This case study was prepared in November 1994 for the (AGOCG)Advisory Group on Computer Graphics Technical Report 26
Keywords: Interactive; calculator; numeracy; Dienes blocks; dyslexia; mulitmedia learning package.
Authors: Clive Richards is Director of the Visual and Information Design (VIDE) research centre of Coventry University. Sue Flynn is a research Fellow in the VIDE researc1t centre.
Note: Certain features of the multimedaa calculator described here are subject to a patent application by Coventry University.
Dyslexia usually implies problems with literacy. A large proportion of dyslexics however, also have some problems with mathematics. It has been estimated that 6% of the school population has serious problems with arithmetic and often there may be little provision for helping these children, especially if they have behavioural problems as well.
The research reported here is a continuing project being conducted in the Visual and Information Design research centre of Coventry University. The aim has been to design an interactive multimedia learning package for teaching numeracy to specific groups of pupils. A long term objective of the project is to investigate the applicability and potential of multimedia systems for such tasks.
The focus of this particular project is the numeracy difficulties of 8 to 11 year old children.
Generally, structured learning materials like Dienes blocks2 and Cuisenaire rods3 are used to concretise the concepts of number. Together with considerable overlearning and the careful use of language, these materials provide a multisensory experience which enhances the learning process and enables the accurate recall of information from the long term memory.
It may be possible to provide the equivalent stimuli in one package using multimedia. The intention of the current investigation is to demonstrate that a multimedia application can present this multisensory learning experience in an efficient and effective way.
Within the context of special learning needs there is an abundance of software for teaching literacy but less for teaching numeracy. In the past, the emphasis has been placed on reading and writing. Many parents are known to say, "Oh well, I was never any good at maths either!" but rarely heard saying, "Oh well, I was never able to read and write!" It is only comparatively recently that deficiencies in number skills are being properly acknowledged. Our society is becoming more dependant upon number based technologies. Therefore, it is necessary for effective teaching of numeracy to reach all groups of children, in order that they may be integrated successfully into society.
Observations conducted as part of the present research in several middle schools during the mathematics lesson showed that this area of the curriculum needs to be addressed. 8 to 11 year pupils of mixed abilities and from a broad range of socio-economic backgrounds have been studied. It has been possible to identify amongst the pupils a set of problems, some of which are indicative of specific learmng difficulties, including dyslexia. These problems appear to be compounded by the use of calculators, now a component of the National Curriculum for all schools.
A design audit of a range of conventional, four function calculators has informed the development of the multimedia calculator interface, described here later, which aims to address problems identified. Through the use of multimedia authoring tools, in this case Macromedia's "Director Interactive", it is possible not only to design a prototype working calculator but also to incorporate within the interface access to representations of multisensory teaching aids, like Dienes blocks. Investigations at special needs schools have reinforced the value of multisensory teaching reported by teachers4. The teaching routines used with Dienes blocks are rigorous and combine the language and actions of the four basic mathematical operations. It was therefore considered appropriate to integrate these established teaching routines into the proposed multimedia learning package.
It is anticipated that a multimedia package can simulate these very teacher intensive learning methods and may provide economic advantages. Such a multimedia package could provide other advantages for the child with difficulties who may lag behind his/her peer group, e.g.
It is the design and operation of 4-function calculators, commonly used in schools, which have become a key feature of the research. It would appear that through their use in the classroom difficulties with arithmetic are compounded for pupils with problems associated with dyslexia, e.g. short term memory deficitS and difficulties with transferring ideas, verbal labelling and abstracting information.67
When used for teaching elementary numeracy, certain features of standard calculators are not helpful for such pupils. Some of these features are listed:
A multimedia calculator8, which is mouse operated, has been designed and protoyped using Macromedia's software "Director Interactive 4.0". The animation capabilities in this authoring tool have been utilised to simulate the calculator operations and manipulations within the various windows such as the Dienes block arena.
The calculator has been designed to address the problems indicated in the previous section. It has other features aimed at supporting learning by dyslexics and attention has been paid to the visual styling of the interface which is regarded as being of great importance to the likely success of the package. (See figure 1.)
It will be noted that the layout of the key pad for the multimedia calculator is the same as that for the telephone, viz:
Research findings show that less errors are made using this layout, which is also faster. We believe that this layout is more likely to correspond to children's expectations than the standard calculator layout:
These two formats are used internationally, but why this difference exists is uncertain and may be due to the original mechanical configuration of adding machines. The multimedia calculator has three modes of operation. In the first mode it performs in the same way as a conventional four function calculator, returning the correct answer when the 'equals' button is depressed.
