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Maths and ICT

Curriculum focus Finding things out; developing ideas and making things happen; exchanging and sharing information; reviewing, modifying and evaluating work as it progresses; developing thinking skills; making and testing hypotheses.

Teaching and learning context Review and reflection. Investigation and Problem Solving. Linking theory and practice. Hypothesising. Hypothesis testing.

As a general rule, ICT should be used to do things The Teacher Training Agency (TTA) suggests that there are three key principles to be taken into account when using ICT in subject teaching. They add that it is important to consider whether ICT is used by A number of features are listed by the TTA which they suggest will make a significant contribution to pupils' learning of mathematics. These include: ICT can also aid teachers to prepare effective teaching materials, keep in contact with experts and sites which provide mathematical resources and to aid record-keeping and reporting. (Using Information and Communications Technology to Meet Teaching Objectives in Mathematics Initial Teacher Training (Primary). Teacher Training Agency publication no 46/5-99, page 3-5).
 * more efficiently (quicker)
 * more effectively (better), and
 * to do things that could not be done before.
 * 1) Decisions about when, when not and how to use ICT in lessons should be based on whether **the use of ICT supports good practice in teaching the subject**. If it does not, it should not be used.
 * 2) In planning and in teaching, decisions about when, when not and how to use ICT in a particular lesson or sequence of lessons **must be directly related to the teaching and learning objectives in hand.**
 * 3) The use of ICT should allow the teacher or pupil to **achieve something that could not be achieved without it**, or allow the teacher **to teach** or the pupil to **learn something more effectively and/or efficiently than they could otherwise.**
 * all the pupils: individually, in groups or as a whole class
 * some pupils only (e.g. for support or extension work, or during breaks, at after-school clubs, or at home)
 * the teacher only (e.g. using a large screen, data projector and/or interactive white board as part of an interactive whole class teaching, downloading lesson plans form the NGfL, or resources from the Internet in advance of the lesson so that pupils can browse the selected material.
 * practice and consolidation of number skills
 * software aimed at developing specific skills (e.g. equivalent fractions, conversion from fractions to decimal to percentage, tables) are available and use by schools.
 * exploring, describing and explaining number patterns
 * software is available which generates required number sequences and/or number grids which can be used for exploring number patterns
 * mathematical modeling by exploring, interpreting and explaining patterns in data
 * graphing software and sensing software produces patterns and trends which can be examined and interpreted
 * experimenting with and discussing patterns in number, shape and space
 * software which generates number sequences and geometric shapes which can be manipulated and examined, is available
 * developing logical thinking and learning from, immediate feedback
 * programmable robots and toys can be given sequences of instructions to complete specific tasks and branching tree software can be used to sort shapes and numbers
 * making connections within and across areas of mathematics
 * graphs can be created accurately and quickly using graphing software, enabling pupils to see the connection between equations and tabulated figures and the graphed results
 * developing mental imagery
 * software which produces patterns as well as masks which cover part of the pattern enables pupils to develop mathematical insights
 * writing of simple proceedures
 * programmable toys can be instructed to solve mazes etc, and software like LOGO can be programmed to drawing geometric patterns.

Some quotes about using ICT to develop numeracy. ICT has the potential to transform the way numeracy lessons are delivered and developed. The Primary National Strategy identified the eight key aspects of ICT (speed, capacity, automation, communicapability, provisionality, interactivity, non-linearity, multi-modality) which allow work in all areas of the curriculum to be approached in alternative ways to those seen practiced in traditional learning environments. Open 'content free' software allows ICT to support children's mathematical thinking through these strengths of the technology. This includes several software applications such as spreadsheets... counter...  Price, H & Moore, D. (2005) Promoting Numeracy with ICT. In Wheeler, S. (2005) Transforming Primary ICT.

ICT can offer a range of contexts and opportunities for developing and extending mathematical work at any stage of mathematic development. Examples... Higgins, Packard and Race. (1999) 500 ICT Tips for Primary Teachers.
 * Floor robots can be used even with very young children
 * Floor robots can be used even with older children
 * Keep the number of drill and practice programmes to a minimum
 * Try to get hold of drill and practice programmes that are flexible
 * Do not underestimate the power of peer tutoring

Using real data in examples for children to work with always used to be problematic. If numbers have to be manipulated without recourse to technology, then it is sensible to, first, keep the numbers simple, preferably whole, and secondly, to keep the number of examples to a minimum. ICT eliminates this problem. A calculator or, even better, spreadsheet allows for arithmetic, using real numerical data, to be carried out swiftly and accurately, and as many times as is needed. Spreadsheets can be configured to give only a manageable or appropriate number of decimal places... Real data collected from real situations gives a meaning to work, which somebody else's contrived or remote data does not. Briggs and Pritchard (2002) Using ICT in Primary Mathematics Teaching. Page 5.

