ICT and Primary Mathematics

A Teacher's Guide

Nick Easingwood, John Williams

• Publisher: Routledge
• Year: 2004
• ISBN:
  9781134201914
• Edition: 1
• Topic: Pedagogía
• Subtopic: Educación general

This book is for teachers who are looking for interesting and practical ways to incorporate ICT into their daily lesson plans. It shows how ICT can be used as a tool for mathematics, but more importantly how its proper use can enhance the mathematics being taught. The authors cover all current aspects of ICT and mathematics, including:

• databases
• spreadsheets
• logo and the use of floor turtles and control technology
• handling of resources including interactive whiteboards
• management of ICT within the classroom
• how ICT can be used to present mathematical topics and links to other areas of the curriculum.

With plenty of suggestions on how to use the software and hardware described in the book, this is a useful resource for all primary teachers, particularly subject co-ordinators for ICT and mathematics. It will also be of interest to students on PGCE and Initial Teacher Training courses.

Chapter 1
Planning the mathematics lesson

If you have read our companion volume, ICT and Primary Science (Williams and Easingwood, 2003), much of what follows will be familiar. We discuss these key issues again here purely because we believe that you cannot have a book about ICT and mathematics, or indeed ICT and any subject, and not include guidance as to how the lesson should be planned, organised, resourced, managed and delivered. If ICT is to be successfully incorporated into any lesson then these are fundamental issues that need to be tackled at a very early stage. The subsequent success of the lesson depends upon this. Employing ICT as part of a mathematics lesson is not difficult, but it adds another dimension and the place and purpose of it needs careful consideration. The introduction detailed why ICT should be used in the teaching of primary mathematics. This, and the following chapter, will expand upon this and detail how it can be used in terms of the practicalities that are involved, such as planning, organising, resourcing and managing the subject. It will also consider the actual teaching, and of course the outcome, i.e. how the children benefit and learn by using ICT.

The most important point to make about the use of ICT is that it cannot and should not replace the teacher. Excellent teaching and effective learning can only occur when a good teacher is present. The key lies in how the technology is used and employed, not in the teaching of the technology itself. As we saw in the Introduction, although computers have many assets, the ability to think for themselves, get to know each one of their pupils on a personal level, engage in conversation about their interests, plan, prepare and assess their work on an individual basis, or interact with their parents at open evenings, are not as yet within their capability. It is these things that make the teacher’s role so crucial.

Planning the ICT lesson

So what does a mathematics lesson where ICT is to be used look like? Much of it will be reassuringly familiar, containing as it does all of the key features that one would expect in a plan for a primary mathematics lesson. This is detailed below:

• Selecting an appropriate topic: Why has a particular mathematics topic been chosen? Because it is in the National Curriculum for England, the National Numeracy Strategy or the Qualifications and Curriculum Authority (QCA) Schemes of Work? The idea for the work needs to have come from somewhere. It might even come from the teacher!
• Key learning objectives: What are the intended learning outcomes as a result of the lesson? What has informed the planning? These should be mathematics rather than ICT objectives. Although it may be possible to address several statements from the National Curriculum for ICT, these are secondary objectives. The primary ones must remain the mathematics objectives.
• Relevant connections and reference to the National Curriculum for Mathematics, the National Numeracy Strategy: It is maybe necessary to be able to directly connect to these, as this will ensure continuity and progression, and will illustrate how this particular lesson fits into an overall sequence.
• The content of the lesson: What exactly is to be taught?
• Details of any prior learning: The starting point may often be the children’s previous experiences, and where this fits into the overall sequence mentioned above.
• Teaching methodology to be used: Particularly crucial whenever ICT is involved. Is the lesson to be a practical lesson where other equipment apart from the computer is to be used? Or will the entire lesson be computer-based?
• Key teaching points: What are you actually going to teach the pupils? What are you going to say to them? What are you going to ask them so as to ensure that they learn what you want them to learn?
• Differentiation: This is particularly difficult in this context, as the teacher has to consider different abilities in ICT as well as in mathematics. But how are you going to differentiate? By ability? By previous experiences? Are any of the pupils on individual education plans (IEPs)?
• The foci for assessment: How are you going to assess what you hope the children have learned? What do you think they will have learned? What are the intended learning outcomes? Were there any unintended learning outcomes?
• Cross-curricular links: Are there any clear and relevant connections to other areas of the curriculum? Avoid contrived links at all costs. (In a later chapter we discuss mathematics and other areas at some length. Although some of the subjects may be unusual, we trust that the connections will be genuine.)
• Follow-up work: Where does this lesson fit into an overall sequence of work?
• Resources: What hardware or software is to be used? Is the equipment appropriate to the age and ability of the pupils and the intended learning outcomes? This could include computers, scanners, cameras, printers as well as more subject-specific mathematical equipment such as scales or rulers, or perhaps other ICT-related equipment such as calculators. Software also needs to be considered at this stage.

