There are many practical resources that can greatly enhance mathematics teaching and learning. In a department with a rich variety of resources teachers can explore materials in a creative atmosphere in which ideas and classroom experiences are shared and discussed. Selecting appropriate resources then becomes a natural part of planning.
The aim of engaging all pupils in real mathematics in a lively and interesting way began to be shared by more and more people in mathematics education during the 1950s. The catalyst was the formation of the Association for Teaching Aids in Mathematics by people (led by Caleb Gattegno) who were already creating and using resources such as films, models, geoboards and other classroom teaching aids.
Since then an enormous variety of resources, including materials for teaching number, resources to enhance the teaching of geometrical ideas, board games and puzzles, calculators, other ICT resources and relevant software, data handling resources, and measuring equipment, have been developed and used widely. So many resources now exist that appropriate equipment or physical materials can be found to support all mathematical learning objectives in key stage 4. Whilst some key stage 4 learners will feel that resources designed for key stage 3 or even younger learners are “too babyish” there is a case for considering these for learners with special needs or clear conceptual misunderstandings. Many of them will be new to the learners having been introduced since their time and, when handled sensitively, can help overcome basic misunderstandings.
When physical materials are easily accessible in the classroom, they become resources from which learners can themselves select to support their learning. Ideally, resources that learners can use whenever they like will include paper printed with various grids, multilink cubes, polydron, shape templates and rulers, angle measurers, compasses, scissors, coloured paper, card, glue, elastic bands, string, pinboards, pegboards, dice, dominoes, ordinary playing cards, blank playing cards, calculators, and computers with spreadsheets, graph plotters, dynamic geometry software and data-handling packages.
In order that learners can select appropriately from a bank of resources they must have previously have been introduced to the items. Therefore teachers will, early in their work with a new group of learners, look out for opportunities for learners to use the materials, encouraging exploration of the resources. For example, learners might investigate sequences using a spreadsheet, 3-D coordinates using models or the equations of groups of curves using a graph plotter.
While learners may, in a well-equipped classroom, know that familiar resources are always available for them to use, teachers will want to use particular resources in particular ways on particular occasions for particular purposes. See Choosing Materials
A teacher might plan a series of lessons involving simple constructions, and making and proving conjectures, during which all the learners use dynamic geometry software. See Dynamic Geometry. Or she might plan for the learners to explore regular polygons using a version of LOGO and MicroWorlds. Other physical materials with which pupils can gain geometrical insight, and that are powerful motivators, include DIME solid materials, which are attractive Plastazote pieces and at key stage 4 often make a useful starter activity to refresh basic ideas before extending. There are many websites that have applets, useful for demonstrating more advanced topics. Many also come with ideas for lessons
Using a spreadsheet as a tool for investigating and solving problems can be a powerful aid in helping learners understand what they are doing when they use algebra (see Spreadsheet Algebra). So a lesson or series of lessons might be constructed around spreadsheet activities.
There are some excellent web based sources of real data to interest learners that can prompt their own statistical enquiries (see Using Real Data) Therefore a module of work might start with all the learners exploring and downloading large sets of data.
On some occasions the learners themselves may be an effective resource. For example learners might be challenged to move according to constraints or rules, as a tool in the exploration of loci, or as the 'pieces' in an investigation of the best strategies in the Adam¹s Move game (see People Maths). Learners already have vast resources of information at their fingertips. They can tell you the “best” phones, mp3 players, social networking sites, web shopping sites and so on. All of these can be a starting point for further investigation involving data, number work or measures.
Revision becomes an important part of key stage 4 as the GCSE and other exams loom closer. Using a selection of resources and tasks for this can relieve the monotony and repetitive format for lessons that tends to set in. There are several internet sites devoted to GCSE revision, some free such as the bbc sites and some, such as mymaths, that you can subscribe to. To bring variety, and occasionally a touch of humour, try searching youtube or similar sites for videos of people explaining maths topics. Your learners could probably do better!
Selecting appropriate resources becomes a natural part of teachers' planning when exploring materials. Doing mathematics together using the resources is a useful, if not essential, part of department meetings.