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to CRME Home PageCollaborative Group for Research in Mathematics Education
Project team included: Mohammed Al-Ghafri, Keith Jones, Keith Hirst
This study investigated trainee-teachers' explanations of students' errors in algebra and their suggested ways for addressing such errors. The theoretical framework for the study derived from Shulman's (1986) idea that teachers' knowledge consists of several types of knowledge. In the model developed for this research, and informed by the work of Askew et al (1997) and Ma (1999), teachers' knowledge about students' errors and difficulties and teachers' belief about mathematics and how it can be taught, have been incorporated.
Data gathering involved administering an open-ended questionnaire to a national sample of 251 trainee-teachers of secondary mathematics across 12 institutions in the UK, followed by a small number of semi-structured interviews for the purpose of validating and extending the data from the questionnaire survey.
The analysis of the completed questionnaires revealed that the majority of trainee-teachers explain students' errors in terms of the incorrect application of the procedures for working out algebra problems. Hence, they recommend re-teaching these procedures to the students so that the students might overcome their difficulties. Other parts of the analysis show that most secondary mathematics trainee-teachers are able to suggest a teaching sequence that takes into account the hardest and the easiest algebra problems. Finally, most of the trainees were able to predict the most likely errors in a set of five algebra problems. However, less than fifth of them obtain R2>0.6 when correlated with Küchemann's (1981) suggestion in regards to the facility level (percentage) of some algebra problems. This indicates that only a small proportion of trainee-teachers understand the sort of characteristics that determine the complexity of an algebra problem such as the number of variables in the problem, the nature of the elements involved and, importantly, students' interpretations of the letters.
The study was supported by an award from the Sultan Qaboos University, Oman.
Publications
Al-Ghafri, M., Jones, K. and Hirst, K., (2002), Learning to Teach Algebra: trainee-teachers' knowledge of students' errors and difficulties. Occasional Papers in Science, Technology, Environmental and Mathematics Education. Southampton: University of Southampton, pp 2-3.
Al-Ghafri, M., Jones, K. and Hirst, K. (2002), Secondary Trainee-Teachers’
Knowledge of Students’ Errors and Difficulties in Algebra. In: A. D. Cockburn
and E. Nardi (Eds), Proceedings of the 26th Conference of the International
Group for the Psychology of Mathematics Education, Vol 1. p259. [extended
abstract]
Click here for
the extended abstract in pdf format.
Conference Presentations
Conference of the International Group for the Psychology of Mathematics Education (PME26), UEA, UK, 2002.
Related CRME Projects
Primary Trainee Teachers' Spatial Subject Knowledge and their Classroom
Performance
This project is part-supported by an award from the UK Teacher Training
Agency.
Manipulatives in Teacher Education in Geometry
This project was supported by a grant from the Brazilian Ministry of
Education Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq),
grant number 201535/93.
Indicative Bibliography
Askew, M., Brown, M., Rhodes, V., Johnson, D. & Wiliam, D. (1997), Effective Teachers of Numeracy. London: Kings College.
Küchemann, D. (1981), Algebra. In K. M. Hart (Ed.), Children understanding of mathematics: 11-16 (pp.102-119). London: John Murray
Ma, L. (1999), Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: LEA.
Shulman, L. S. (1986), Those who Understand: knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Page updated 08 September 2006
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