6th Dimension: Developing Teaching Styles in A-level Mathematics

During 1986 a group of teachers met to consider alternative styles of teaching A- level students. The Cockcroft Report is influencing work in lower years, but often post 16 teaching has remained closest to lecturing. These offerings are to indicate the themes explored and give a flavour of possibilities.

Section 1: Ways of working includes: Beginning the lesson using a video or a film as inspiration. Examples given are the Dihedral Kaleidoscopes and the hypercube. Questioning considers introducing vectors using a puzzle and ‘dirtying clean problems’ in which simplified problems are made more real-life thus removing ‘neat’ solutions. Proving considers simple starting problems leading to formal proofs. Reading considers using newspaper articles as stimulus to discussion and suggest a students’ reading list. Challenging considers a variety of methods of challenging students using ‘overnight problems’.

Section 2: What about skills? includes: looks at numerical methods of integration, mental mathematics, algebraic skills, compass needle diagrams, activities with a function graph plotter and work on ellipses.

Section 3: Applied problem solving suggests a number of practical tasks to introduce topics of friction, loci, coefficient of restitution, statics, centre of gravity, power, vectors and using calculus to find the minimum distance between points.

Section 4: Topics contains a number of ideas for introducing and exploring topics including using integration to find the volume of a cone, sequences on two dimensions, summing sequences, infinite series and methods of introducing the function ‘e’.