Classroom discourse facilitates understanding of Maths
Children’s actual opportunities to learn depend not only on the type of mathematical tasks that teachers give during class discussions, but also the kind of classroom discourse that characterise such tasks.
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The National Council of Teachers of Mathematics (NCTM) based in the US defines discourse as the ways of representing, thinking, talking, agreeing and disagreeing that teachers and children use to engage in instructional tasks.
Through discourse, children explain and justify their thinking and challenge the explanations of their peers and teachers. They also clarify their thinking as they gain autonomy of their own learning styles.
Instructional delivery
The means to improve instructional delivery in schools has compelled many mathematics educators to find concrete instructional techniques and strategies in order to provide a panacea to the seemingly complex challenges facing mathematics instructional delivery in schools. In fact, effective instructional delivery acknowledges that every child can develop positive mathematical identity and become a powerful mathematics learner.
Mathematics classroom discourse could be facilitated if teachers’ educational practices in the classroom became child-centered and were able to provide an avenue for nurturing the potential of children of varied ability levels.
These teachers could establish the academic capabilities of their children through assessments on assigned mathematical tasks, taking into consideration the social and cultural milieu in order to determine the best approach to facilitate learning.
Perfect classroom culture
Creating a perfect classroom culture conducive for teaching and learning should be the joint responsibility of both teachers and children. For example, teachers can advance their instructional delivery towards an open child-centered discourse if they motivate children to participate in the process.
By allowing teachers and children to set the classroom norms (i.e., the acceptable ways of behaviour in the classroom) and agreeing on the mathematical norms (i.e., things that count as evidence in mathematics), children gradually become actively involved in the learning process.
Mathematical classroom discourse could also be facilitated if teachers allowed students’ thoughts and ideas to shape discussions. In fact, research shows that children learn best when they participate in discussions about ideas and concepts.
Discussions could provide children with opportunities to engage their peers in argumentation and reasoning in small groups and in whole-class discussions. In discussion oriented classrooms, children’s responses inform the choice of questions available to teachers and shape the course of the classroom conversation. These teachers validate children’s ideas by incorporating their responses into follow-up questions.
An important result of this approach is for teachers to ask questions that can potentially result in upper cognitive thought processes among children. These enable children to apply lower level concepts to formulate more robust and complex ones.
Opening discussions
Open questions are better for opening discussions and maximising the chances of children to contribute to the discussion than close ones. For a well-formulated open question, teachers could, for example, ask children to investigate the relationship between a solution to a linear equation and its graph.
Mathematical classroom discourse could be facilitated if teachers selected and sequenced ideas in a discussion. Teachers’ main role in a discussion-based classroom is to encourage children to participate in talking and explaining themselves in the classroom.
By monitoring children as they explore given tasks, teachers will be able to select ideas that can be shared in a discussion. Such selection of ideas should be guided by a mathematical goal which would encourage teachers to offer praise to children when due and to offer supportive statements that will encourage their participation in classroom discussions.
Participating in a mathematical community through discourse is as important as establishing a mathematical concept. As children agree or disagree to solution approaches, they are learning the essence of what it means to do mathematics.
To encourage the participation of all children, teachers must foster classroom discourse by providing a welcoming community to improve teaching and learning.
*The writer is a lecturer, Department of Mathematics Education, University of Education, Winneba