Learning extrema problems using a non-differential approach in a digital dynamic environment: the case of high-track yet low-achievers

Assaf Dvir, Michal Tabach

Research output: Contribution to journalArticlepeer-review

Abstract

High schools commonly use a differential approach to teach minima and maxima geometric problems. Although calculus serves as a systematic and powerful technique, this rigorous instrument might hinder students’ ability to understand the behavior and constraints of the objective function. The proliferation of digital environments allowed us to adopt a different approach involving geometry analysis combined with the use of the inequality of arithmetic and geometric means. The advantages of this approach are enhanced when it is integrated with dynamic e-resources tailored by the instructor. The current study adopts the abstraction in context framework to trace students’ knowledge construction processes while solving extremum problems in an e-resource GeoGebra-based environment using a non-differential approach. We closely monitored the learning of 5 pairs of high-track yet low achieving 17-year-old students for several lessons. We further assessed the students’ understanding at the end of the learning unit based on their explanations of extrema problems. Our findings allowed us to pinpoint the contributions (and pitfalls) of the e-resources for student learning at the micro level. In addition, the students demonstrated the ability to solve extrema problems and were able to explain their reasoning in ways that reflect the e-resources with which they worked.

Original languageEnglish
Pages (from-to)785-798
Number of pages14
JournalZDM - International Journal on Mathematics Education
Volume49
Issue number5
DOIs
StatePublished - 1 Oct 2017

Keywords

  • Abstraction thinking
  • Creative reasoning
  • Dynamic e-resource
  • Knowledge construction
  • Non-differential math

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