The basic difference between the display of the multimedia calculator and the display of most conventional calculators is that the complete vertical algorithm is displayed in the window step by step for each of the four basic mathematical functions: +, -, + and x. Each number is displayed in columns and the chosen operator is placed to the left of the sum. The answer is returned below a line, which appears when the 'equals' key is selected. The answer to a division sum can be displayed as a quotient and remainder if the numbers input do not contain a decimal point, otherwise the solution is displayed as a decimal value.
The display layout, in columns, is representative of the formal notation expected in the classroom and should help to reinforce the concept of place value. This may assist those who have difficulty with the accurate notation of their sums. This design is not reliant upon a good short term memory as is the conventional calculator where only the last digit input, or the solution is displayed. Relief of overload on the short term memory could mean that the user will be able to concentrate more clearly on the basic arithmetical task.
In the second mode, the design provides a means for 'guessing' or estimating the answer to the problem. By selecting the 'guess' keylų a numerical keypad pops-up, which is colour coded to match the 'guess' key and the 'guess' display (the smaller display area of the calculator interface). Digits input using the keypad in this window are automatically entered into the 'guess' display. The correct answer is accessible by selecting the 'equals' key on the calculator. The two answers can then be compared.
The third mode of the calculator is the 'work out' mode. If the input sum is addition or subtraction, selecting the 'work out' key will pop- up the Dienes work area, (see figure 2). The Dienes area is fully interactive and can be used for either addition or subtraction. This area has been designed to conform with good teaching practices mentioned earlier and gives the opportunity for the pupil to experiment with virtual Dienes blocks in various ways, similar to actual Dienes blocks. Through the concrete operation of manipulating the blocks, the answers to addition and subtraction problems can be obtained. Research has shown that a key learning feature for the user in such operations is the exchanging of units into tens and tens into hundreds, together with the reverse processes. These processes are critical to the understanding of place value and the exchange should be initiated by the user. The computer prompts the user to do this by the use of colour. If the user wishes to exchange a hundreds 'tile', for ten 'rods' of ten, then he/she has to select the 'exchange' key. This action will result in the current 'tile' breaking into its ten component rods and changing colour from yellow to blue, blue being the colour of the tens rods. The change of colour, but not position, (i.e. the rods stay in the hundreds column), indicates to the pupil that the rods have to be moved out of the hundreds column into the tens column. When the pupil has completed all transactions and arrived at a solution, he/she can enter the solution into the 'guess' display and compare it with the correct solution on the calculator.
At every stage throughout the calculator's various modes, there is audio feedback and voice reinforcement. This use of sound is important to ensure that the correct language is used with each mathematical process.
If the 'multiply' or 'divide' keys are used on the calculator and then the 'work out' key is selected, one of the interactive multiplication squares pop-up (see Agure 3.). These windows are examples of 5 x 5, or the 10 x 10 multiplication squares and are interactive. The teacher is able to preselect which multiplication square appears, using the preferences window described next. The purpose of the multiplication square is to provide prompts for users who may not have the necessary number facts to complete a multiplication problem. According to Milesl2, this is a particular problem for dyslexics.
Both the Dienes work area window and the multiplication square window appear partially overlayed on the top of the calculator. It is important that the user does not lose sight of the main calculator screen whilst working in the various modes. Using these overlaying methods for presentation, the original problem input and displayed as a vertical algorithm on the calculator remains visible as a reference in the same place on the screen. The use of familiar metaphors, which operate according to real world environments, are expected to lead to intuitive use of the packagel3 '4. Within the package the user can either click on the top left hand corner of an overlaid window, or click on the calculator behind, to make the calculator active again.
A survey of teachers' preferences indicated that they would like to have a calculator on which they could limit the access to the keys. The 'preferences' window (seefigure 4) enables the teacher to disable any keys on the calculator. The teacher can create a new file for each pupil, which is written onto the hard disc of the computer, save a file or print a file. The file is a track record of the pupil's activities whilst using the multimedia calculator. The sound can also be adjusted in the preferences window, a useful facility when one has a classroom full of children with computers!
At the time of writing, the prototype calculator interface is fully functional and has been informally trialled.
These informal trials were carried out in the classroom with a group of pupils. Each user was video recorded and any remarks and comments noted. These trials sought to establish if the application was easy to use, whether pupils liked the look of it and what their expectations of it were.
The results of these trials were interesting and some expectations were exceeded. In particular, a statemented dyslexic, who has a very short attention span and is a disruptive influence in her class, spent a quiet twenty minutes accurately completing a series of calculations using the multimedia calculator. Compared with her previous performance using various hand held calculators, there was a significant improvement in the quality and accuracy of her work. The possibility of a novelty factor should not be overlooked in this instance because the children were excited by the change of routine, etc., although it could be argued that novelty alone is unlikely to increase one's competence in mathematics.
The results of the initial tests of the design are encouraging and will inform the further development of the prototype and its more formal evaluation.