The Language of Functions and Graphs (1985)
The Language of Functions and Graphs is now regarded as a classic book on the teaching and assessment of graph interpretation skills.
It focuses on developing fluency in using various mathematical representations to describe and analyse the real world, and on the teaching tactics needed to handle pupil discussion in groups and with the whole class. Unit A of the classroom materials tackles the interpretation and sketching of scatter graphs and line graphs - an area where most pupils need help if they are to go beyond the plotting and reading of points to the global meaning of the graph; this material is accessible to a wide range of abilities. Unit B develops modeling skills - the search for patterns in a realistic situation and their expression in verbal, graphical and algebraic forms: this unit is more challenging. Each Unit takes about two weeks of mathematics time in the 13-16 age range. In addition there is a collection of further problems, as well as the assessment tasks with marking schemes for GCSE.
"By addressing the query of 'how do you assess open ended problem solving', the Shell team generated a classic resource, from which has grown the substantial literature of alternative assessment of today." - AAMT
"The materials are very well produced with attractive worksheets and an abundance of materials from which to select." - Mathematical Gazette
El lenguaje de funciones y gráficas, the Spanish language edition of The Language of Functions and Graphs is available from Servicio Editorial, Universidad del País Vasco, Apdo. postal 1.397, E-48080 Bilbao, Spain (and not from the Shell Centre).
The materials comprise a teacher's guide and a set of worksheet masters for photocopying.
Unless stated otherwise, these materials are Copyright © Shell Centre for Mathematical Education (see the materials for full details). You may download these materials for personal use and freely repoduce them for non-commercial purposes including teaching, research and staff development within your institution. For other uses, please contact the Bell Burkhardt Daro Shell Centre Trust at firstname.lastname@example.org for information.
Teaching Strategic Skills series
These materials were originally developed with the Joint Matriculation Board as modules for an O-Level/GCSE mathematics examination. This was initially successful, but the program had to be dropped as a result of changes to the examination system. However, the two books that were produced recieved widespread acclaim and have influenced mathematics teaching around the world, with The Language of Functions and Graphs winning the 2008 ISDDE Prize for Excellence in Educational Design.
The aim of this series of Modules was gradually to introduce into the examination questions that would encourage a balanced range of classroom activities. It was particularly concerned with those activities highlighted by the Cockcroft Report: problem solving, practical mathematics, discussion and open investigation.
Although the specific references to O-Level examinations are clearly outdated, these are rare. The teaching approaches and activities described remain valid and applicable to any Mathematics curriculum.