The study examines a geometry teacher’s use of a metaphor and a prototypical image. The teacher organized students’ knowledge for retrieving that knowledge later. Radius and tangent of a circle lesson pdf metaphor reminded students of heuristics for working with diagrams.

The metaphor mediated the work on a problem and the introduction of a theorem. The metaphor helped to consolidate the collective memory of the mathematics class. How does a teacher use a metaphor in relation to a prototypical image to help students remember a set of theorems? This question is analyzed through the case of a geometry teacher. The findings show that the teacher used the metaphor to help students recall the apprehensions of diagrams when applying several theorems. The metaphor was instrumental for mediating students’ work on a problem and the proof of a new theorem. The findings suggest that teachers’ use of metaphors in relation to prototypical images may facilitate how they organize students’ knowledge for later retrieval.

Check if you have access through your login credentials or your institution. Please forward this error screen to 216. Screen reader users, click the load entire article button to bypass dynamically loaded article content. Please note that Internet Explorer version 8. Click the View full text link to bypass dynamically loaded article content. This chapter focuses on the origins of students’ beliefs about mathematics.

It examines these sessions in terms of all four categories of the analytical framework, with an emphasis on the ways that belief shaped the students’ behavior. These analyses provide the opportunity to see the way the full framework is implemented. The major lesson that LS and TH seem to have learned from their encounters with geometry is that geometric argumentation has nothing to do with learning or discovery. Although they were capable of making deductive arguments, the students avoided making them in situations where they could be used to advantage.

This kind of behavior is much more the rule than the exception. The prevalence of such behavior raises some serious questions about what students are really learning in the mathematics classrooms. Selections from some ongoing classroom studies suggest that there is cause for concern. They indicate that the roots of students’ empiricism can be traced directly to the ways that they are being taught mathematics. This article has not been cited. Martindale’s Calculators On-Line Center: Physics Center: Q-Z – Databases, Courses, Textbooks, Lessons, Manuals, Guides, Publications, Technical Reports, Videos, Movies, Calculators, Spreadsheets, Applets, Animations, etc.

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