Models of the modern world
Age range 16-18
Peter Wilder assesses different approaches to A-level mechanics
There has been a growing emphasis on mathematical modelling in A-level mechanics books over the past 10 years. The three books reviewed here vary slightly in approach, but they all give some attention to modelling.
Exploring Mechanics New Edition is a re-issue of material first published in l989 as a student booklet and a book of teacher notes. In this new edition the student material is included with the teacher notes, and is now photocopiable, which may explain the rather high price.
This A4, spiral-bound book is a teacher's resource book rather than a textbook. It contains a collection of A-level investigations in which the mechanics is applied to model real world situations.
When first published the aim was to show what investigations and problem solving might look like in A-level mathematics, but today the ideas can be used to develop the modelling skills required by the School Curriculum and Assessment Authority core for mathematics. If you do not already have a copy from 1989, this will be a valuable resource.
The series Discovering Advanced Mathematics is produced by a team of writers which includes some of the contributors to Exploring Mechanics. This common background can be seen in Ted Graham's book, Mechanics, where there is a strong emphasis on simplifying real situations to model them mathematically using mechanics. Some of the examples are similar to problems in Exploring Mechanics.
Many of the problems and activities draw on real examples and, at the end of each chapter, there are possible modelling tasks, which apply some of the ideas and could be used for course work.
Many chapters end with a mathematical modelling activity which takes the reader through all the phases of mathematical modelling, and invites justification of the assumptions and criticism of the model.
R C Solomon adopts a more didactic style than Ted Graham and his treatment of the modelling process is not as thorough as Graham's, although similar ideas are introduced. Solomon's Mechanics follows the same format as his earlier Pure Mathematics.
There are plentv of worked examples and exercises, clear chapter summaries, and two short collections of investigations, in which students are encouraged to experiment and explore.
If you liked Solomon's Pure text, then you might like to see this.
Peter Wilder is senior lecturer in mathematics education at De Montfort University, Bedford