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

Learning extrema problems using a non-differential approach in a digital dynamic environment: the... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ZDM Springer Journals

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

ZDM , Volume 49 (5) – May 30, 2017
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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by FIZ Karlsruhe
Subject
Education; Mathematics Education; Mathematics, general
ISSN
1863-9690
eISSN
1863-9704
D.O.I.
10.1007/s11858-017-0862-8
Publisher site
See Article on Publisher Site

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.

Journal

ZDMSpringer Journals

Published: May 30, 2017

References

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