Educational Designer

Even a very simple computer application can be used as the basis for a rich mathematical investigation. The Investigations in Teaching with Microcomputers as an Aid project was a 1980s collaboration between the College of St Mark and St John in Plymouth, the Shell Centre in Nottingham and Longmans publishers. In the early 1980s when the majority of UK schools were getting computer equipment for the first time, a typical school would only have a few computers, so the norm would be one computer, mostly operated by the teacher, at the front of the class, with a large TV screen. The ITMA project, therefore, set out to use the computer as a 'teaching assistant' providing visualizations and simulations (“microworlds”) with extensive supporting lesson plans and worksheets.

Some of the applications were very simple – one was a variation on the classic ‘function machine’ activity, albeit with well-developed lesson plans – another simply displayed a sequence of ‘traditional’ calculations and paused before showing the answer (with the optional twist that the computer sometimes made deliberate mistakes). It proved surprisingly compelling for students trying to beat the computer. Some of the more sophisticated applications are illustrated below:

Eureka

graph interpretation for younger students, telling the story of taking a bath based on a water level vs. time graph. The challenge comes when only the graph is shown: what is the story?

Bottles

more advanced graph interpretation with a pre-calculus flavor.

Traffic

introducing distance-time graphs by relating then to snapshots of vehicles moving down a road.

Bridges

simulation of the classic strength of a bridge vs. length, breadth and thickness experiment.

Many of the Bowland Maths case studies (see elsewhere) were built around small software “microworlds”. Additionally, several of the PD modules featured shorter, microworld-based exemplar lessons. Extensive video of a lesson using a very simple applet to calculate Body Mass Index (BMI) can be found in the “Tackling Unstructured Problems” PD module.

There are many well-known examples of interactive geometry software dating back to the 1980s, such as:

• The Geometric Supposer (see e.g. Schwartz & Yerushalmy 1987)
• The Geometer’s Sketchpad (https://www.keycurriculum.com/)
• Cabri Geometry (https://cabri.com/en/)
• Geogebra https://www.geogebra.org/

…and too many graph plotters and graphing calculators to list (some of the above Interactive Geometry packages include function and data graph plotting) – one free, online example being Desmos (https://www.desmos.com/).

Watch the video

reSolve materials courtesy Australian Government Department of Education reproduced under Creative Commons Attribution 4.0 International (CC BY) licence.

Geometry or graphing packages can allow teachers and materials designers to create such microworlds with less effort and technical knowledge than writing software applets ‘from scratch’. The websites for most of the geometry packages listed above have copious examples of demonstrations and microworlds.

Pre-prepared spreadsheets can also be used for investigating mathematical models and data.