Understanding graphs – does metacognitive questioning help students develop and refine their mathematical ideas?

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Thinking skills
Mathematics

What are the implications of this work?

Whilst writing this digest the author became aware of a number of implications for teachers:

The research suggests that alternative conceptions or misconceptions of graphs limit pupils' ability to make sense of what they are doing and help them move forward. Would it help in mathematics teaching in your department or school to identify and collate the kinds of conceptual problems your pupils have in relation to graphs or other areas of mathematics?
The study highlights the importance of using pupils' conceptual difficulties in mathematics and as a starting point for helping them construct new understandings. Would it be useful for you and your colleagues to work together to build more effectively on students' existing understanding, for example, by designing tasks which require students to firstly describe and then to act out the relationships expressed in graphs for themselves?
The study findings show that working in cooperative groups does not by itself bring about the kind of discussion which helps children to construct a deep understanding of mathematics. Would it be possible to provide your pupils with explicit instruction in the use of questions designed to foster discussion prior to organising them for group work? Potentially useful questions could relate to: understanding the problem, making connections to previous knowledge, identifying strategies that might be useful for solving the problem and reflecting on the solution and on the processes.

An implication for headteachers and others involved in raising achievement is:

The research implies that the idea of instructing students in using metacognitive questions could be introduced in other areas of the curriculum. Is this an activity you could develop on a whole school basis or across a range of departments? What do you or your colleagues know and/or need to know about current conceptions and misconceptions in particular areas of the curriculum to identify a good place to start?

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Research Home Themes \| Find digests \| About the digests resources glossary researchers contact TRIPS Introduction What sorts of conceptual problems did the students have? How did the intervention affect students' mathematical understanding? What was classroom discourse like and how did it differ between the two samples? What classroom activities did the intervention involve? What questions were used to foster metacognition? How was the study designed and carried out? What are the implications of this work? Where can I find out more? Send us your feedback Collated digests To view/remove/add notes and save your collated digests click here Get Word Reader Understanding graphs – does metacognitive questioning help students develop and refine their mathematical ideas? This digest found in Thinking skills Mathematics Send to a friend Word doc 80KB Printer friendly Collate for later What are the implications of this work? Whilst writing this digest the author became aware of a number of implications for teachers: The research suggests that alternative conceptions or misconceptions of graphs limit pupils' ability to make sense of what they are doing and help them move forward. Would it help in mathematics teaching in your department or school to identify and collate the kinds of conceptual problems your pupils have in relation to graphs or other areas of mathematics? The study highlights the importance of using pupils' conceptual difficulties in mathematics and as a starting point for helping them construct new understandings. Would it be useful for you and your colleagues to work together to build more effectively on students' existing understanding, for example, by designing tasks which require students to firstly describe and then to act out the relationships expressed in graphs for themselves? The study findings show that working in cooperative groups does not by itself bring about the kind of discussion which helps children to construct a deep understanding of mathematics. Would it be possible to provide your pupils with explicit instruction in the use of questions designed to foster discussion prior to organising them for group work? Potentially useful questions could relate to: understanding the problem, making connections to previous knowledge, identifying strategies that might be useful for solving the problem and reflecting on the solution and on the processes. An implication for headteachers and others involved in raising achievement is: The research implies that the idea of instructing students in using metacognitive questions could be introduced in other areas of the curriculum. Is this an activity you could develop on a whole school basis or across a range of departments? What do you or your colleagues know and/or need to know about current conceptions and misconceptions in particular areas of the curriculum to identify a good place to start?