The above should reassure teachers as these are elements of any good lesson and should be present regardless of whether ICT is being used or not. At first glance it might appear that ICT has a surprisingly low profile, but this should reinforce the idea that ICT is embedded within the subject, and does not dominate it. The role of ICT is mostly to act as a tool for children’s learning through the ability to organise, display and analyse the collected data. At all times the children remain engaged in the key mathematical enquiry skills of calculating, hypothesising, predicting, observing, recording and analysing; therefore, these must have a high profile in the lesson plan. Additionally, the teacher needs to consider the teaching methods that are to be used, including the use of focused but open-ended questioning that extends pupils’ thinking about mathematical knowledge, and extends their understanding of the subject. A good lesson is reliant upon interactive, imaginative and creative teaching. The truly effective lesson where ICT is used occurs when the teacher ensures that the key features of the computers, the ones that give it the ‘value-added’ component—speed, automatic function, provisionality and interactivity—are all harnessed to the full. This is entirely reliant upon the teacher, not the technology.

When planning a mathematics lesson that includes the use of ICT, the teacher needs to be clear about the role that ICT will take. The National Curriculum for England stresses the importance of using ICT to support teaching and learning for all subjects and mathematics is one of the subjects that can benefit the most from this support. However, the very existence of a National Curriculum document for ICT ensures that it has the status of a subject in its own right. Although this book is primarily concerned with how ICT can support the teaching of primary school mathematics, there are however many strong elements of the ICT National Curriculum that can be successfully and effectively delivered through the teaching of mathematics. At Key Stage 1 this includes entering and storing information (finding things out) and selecting and adding information for particular purposes, planning and giving instructions to make things happen (developing ideas and making things happen). At Key Stage 2 this knowledge and these skills are extended to include the preparation and interpretation of information for development, the creation, testing and refinement of sequences of instructions to make things happen and to monitor and respond to events. Additionally, at Key Stage 2, there is a requirement to use simulations and explore models for the investigation and evaluation of changing values and the identification of patterns and relationships. Specific mention is also made of the need to ask open-ended, what if? type of questions. All of these requirements can be easily addressed in a way that provides an appropriate context, yet taking a primarily mathematical focus.

It needs to be remembered at all times when planning a lesson that a computer is a hugely powerful and very expensive tool that needs to be used effectively. It is the distinctive ‘value-added’ component that it offers teaching and learning that makes the computer such an effective instrument. For example, data collected as a result of practical mathematics work can be sorted and displayed in a number of different ways at the click of a mouse button. Information might be displayed as a graph or as a chart, and several different versions of each can be produced depending on how the user wishes to sort, display and analyse the information. Drawing graphs by hand can take a whole lesson, but by using a computer the time saved can be spent by the children engaging in higher order skills such as the analysis and interpretation of the information that is displayed in front of them. The practical element of the lesson has not been replaced, but the power of the computer has been harnessed to enable pupils to access levels of understanding that would not otherwise be available to them. It is the teacher’s responsibility to ensure that this power is harnessed, and this is discussed below.

Planning the mathematics lesson where ICT is to be included

Why choose this topic and these objectives?

The opportunity for primary teachers to choose the topic of the lesson and devise the content is now rare. Usually the main objectives for a lesson or sequence of lessons will have been taken from the schools’ long- and medium-term plans. These in turn will have been prepared subject to the requirements of the respective Mathematics and ICT National Curricula as well as the National Numeracy strategy for the given age group. These are the factors that directly determine what will be taught, and they will normally be drawn directly from the National Numeracy Strategy (it needs to be remembered that, unlike the National Curriculum for England, the National Numeracy Strategy is a non-statutory document), although they may have been prepared by the schools’ mathematics co-ordinator. Wherever the planning originated it identifies what needs to be taught, and the way in which it could be taught. In this particular instance, though, we are principally interested in the objectives. As mentioned elsewhere in this chapter, these main objectives will have a definite mathematical, rather than ICT, focus and this component will be refered to in the relevant attainment targets from the National Curriculum Mathematics and National Numeracy Strategy documents.

Prior learning

As mentioned above, all lessons have to be informed by something, regardless of the source. Failure to make reference to a medium-term plan, scheme of work or the National Numeracy Strategy can lead to a lack of continuity and progression, whereby skills, knowledge and understanding are either omitted from year group to year group, or are repeated in different years without any progression on the part of the teacher or the learners. This was one of the problems recognised by those who advocated a National Curriculum in the first place and rightly highlighted this. Much good imaginative teaching did take place in many schools, but all too often it was never followed up as the children became older. Very often it was even ignored by the secondary school, and children found themselves—to use a mathematical metaphor—back at square one. It was inevitable that some kind of plan should be produced to correct this. The problem now is that we might have too many plans, and those that we have might be too inflexible. Nevertheless, the teacher needs to ensure that there is a structured progression, so that concepts, skills, knowledge and understanding are consistently taught through introduction, development and extension.

