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A Study of Prospective Primary Teachers’ Conceptions of Teaching And Learning School Geometry

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Abstract

There are two basic guiding referents in the present investigation: the teaching and learning of school-level geometry (basic concepts of Euclidian geometry and measure) and the analysis of the conceptions of prospective primary teachers in Spain. The work assumes that such conceptions appear and develop during school years, and that consequently, for the prospective teachers to learn to teach mathematics, account must be taken of the requirements that arise from these conceptions themselves and from the prospective teachers’ knowledge of school-level mathematics. The objective of the study was to describe and analyse prospective primary teachers’ conceptions of school-level geometry and it teaching and learning. To this end, we considered the hypothesis that the students’ memories and expectations provide information with which to characterize their conceptions of the field of geometry and its teaching/learning at the primary school level.

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Correspondence to Lorenzo J. Blanco.

Appendix A

Appendix A

Below are some significant items from the two questionnaires. Those beginning with 1 are from the Recall questionnaire, and those with 2 from the Expectations questionnaire. They are arranged in the order of the categories named in the main text.

  • 2-2. Do you believe that geometry is harder or easier than other areas of mathematics? 2-2a. Why?

  • 2-3. In the school curriculum, which concepts do you consider more important than the concepts of geometry? List them in order of importance.

  • 1-13. Describe briefly what general methodology (the way you were taught) was used in geometry by your primary teachers.

  • 1-14. Do you recall some special method used by any of your primary teachers? Describe it.

  • 1-4. List some educational materials that you used when you were learning geometry (only name them).

  • 1-4a. Describe briefly how you used them. If necessary, comment on some specific cases.

  • 1-11. Which resources did primary teacher use to teach you?

  • 1-11a. How regularly did he or she use them?

  • 1-11b. How and when did he or she use them?

  • 1-6. What type of geometry activities did you do?

  • 1-7. Do you recall some out-of-the-ordinary activity that you liked most?

  • 1-15. What value did the teacher give to the knowledge of geometry that was learned by rote?

  • 2-15. What value do you give to knowledge learned by rote?

  • 2-16. Which other aspects relative to learning would you value in your pupils?

  • 2-17. How do you think you would achieve true learning on the part of your pupils?

  • 2-19. What do you consider more important to take into account in learning: your pupils’ interests or the knowledge of geometry that you have set yourself to teach? 2-19a. Why?

  • 2-23. Do you consider that the pupil should participate in designing activities? 2-23a. Why?

  • 1-21. How were you all evaluated in geometry? Describe it.

  • 2-28. Would evaluation be quantitative (reduction of the final results to numerical terms), or a report of a qualitative type?

  • 2-29. What would the quantitative type of evaluation consist of?

  • 2-30. What would you evaluate in the qualitative type of report?

  • 2-31. What would the main role of evaluation be? In other words, what would you aim to achieve with it?

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Barrantes, M., Blanco, L.J. A Study of Prospective Primary Teachers’ Conceptions of Teaching And Learning School Geometry. J Math Teacher Educ 9, 411–436 (2006). https://doi.org/10.1007/PL00021938

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  • DOI: https://doi.org/10.1007/PL00021938

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