Case study 3: Improving the quality of student mathematical conversations

last updated:February 2010

Case study 3: Improving the quality of student mathematical conversations
We chose this case study as it shows how a small group of teachers working together and providing challenge to each other improved the quality of students’ mathematical conversations.

What was the background to the study?
Three teachers from a secondary school near Gloucester recognised that mathematical conversations between some pairs of students were not as deep as they could be and were therefore not affecting attitudes and achievement as positively as they might. They therefore set out to improve the quality and depth of these conversations.

How did the teachers carry out the study?
The study moved through four stages:

• firstly a top set Year 11 mathematics lesson on quadratic equations was videotaped and observed;
• secondly one of the teachers tried out new strategies to encourage student talk in a Year 8 lesson on sequences and rules;
• the approach was refined and then tried out on a top set Year 8 lesson on transformations; and
• finally one of the teachers applied all they had learned to a bottom set Year 7 lesson on symmetry.

How did the teachers try to improve student conversations?
The teachers used three main approaches. Students were told to:

• explain their thinking;
• convince their partner; and
• ask their partner to convince them.

The teachers modelled particular phrases to facilitate good conversations, including:

• convince me…;
• how would you convince another student that…; and
• explain why you think that…

Students were also required to make posters displaying their explanations and examples.

What was the impact of the study?
The teachers found that it was possible to help students improve the quality of their conversations. In the last lesson the teachers were pleased to find that many of the students, even the weaker ones, gave unprompted explanations to their partners and were thinking critically about what their partners said. May students were observed using the language which the teachers had modelled.

Examples from the bottom Year 7 class included:

'It’s a right angle here (pointing to a corner)'

'Just count the corners (student to partner talking about symmetry)'

'coz when you twist it, it fits two times, look (student demonstrates by turning the object)'

Many of the weaker students who were not able to articulate convincing arguments were observed effectively discussing using showing and pointing.

What did the teachers learn?
The teachers learned that there was much they could do to facilitate deeper student conversations:

• model good practice;
• plan both the activity and how students were going to talk about it;
• prepare students at different points in the lesson;
• make explaining a key part of the activity;
• include written explanations but provide writing frames and other creative ideas; and
• praise good conversations when they occur.

 
One teacher commented:

I think one of the main lessons we learned was that children don’t naturally know how to talk to each other. We have to tell them how to do it. Even weaker children can do it, if you show them how.

Reference
Pinco, E. (2008) How can we improve the quality of students’ mathematical conversations?
National Centre for Excellence in the Teaching of Mathematics grant report