Teaching methodology

The teacher needs to consider how the lesson is to be taught, and this in turn will directly influence the section below, which concerns actual classroom techniques. These will depend largely on the content of the lesson, but the teacher may also want to make the lesson a practical one. The teacher will therefore need to devise activities that enable the children to engage in practical work and then enter the findings into the computer for subsequent analysis. Where possible, the teacher should base the methodology on relevant underlying educational theory. So, for example, if the teacher is delivering a lesson where LOGO is to be used, consideration needs to be given to the underlying philosophy as espoused by Seymour Papert, who in turn was strongly influenced by the writings of Jean Piaget. If the teacher appreciates exactly what it was that Papert was intending to do when developing the LOGO language, then the teaching strategies involved will be geared to facilitating experiential learning, rather than just directly instructing the children. This will involve providing appropriate resources and using a teaching style that employs open-ended questioning and a considered approach that allows the children to learn through ‘doing’. It would be wholly inappropriate for pupils to be sitting at a computer and being told what to type into a LOGO program in ‘battery hen’ mode.

Teaching points

If the previous section discussed the importance of methodology, then this section details what the teacher needs to say or do to ensure that the intended learning takes place. This is the ‘nuts and bolts’ section, where the teacher does most of the actual teaching.

Differentiation

This is a particularly difficult area because differentiation needs to refer to both the mathematics and the ICT. It is therefore especially important to consider it at the planning stage. In a typical primary school class, it is entirely possible that there may be pupils who are high attainers in mathematics but lower attainers in ICT. Indeed, there may be up to seven years mathematical ability span in any typical Key Stage 2 class (DES, 1982). Conversely, high-attaining ICT users may struggle with mathematical concepts. Given that the focus of the lesson remains solely on the mathematics component, with the power of the computer being engaged to develop the appropriate mathematical knowledge, skills and understanding, then this apparent contradiction should actually assist the teacher in solving the potential difficulty. The teacher can harness the children’s abilities in one area to help those with difficulties in another. The issue of differentiation highlights clearly the point at which the skill and professional judgement of the teacher becomes crucial and helps to explain why the teacher can never be replaced by a computer.

Despite the main focus of the lesson being firmly upon the mathematics, it remains important that the ICT being used is appropriate to the capabilities of the pupils and to the teaching and learning objectives for that particular lesson. There is always a danger that it will be incorrectly matched to ability. This may be due to the teacher’s general lack of experience in the use of ICT within the lesson or because the teacher has a particular knowledge of a piece of software that he or she knows will work, and thus tries to use it in the wrong context. An example of this might be in choosing to use a Key Stage 2 piece of software for Key Stage 1 or vice versa, even though the mathematical concepts to be taught are relevant and appropriate.

Assessment

Crompton and Mann (1997) have stated the main problem with assessment where ICT is involved is that many teachers see the word ‘technology’ and misinterpret exactly what this means, electing to assess the child’s use of the computer, rather than the subject element that should provide the main focus for this. Therefore, it is extremely important to determine how assessment is to be undertaken at the planning stage, as it forms an integral part of the planningassessment-planning cycle. It should be recognised that a child’s progress may have been hampered simply by an inability to enter information, perhaps due to unfamiliarity with the keyboard or the program, and therefore the focus of the assessment must remain on the mathematics content. As a consequence of this, assessment is not an afterthought to the lesson; it is an integral part of it and is used for the following reasons:

• To determine whether teaching has been effective. Have the children learned what you intended them to learn? Were there any unintended outcomes? If so, are they relevant?
• Were all of the intended learning outcomes covered?
• Were the children working at an appropriate level?
• What additional practice may they need?
• Which concepts, knowledge and skills need to be reinforced? Which ones need to be extended?
• Where next do the children need to go with this topic?

Effective planning for children of differing ability levels can only occur when the teacher is aware of the level at which the children are working. If a task is too easy or too difficult then learning...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• List of illustrations
• About the authors
• Foreword
• Acknowledgements
• Introduction
• Chapter 1: Planning the mathematics lesson
• Chapter 2: Delivering the lesson
• Chapter 3: Using an interactive whiteboard
• Chapter 4: The use of floor and screen turtles
• Chapter 5: The transition from floor turtle to screen turtle
• Chapter 6: Why does LOGO merit a place in the primary mathematics curriculum?
• Chapter 7: Handling data
• Chapter 8: Using graphs
• Chapter 9: Mathematics across the curriculum
• Chapter 10: Some ideas for other mathematics and the use of ICT