An image of Heer de Beer

Heer de

Exploring the Computational Medium

Exploring Instantaneous Speed in Grade 5

A Design Research

Huub de Beer



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 instantaneous speed in the cocktail glass at the red point is the same as the constant speed in the cylindrical highball glass (dashed line); the highball’s graph, the straight dashed line, is the tangent line on the cocktail glass’ curve at the red point. (This Figure is taken from de Beer, Gravemeijer, & van Eijck (2015))

The local instruction theory developed in the design research project assumes that fifth-grade 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 segmented-line graph. When scrutinizing the segmented-line graph, they will realize that the segmented-line 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 tangent-lines may be expanded into a more generalized, quantitative understanding of instantaneous speed.


Download my thesis as a PDF file (2.7 MB).

Educational materials created and used during the design research

The software used in the latest experiment is released as a standalone application FlaskFiller.