is a “rehearsal” for the written response. Through talk, students are able to formulate ideas, evaluate hypotheses, and reach decisions in a context that is not constrained by the more formal demands of written language (Gibbons, 1991).

ELLs often find symbols more accessible than language by itself. If learners are familiar with these symbols, they provide links to the corresponding English terms. Using symbols alongside mathematical language and abstract concepts can make them more comprehensible to ELLs (Gibbons, 2009). Giving students time to work out mathematical problems using symbols initially and then discussing the reasoning may also be an effective way to scaffold mathematical understanding.

When students are treated as capable learners, when they are actively engaged in challenging tasks … and when they are given opportunities to use knowledge in meaningful ways … ELLs not only achieve at higher levels, but also expand their academic and personal identities and their own beliefs about what is possible.

Gibbons, 2009

Scaffolding can support students to take increased responsibility for their learning. Vygotsky (1978) talks about “the zone of proximal development” – the gap between what a student can do independently and what they can do with help. Teachers need to consider how they can provide high levels of support when necessary while ensuring that students are challenged enough to make progress.

See resource 4 for particular strategies you can use to build ELLs’ mathematical language.

Back to Resource 3: Supporting English language learners with the language of mathematics