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

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How was the study designed and carried out?

The study drew on a sample of 196 eighth grade (Year 9 in the UK) students (96 boys, 100 girls) from six classes in two different schools. The schools were similar in terms of size and socioeconomic range of pupils. Within each school, three classes were randomly chosen from a pool of seven classes in which mathematics was taught in mixed ability classrooms. The students in each class were similar in terms of academic ability and prior mathematical knowledge.

The teachers were all female, with a degree in mathematics and at least five years experience in teaching mathematics. All the teachers received two days of training on pedagogical issues related to the teaching of the mathematics unit on linear graphs. Except for practising the use of questions intended to prompt metacognitive discussion on the part of the students, the teachers' training was identical. The students were given the same test before and after the intervention.

The results of the pre and post intervention tests were analysed for the two samples and compared statistically. Two separate tests, one of graph interpretation and one of graph construction, which was intended as a measure of knowledge transfer, were used. Each aimed to assess the "alternative conceptions" held by students and to see whether they were replaced by the generally accepted ones as a result of the intervention. The students' test responses were judged by two experts in mathematics education.

In order to compare the discussion behaviours of the two samples, a research student blind to the purpose of the study made observations of the interactions between students in 24 small groups (four groups selected randomly from each of the six classrooms). The research student was prepared for the coding of the behaviours by prior watching and analysing videos of cooperative learning settings. The observer recorded observations of each student in the group four times for 1 1/2 minutes each time and also coded the interaction level of the entire group. The total observation time for each group of four in one lesson was almost ten minutes. Observations were made twice a week so the total observation time for each group was forty minutes.

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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 How was the study designed and carried out? The study drew on a sample of 196 eighth grade (Year 9 in the UK) students (96 boys, 100 girls) from six classes in two different schools. The schools were similar in terms of size and socioeconomic range of pupils. Within each school, three classes were randomly chosen from a pool of seven classes in which mathematics was taught in mixed ability classrooms. The students in each class were similar in terms of academic ability and prior mathematical knowledge. The teachers were all female, with a degree in mathematics and at least five years experience in teaching mathematics. All the teachers received two days of training on pedagogical issues related to the teaching of the mathematics unit on linear graphs. Except for practising the use of questions intended to prompt metacognitive discussion on the part of the students, the teachers' training was identical. The students were given the same test before and after the intervention. The results of the pre and post intervention tests were analysed for the two samples and compared statistically. Two separate tests, one of graph interpretation and one of graph construction, which was intended as a measure of knowledge transfer, were used. Each aimed to assess the "alternative conceptions" held by students and to see whether they were replaced by the generally accepted ones as a result of the intervention. The students' test responses were judged by two experts in mathematics education. In order to compare the discussion behaviours of the two samples, a research student blind to the purpose of the study made observations of the interactions between students in 24 small groups (four groups selected randomly from each of the six classrooms). The research student was prepared for the coding of the behaviours by prior watching and analysing videos of cooperative learning settings. The observer recorded observations of each student in the group four times for 1 1/2 minutes each time and also coded the interaction level of the entire group. The total observation time for each group of four in one lesson was almost ten minutes. Observations were made twice a week so the total observation time for each group was forty minutes.