Teaching Mechanics through modelling, mistakes and misconceptions
Introducing Newtonian Mechanics is one of the greatest pleasures of teaching level 3 Maths, and it is also one of the greatest responsibilities: it’s so important when choosing the first examples and scenarios for your students to consider that the right thought-trains (pulling wagons against negligible resistance with light inextensible couplings between them, of course!) are set in motion. A seemingly simple question – “why do you fall backwards when the bus lurches forward?”, “if action and reaction are equal and opposite, why does something move when I push it?” – can generate deep and enlightening discussions that open students’ eyes to the power and the elegance of Newton’s insight. If only there were a more modern and appealing name for this area of applied mathematics than Mechanics! This is a word that seems to put students off rather than draw them in: so how about “Modelling Reality” instead? There are many web resources that can be used to inspire students’ interest: a particular favourite is Assembler, which like all the best games is so simple, so frustrating, so instructive and so addictive! The NRICH site has the rich sub-site Mathematical Models in Mechanics, with lots of puzzles, challenges and problems that will help your students develop and refine their mechanical thinking.
The excellent National STEM Centre eLibrary is available – for free! – to all teachers. It includes some splendid resources both old and new for teachers of mechanics in level 3 Maths. A quick search in the eLibrary using the key word “mechanics” comes up with lots of practical approaches to developing modelling skills, and to challenging the common misconceptions that often occur when students first study Newtonian mechanics.
Mechanics in Action by Savage and Williams (CUP 1990) and The Teacher’s Guide to the Leeds Mechanics Kit by Jagger, Roper and Savage (MAP 1990) give lots of practical ideas for conceptual understanding across mechanics topics, from introductory vector quantities in AS Level Mathematics to forced and damped harmonic motion in A Level Further Mathematics. The rich ideas here are still valid, even though some teachers may themselves have first met these when they were in the sixth form themselves – fortunately, Newton’s Laws have not changed in the last 25 years! Old textbooks advocating similar approaches are also available in the eLibrary: try Nuffield Advanced Mathematics: Mechanics 1 and Mechanics 2 by Hugh Neill (Longman 1994). For more motivational content, try Exploring Mechanics from the Centre for Teaching Mathematics (1995) or Realistic Applications Of Mechanics from the SPODE Group (OUP 1986).
If you already use all of the above and want something new, then content such as the Bloodhound SSC Secondary Topics from 2008 to present and Integrating Mathematical Problem Solving: Physics – Simple Harmonic Motion (MEI 2012) are up to the minute. They make considerable use of modern ICT such as Flash demos … but do check that your school firewall will let you access these sorts of resources before planning an hour's lesson that hinges on them!
Page header by Richard Gray (adapted), some rights reserved