Classroom dialogue in mathematics education

This systematic review – the first to be published by the Swedish Institute for Educational Research – examines classroom dialogue within the subject of mathematics. Our aim has been to give an account of what a systematically sampled body of primary research taken together says regarding teacher’s work to engage pupils into whole class mathematical discussions.

What are the main results?Omslag Klassrumdialog

The main findings of this systematic review illustrate how teachers can lead dialogues where the pupils are active, constructively critical participants in collaborative mathematical reasoning. This particular kind of conversation is here referred to as exploratory talk. Exploratory talk differs from disputational talk, where the participants focus on defending and maintaining control over their own ideas, as well as from cumulative talk, a form of talk where participants uncritically accept another’s ideas.

Exploratory talk

In exploratory talk, the participants express and motivate their own mathematical ideas, but also engage in the ideas of other pupils, and strive to reach a common agreement. The teacher’s role in exploratory talk differs from teaching where the teacher acts as a dominating party, and the task of the pupils’ is limited to providing correct answers to the questions asked by the teacher. This discussion pattern is sometimes referred to as “IRE” = Initiation, Response, and Evaluation. In exploratory talk, the teacher acts supportive of pupils’ participation, by, for instance, asking open questions, listening carefully and make use of their mathematical ideas, and encouraging the pupils’ active involvement in ideas expressed by other pupils.

The research included in this review illustrates that the teacher’s role is pivotal in establishing a classroom dialogue that engage pupils in mathematical reasoning.  Mainly, this is illustrated in studies where the character of pupil talk changes parallel to how the teacher leads the conversation onwards. However, pupils are different, both in terms of abilities and experience. Other contextual factors, of course, also vary. Thus, research cannot provide quick-fixes for teacher actions or activities, guaranteed to work regardless of the context. However, research can provide us with useful knowledge of actions that have the potential of engaging pupils in collaborative mathematical reasoning, as well as knowledge of how and why these actions are of importance.

Teachers can guide pupils in the collective dialogue

Also, these actions can help teachers meet and make use of the multitude of individual qualities in a classroom. As the pupils take part in exploratory talk, they will express their own ideas publicly, and they will ask other pupils to motivate their ideas. This way of talking may be challenging to some pupils. The research material demonstrates how teachers, by undertaking different actions such as modelling, exemplifying and reinforcing desired behavior, can guide the pupils in the collective dialogue. And – perhaps more importantly – how they can support pupils who experience reluctance towards participating in collective reasoning, by legitimising behaviors that the pupils feel uncomfortable with.

Involve pupils in mathematical discussions

The research sheds light on how teachers embrace and make use of pupils’ different mathematical ideas, using them as a resource for promoting the pupils’ involvement in the mathematical discussion. By, for example, asking the pupils to motivate their statements and strategies for solving a given problem, or to compare different solutions or to evaluate different statements, the teacher stimulates the pupils to explore the mathematical aspects of the ideas expressed. The research also helps teachers realize, if the explanations provided by the pupils actually concern mathematics on a deep level, or if they, for instance, merely consist of step-by-step, procedural explanations.

It is also shown, that even when pupils are actively participating, teacher involvement is still needed, both to guide the reasoning, and to support the discussion at times. Moreover, the teacher needs to take on increased responsibility when, for instance, new content is introduced, or if the students are experiencing difficulties grasping certain content. Also, there is not always a need for mathematical talk to be of an exploratory nature: sometimes the teacher needs to take charge of the conversation to a greater extent, in order to keep the group focused.

Time is yet another aspect of reaching a climate that allows for exploratory talk. The studies in this review show that making this change in a classroom takes time. If the pupils are not accustomed to exploratory talk, the change may demand that the pupils both learn new ways of participating in whole class discussions and become comfortable with the new expectations for these new expectations for the forms of that participation.

What is the aim of this review?

This systematic review can offer teachers valuable insight into one’s own teaching practices, and ideas for how it can evolve. The research presented puts into words the events in the classroom, and identifies patterns and structures commonly recognized by teachers. In the review, we give examples of dialogues between teachers and pupils, illustrating teacher actions and how they relate to the participation of pupils.

We have gathered and synthesized results from relevant international research. This review allows teachers to accessibly use research-based knowledge to support, plan and conduct mathematical classroom dialogues.

What is the main focus of the review?

The research question that this review aims to answer is: What signifies classroom dialogues that engage pupils in mathematical reasoning, employs the individual qualities of different pupils, and what marks teacher guidance of such dialogues? The studies included vary and have somewhat different foci; taken together, they provide a rich and nuanced answer to the research question.

What studies are included in this review?

The literature searches, conducted in Swedish and international research databases, resulted in 10 528 studies. After being evaluated according to relevance- and quality criteria, a total of eighteen studies remained. These constitute the basis for the synthesis presented in this systematic review. All of the studies employ observational methods in the analyses of whole-class dialogues between teachers and pupils.