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Mathematical communication and language : Post 16 Level 2 : Mathematics-specific Pedagogy


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Post 16 Level 2
Mathematical communication and language
Question 1 of 3

1. How confident are you that you can facilitate dialogue that is focussed on mathematical ways of thinking and speaking?

a. Activity One


Activity

Watch the video Questioning Small Groups which was produced as part of Improving learning in mathematics and think about how the teacher intervenes and questions the learners during the group work.

Prompt 1.

As you watch the video sequence, you might find it helpful to consider the following questions:

  • What sorts of questions does the teacher use?
  • How does she respond to the answers?
  • How does she ensure that each learner is involved?
  • What do you think she is trying to achieve in each of the interactions?

Prompt 2.

You may want to view the video several times.

Commentary

It is clear from watching the video that planning and managing group work demands real skill from the teacher: students need to be helped to move from an initial position of unplanned discussions in a lesson to become reflective, independent thinkers, who can analyse information, formulate opinion and argument, incorporate new ideas and critically evaluate a range of opinions.

Whilst working in a group, learners can explore ideas verbally, among themselves, even if the final product is written or practical. Group talk can be both collaborative and competitive. Lev Vygotsky (Vygotsky, L. Thought and Language (1973) MIT Press: Cambridge, MA) believed that it is learners’ linguistic interactions with others, including their peers, which most strongly influence the level of conceptual understanding that they can reach.

Group work improves social and communication skills and learners’ self-esteem grows as they realise that it is acceptable to make mistakes. Learners become less dependent on the teacher for their learning and they develop the ability to empathise with others whilst they are more actively involved in their own learning. This results in improved levels of engagement and motivation; so learners enjoy their learning. The skills they develop are vital if they are to be effective when working collaboratively and communicating their ideas in later life.

In mathematics, learners need to know and use the correct mathematical vocabulary, choose the right words at the right time and employ them accurately. They need to make choices about the mathematical language that they use to explain ideas in formal contexts to move beyond tentative, exploratory talk into more incisive comments. Learners need to ask relevant questions to test and improve ideas. They should be willing to evaluate and modify their own ideas by taking into account the suggestions of others.

Teachers should allow learners to:

  • articulate and develop their understanding and knowledge of accurate mathematical language;
  • use precise language to share and develop their ideas;
  • ask relevant questions;
  • pose and define problems;
  • give reasons for opinions and actions;
  • generate and extend ideas;
  • judge the value of what they read, hear and do;
  • develop criteria for judging the value of their own and others’ work or ideas.

Using group talk and argument is important in fully developing a language for learning in mathematics and can help learners produce effective high-quality written work.

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