Exploring Instantaneous Speed in Grade 5
A Design Research
Huub de Beer
2016
Introduction
In answer to the call for innovative primary school STEM education to better prepare our children for participation in the information society, a design research project was started to explore how to teach instantaneous speed in the 5th grade.
The local instruction theory developed in the design research project assumes that fifthgrade students are familiar with the context of filling glassware with water, and starts with the task to model the speed with which a cocktail glass fill ups. Via a process of repeated modeling and refinement, in which they improve their model, the students are expected to develop two models of the changing water height, a discrete bar graph and a segmentedline graph. When scrutinizing the segmentedline graph, they will realize that the segmentedline graph does not fit their intuitive understanding of a constantly changing (instantaneous) speed, and reason that a continuous graph better represents the process of filling a cocktail glass. That conception is then deepened qualitatively and quantitatively by comparing the speed at a given point in the cocktail glass with the constant speed in a cylindrical highball glass with a corresponding width. Supported by a computer simulation, students are enabled to construe an imaginary highball glass as a tool for determining the instantaneous speed at a given point in the cocktail glass. Next, this conception is extended to graphs by linking the linear graph of the highball glass with the tangent line at a corresponding point of the cocktail glass’ curve.
This understanding of instantaneous speed in terms of graphs and tangentlines may be expanded into a more generalized, quantitative understanding of instantaneous speed.
Thesis
 Chapter 1. Introduction
 Chapter 2. Investigating 5th grade students’ level of covariational reasoning
 Chapter 3. Discrete and continuous reasoning about change in primary school classrooms
 Chapter 4. Design research as an augmented form of educational design: Teaching instantaneous speed in 5th grade (not yet published)
 Chapter 5. A proposed LIT for teaching instantaneous speed in grade five
 Chapter 6. Conclusions and discussion
 Summary
 Bibliography:  as a bib file  as a html file
Download my thesis as a PDF file (2.7 MB).
Educational materials created and used during the design research
 Starting Up
 Design Experiment 1
 Design Experiment 2
 Design Experiment 3
The software used in the latest experiment is released as a standalone application FlaskFiller.
Publications

Huub de Beer, Koeno Gravemeijer, & Michiel van Eijck (2017) ‘A proposed local instruction theory for teaching instantaneous speed in grade five’ The Mathematics Enthusiast Vol. 14, No. 1, 435—468. http://scholarworks.umt.edu/tme/vol14/iss1/24/.

Huub de Beer (2016) Exploring instantaneous speed in grade 5. A design research PhD. Thesis Eindhoven University of Technology (htmlpdf)

Huub de Beer, Koeno Gravemeijer, & Michiel van Eijck (2015) ‘Discrete and continuous reasoning about change in primary school classrooms’ ZDM Mathematics Education, doi:10.1007/s1185801506845 (htmlpdf)