There are many of ways of using ICT to support the learning and teaching of numeracy. A number of programmes provide examples of work together with graphics which make it easier to understand what is happening. These include programmes which use diagrammatic representations of fractional parts, graphical representations of rotation about a point, graphical representations of number lines of different sorts etc. These programmes are often used by teachers for whole class demonstrations, using a computer, projector and/or interactive white board, but they can be used by groups of children or individuals. This kind of subject specific software generally falls into the tutor class. Interactive White boards (IWBs) are changing classrooms dramatically, providing a highly interactive way of working with data. Many schools are investing in this new technology. IWBs make demonstrations much easier and clearer than traditional whiteboards and provide a rich interactive environment in which to work. See the year six examples that follow. These video clips may take a while to download. What did you think of the virtual protractor? consider the difficulties you would face as a teacher trying to demonstrate measuring an angle using traditional materials. Generic computer software, such as spreadsheets (E.g. Microsoft Excel, Lotus 123), can also be used to good effect. It is especially useful for providing an environment which supports experimentation, where children can look for patterns, as in mathematical investigations. Spreadsheets are designed especially to deal with numeric data and are extremely powerful 'number crunchers', capable of doing thousands and sometimes millions of calculations per second (depending on the power of the computer being used). Spreadsheets provide the facility whereby the computer takes care of the calculations, enabling users to avoid what some call inauthentic labour (procedural practicalities, such as doing time consuming calculations) and to concentrate on MATHEMATICS (thinking about numerical patterns, numbers, the ways they relate to one another). This releases children to 'think' about the content and more fundamental issues. For example, the children can be released from 'drawing' a graph or graphs and can spend time analysing and interpreting the data presented in the graphs. Other higher order benefits that this kind of approach facilitates include: Graphs produced by spreadsheet packages can also be used for teaching children to draw their own graphs, something which they generally tend to struggle with because of the difficulties they face when trying to understand equal interval scales and when trying to deal with the limitations that the size and shape of a physical page presents. Looking at the way the software handles these functions can be a great help, but needs good facilitation on the part of the teacher. Spreadsheets tend to use a range of mathematical operations such as: add +, subtract -, multiply *, and divide /. Additionally functions such as SUM, AVERAGE, MODE etc. are readily available. Finally conditional statements can be applied, taking the form: > IF this is the case - do something - otherwise do something else. It is important to recognise that often the ICT resources/tools used in schools may appear to be less useful than some of the standard tools used. There can be a tendency for adults to write them off as inadequate. You need to appreciate that the software used in the school setting, particularly in Primary schools has been developed and designed for children’s use and specifically to assist their learning. If children are to understand when and how to best employ these tools they will need to use them over several years. They need to start in a modest way. They may begin by using the spreadsheet as a graph drawing tool, without using it for calculation purposes (Keeling, R. & Whiteman, S 1990, Simply Spreadsheets). It is also important that you understand that ICT includes equipment such as electronic calculators, slide rules, programmable robots. The Logo programme, which enables one to draw geometric shapes on the screen as well as patterns, can also help children develop effective mathematical concepts. The resources below are examples of spreadsheets which can be used for teaching, learning and administrative purposes.
 * [|Angles] || [|Muffins] || [|Division] || [|Sequences] ||
 * What The Standards Site says about Mathematics ||
 * What the National Curriculum Site says about Mathematics ||
 * Looking for patterns and relationships;
 * Developing and testing hypothesis;
 * Formulating questions, posing problems (what would happen if... can I use this to find out whether... and using what they know to solve problems;
 * Analysing data/constructing information;
 * Testing ideas and developing high level thinking skills.
 * Useful files to download and inspect: ||
 * PNS IWB resources || Aunt Lucy doc || Aunt Lucy Spreadsheet ||
 * A useful site for mathematics teachers || Paula's Party || Paula's Party Spreadsheet. ||
 * [|Magic squares] ||
 * A useful paper - Using spreadsheets as investigative tools with primary mathematics pupils ||
 * Another useful paper - [|Do women live longer than men?]- using database and spreadsheet software to turn opaque data into useful information ||
 * Basic Spreadsheeting skills - video help files from Phil's site ||
 * Spreadsheets - progression of skills from Phil ||

See http://www.mathsonline.co.uk [|Directed activities - click here]
 * A reminder: As you develop your skills, remember to add any resources you have found to the learning resources wiki. ||

Reading Potter and Darbyshire (2005) Understanding and Teaching the ICT National Curriculum. Some other useful readings.
 * Abbott: C. (2001) ICT: Changing Education. Routledge Falmer, London. pages 52-54 on Logo.
 * Briggs, M. & Pritchard A. (2002) Using ICT in Primary Mathematics Teaching
 * Papert, S. (1980) Mindstorms: Children, Computers and Powerful Ideas. Harvester Wheatsheaf, New York.
 * Teacher Training Agency. (1998?) Using Information and Communications Technology to Meet Teaching Objectives in Mathematics Initial Teacher Training (Primary). Teacher Training Agency publication no 46/5-99.
 * Wheeler, S. (2005) Transforming Primary ICT. Chapter 3 – Promoting Numeracy with ICT. Article by Price and Moore.
 * Ager, R. Information and Communications Technology in Primary Schools. Chapter 7, pages 105-110.
 * Wegerif, R. & Dawes, L. (2004) Thinking and Learning with ICT. Chapter 7. (Maths talk and ICT).