Introduction
This chapter addresses a number of different types of lessons and approaches to teaching.
They are chosen to exemplify a range of resources and options that you may or may not wish to try in the classroom. The aim of this chapter is to encourage you to experiment with novel ideas when teaching mathematics and to illustrate some of the opportunities for creativity in the maths classroom. As you become more experienced as a teacher, you will adjust and refine these ideas to suit the needs and abilities of your pupils.
Learning outcomes
By the end of this chapter you should have a number of ideas on how to use the following resources in the maths classroom:
• textbooks and pens on whiteboards;
• visual aids;
• generic ICT packages;
• subject-specific software;
• graphics calculators.
Overview
In Parts I and II of this book, the reasons for lesson planning were discussed and the advantages of advance preparation in the light of classroom management, control and achieving content coverage were also emphasised. The importance of being prepared and having all the relevant subject knowledge at your fingertips assists you in maintaining the flow of the lesson and therefore sustaining the pupils’ attention. Teachers who are disorganised and have to dash around gathering together all their resources and equipment at the last minute are not valued or respected by pupils. Lack of preparation implies lack of interest in the welfare of your class. Pupils also notice the teacher who has taken the time and effort to put together an effective and stimulating learning experience.
Clearly, you will exhaust yourself if you ‘put on a performance’ for every lesson when you are teaching full-time. However, during ITE you are teaching a restricted timetable, so you should have surplus time and energy to expend on developing such lessons.
Lesson plans
The structure of a lesson plan has already been discussed. However, the following template (Figure 9.1, pp. 120–121) highlights each of the stages and emphasises the need to plan and think through the skills and steps required in the learning process. In keeping with the NNS and Key Stage 3 strategy, each lesson should have three stages: mental maths, main part and a plenary. Chapter 5 made the links between each of these stages and the Stones’ heuristic of identifying, remembering and doing (Stones, 1994). In most cases, the introduction to the lesson followed by the presentation phase assist pupils in identifying the criterial attributes of the skill or concept being taught. The remembering phase is assessed through the use of exemplars and non-exemplars that challenge the pupils to recognise the application of the criterial attributes in an unseen example. The doing comes in the application phase when the pupils are asked to complete a particular exercise, worksheet or activity that requires them to practise using the skill or concept just learned. Within the template, you will notice the presence of sections such as resources, prerequisite (or assumed) knowledge, language, numeracy, ICT and differentiation.
Teaching resources In terms of resources, maths teachers frequently use:
• textbooks, worksheets, coloured pens for the whiteboard or chalk on a blackboard;
• rulers, protractors, compasses, set squares;
• calculators—graphics calculators or calculators connected to the OHP;
• overhead transparencies—of charts, graphs, notes, maps, exemplars and non-exemplars;
• visual aids—nets, blocks, rods, straws, paper shapes for symmetry, three-dimensional solids such as boxes (Toblerone, Smarties tubes, cuboid and cubic boxes from chocolates, pyramids), polystyrene solids cut into fractions, scale models, mirrors;
• digital cameras;
• laptop with generic software such as spreadsheets, databases, presentation, word-processing or computer art packages;
• subject-specific software—NNS packages, CD-ROMs, LOGO or Zeno, Omnigraph, Derive, Cabri-Géomètre or Geometer’s Sketchpad and SPSS;
• interactive internet sites;
• sensors and data loggers;
• Integrated Learning Systems.
Language
The literacy or language elements of teaching have already been stressed through reference to the National Literacy Strategy in particular, the importance of learning how to pronounce and spell mathematical vocabulary. In each lesson, teachers reinforce the new terminology in the context in which it should be used and also offer opportunities for the pupils to explain and use these new words too—either in whole-class teaching, groupwork or paired work. Both young and old learners should have the chance to practise using new words. Most of these opportunities arise in the Introduction and
Presentation phases, and also in the Conclusion when teachers are recapping on the learning outcomes achieved in the lesson.
Numeracy is usually thought of as mental arithmetic in the maths classroom since all classroom work is numerical. By practising and reinforcing pupils’ mental maths skills regularly, teachers are assisting in developing pupils’ listening skills and their ability to visualise the maths. Depending on the age and ability of the pupils, this mental maths could range from number bonds or times tables, to knowledge of the Pythagorean triples in a context, or simple geometric identities. In most cases, the mental maths activities are revising and reinforcing concepts or subject knowledge covered in the previous lesson and prerequisites of the current lesson.
This chapter emphasises the role of ICT as an integral part of mathematics teaching and learning. A range of resources has already been mentioned, but the list is by no means exhaustive.
Differentiation
Differentiation occurs by ability in the normal classroom. Many teachers have a restricted view of differentiation and only deal with the less able students when preparing materials and considering the usefulness of resources. In keeping with the ethos of the NNS and Key Stage 3 Strategy, gifted pupils need to be given challenging materials to extend their existing range of skills and encourage the use of higher-order thinking and reasoning.
Repeated use of ‘more of the same’ as a means of keeping these pupils working is of little advantage to the more able student—they just become quicker and quicker at the maths being covered in the exercise or task. Alternatively, they resort to misbehaviour through boredom with the mundane nature of the tasks being set.
Ideas for teaching
The remainder of this chapter will consider a variety of maths topics which are taught as part of the National Curriculum. Each topic is categorised by the type of teaching resources used—these categories are used for descriptive purposes only and should not be considered as the ‘best’ or ‘the only way’ of teaching this aspect of maths. The following sections will be considered:
• traditional ‘chalk and talk’—using textbooks, worksheet resources and a board;
• using visual aids and OHTs;
• using ICT—a laptop, data projector and whiteboard or Smartboard.
The final section is by far the largest since it represents the move towards using ICT as a teaching resource in the classroom in the same way as the overhead projector was the educational technology of the 1970s and 1980s. This final section will be split according to