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ERIC Number: EJ1076960
Record Type: Journal
Publication Date: 2015-Oct
Pages: 16
Abstractor: As Provided
ISSN: ISSN-1863-9690
Discrete and Continuous Reasoning about Change in Primary School Classrooms
de Beer, Huub; Gravemeijer, Koeno; van Eijck, Michiel
ZDM: The International Journal on Mathematics Education, v47 n6 p981-996 Oct 2015
To prepare students for participation in our society, where interpreting, representing, and manipulating of dynamic phenomena are becoming key activities, we believe that one should start developing a mathematical understanding of change at an early age. We therefore started a design research project to teach the concept of instantaneous speed in 5th grade. We report on the last design experiment in which we used a modeling-based learning approach and interactive computer simulations to try to have students construe the Cartesian graph as a fitting representation to describe and reason about filling glassware from both a discrete and continuous perspective. We showcase how new explanatory conjectures can be generated in the retrospective analysis of design research by a process of abduction. The retrospective analysis started with formulating and testing seven conjectures about what happened during the design experiment and one conjecture to account for what happened. This analysis then triggered an abductive process which generated a new explanatory conjecture pivotal to the local instruction theory: average speed is a hindrance rather than a necessity in teaching instantaneous speed.
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Publication Type: Journal Articles; Reports - Research
Education Level: Grade 5; Intermediate Grades; Middle Schools; Elementary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A