Concept mapping in research on mathematical knowledge development: Background,methods, findings and conclusions |
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| Authors: | Klaus Hasemann Helen Mansfield |
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| Institution: | (1) FB Mathematik/Informatik, University of Osnabrück, D-49069 Osnabrück, Germany;(2) Curriculum Research and Development Group, University of Hawaii, 96822 Honolulu, HI, USA |
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| Abstract: | The theoretical background and different methods ofconcept mapping for use in teaching and in research on learning processes are discussed. Two mathematical projects, one on fractions and one on geometry, are presented in more detail. In the first one special characteristics of concept maps were elaborated. In the second one concept mapping allowed students' individual understanding to be monitored over time and provided information about students' conceptual understanding that would not have been obtained using other methods. Regarding the students' individual concept maps in more detail there were some additional findings: (i) The characteristics of the maps change remarkably from fourth grade to sixth grade; (ii) There is some evidence that prior knowledge related to some mathematical topics plays a very important role in students' learning behaviour and in their achievement; (iii) Concept maps provide information about how individual students relate concepts to form organised conceptual frameworks; (iv) Long-term difficulties with specific concepts are able to be traced. These findings are discussed with regard to results of other studies as well as to their implications for the teaching of mathematics in the classroom. |
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