Reflections on Visualization in Mathematics and in Mathematics Education

摘要: Mathematics education research is far from consensus on the roles visualization can play in teaching and learning of mathematics. This chapter offers similarly diverse perspectives: Kupferman illustrates a university teacher’s endeavour to integrate with an example introducing formal definition limit Year 1 students. He concludes that benefits visually rich approach cannot be taken for granted, especially when students are not yet accustomed it. To bring into students’ mathematical ‘custom’ Presmeg calls visuality, recognising relationship between logical visual thinking mathematics polarized but orthogonal, reminding us effective visuality originates teachers whose own preferences mixed flexible. Analogously, Nardi new didactical contract makes rules about explicit learners, while deliberate ‘fuzziness’ this also allow manoeuvring often so potent Much like Kupferman, support Presmeg’s call Hershkowitz, through examples, acknowledges as one languages several ways mathematically. expressed, needs language, or other; meaningful, attached some conceptual entity. Finally, Yerushalmy picks up Hershkowitz’s cue meaningful integration such interactive diagrams algebra, illustrate challenges, affordances profound epistemological shifts inherent sensitive curriculum design.