"Maths and photos"
This session considers various ways in which photographs help our understanding and teaching of mathematics. It illustrates some of the ways photos provoke discussion, pose problems and provide data. The approach works with a wide range of teaching styles and student abilities.
Richard Phillips has a background in education, psychology and design. He has worked at the Shell Centre for Mathematical Education at Nottingham University, and now runs Badsey Publications. Personal webpage - www.richardphillips.org.uk.
Report on the workshop:
The basic idea is that we use a photograph as a starter for a lesson as it can build a link between the real world and Maths.
The first example was a photograph of a Wall in Melbourne, Australia, which was covered in triangular tiles. A suitable problem for students is:- "What do the triangles have in common?"
Ideas which could be developed from this photograph include similar and congruent triangles, ratio, symmetry, transformations, and the properties of other two dimensional shapes.
Examples of other thought provoking photographs included:-
The Minimal Clock which consists of two hands only from which problems might be:-
"What is the time?"
"What is the angle between the hands?"
The Hoarding Heights photograph shows celebrity names displayed vertically to the same height as the celebrity. A problem for students is:-
"What font size will be needed for you to write your name?"
A Conical Rain Gauge with possible problems:-
"Why is it this shape?"
"If it rains steadily then what will the graph of depth against time look like?"
Students should be encouraged to contribute their own photographs to the lessons. An example of this is a photograph of a Playground Meter taken (by a 6 year old) which could be used as a starting point for children to design their own meter.
Software, such as Sketchpad, enable us to sketch a graph over a photograph. The Hanging Chain photograph is an example of where Sketchpad will help when to discover the equation of the curve.
For more information and details of Problem Pictures and Richard's CD Rom's go to www.problempictures.co.uk.