Functions and the Volume of Vases

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.Keywords Design research · Graphing · Instantaneous rate of change · Modeling-based learning · Primary education Deceased: Michiel van Eijck.

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Discrete and continuous reasoning about change in primary school classrooms

Beer

Gravemeijer

Eijck

2015

ZDM Mathematics Education

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Connecting Research to Teaching: Reasoning about Quantities That Change Together

Johnson¹

2013

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Functions and the Volume of Vases

Abstract: While filling vases with water and observing volume and height relationships, students learn the fundamentals of functions.

Cited by 2 publications

References 3 publications

Discrete and continuous reasoning about change in primary school classrooms

Discrete and continuous reasoning about change in primary school classrooms

Connecting Research to Teaching: Reasoning about Quantities That Change Together

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