ace2009The Asian Conference on Education 2009

‘Local Problems, Global Solutions?’

Saturday October 24, 2009 – Sunday October 25, 2009, Osaka, Japan

Official Conference Proceedings

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Cross-Cultural Transfer of the Abacus for Teaching Mathematics

Poo-Huat Tan1, Louise Moody

1, Adrian Bromage

2, Clive Richards

3

1Design and Ergonomics Applied Research Group, Coventry University

2Interprofessional and Interdisciplinary Learning Applied Research Group, Coventry University

3Coventry School of Art and Design, Coventry University

Abstract. In the Far East the abacus is widely used as a teaching tool. It is argued

that a computer- based abacus could provide a useful teaching aid in the UK for

children with mathematics difficulties. This paper will outline research undertaken in

UK schools to examine teaching and learning needs of children aged from 5-7 in the

area of mathematics. Current design work and future evaluation of a computer-based

abacus will be described.

Keywords: Computer-based abacus, mathematics difficulties, dyscalculia, interactive multimedia,

multi-sensory learning

1 INTRODUCTION

Research suggests that 6-7% of school children in the UK have mathematics difficulties (Butterworth,

2005). Difficulties in language and mathematics appear to be closely related (Chinn and Ashcroft

1993) and many children with dyslexia are found to have difficulties in mathematics as well as

language (Miles and Miles 1992, Bynner and Parsons, 1997).

Dyscalculia is a specific learning difficulty that results in problems understanding and learning

mathematics (Rittle-Johnson et al., 2001). In the UK, dyscalculia is defined by the Department for

Education and Skills (2001) as:

"A condition that affects the ability to acquire arithmetical skills. Dyscalculic

learners may have difficulty understanding simple number concepts, lack an intuitive

grasp of numbers, and have problems learning number facts and procedures. Even if

they produce a correct answer or use a correct method, they may do so mechanically

and without confidence."

In information processing terms, the child may have problems with short term (working) memory

(McLean & Hitch, 1999), retrieving arithmetic facts from long term memory (Bull & Johnston, 1997),

visuo-spatial perception (McKenzie et al., 2003), sequencing (Geary, 2004), spatial awareness

(Gifford, 2005), problem solving (Geary, 1994) and perceptual motor difficulties (Staves, 2001) and

directional confusion (Geary, 2004). As a result, children who have dyscalculia may have difficulty

with calculations, and with rapid processing of maths. They may find it hard to understand the concept

of numbers, to add and subtract, remember sequences, and may reverse or transpose numbers

(Dyscalculia Centre).

Research suggests that the area most commonly found to create difficulties is ‘memory for arithmetical

facts’ (Dowker, 2004). This refers to the ability of a child to grasp simple mathematical concepts,

thinking about numbers and the relationship between them (e.g. 8 + 5 = 13, 24 - 13 = 11, 6 � 9 = 54).

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Children experiencing difficulties, often rely on counting strategies (e.g. counting fingers/objects);

whereas unaffected children at the same age are able to rely much more on fact retrieval (Ostad, 1998;

Cumming and Elkins, 1999). Other common mathematics difficulties include use of the language of

mathematics, basic numeracy concepts such as the immediate recall of simple number bonds, learning

multiplication facts and tables, as well as sequencing and directional problems.

There is little research on dyscalculia in general, and those studies carried out, have not received wide

publicity (Dowker, 2004). There is a much stronger focus in the research literature on literacy

problems (Cohen Kadosh & Walsh, 2007). However, it is argued that poor arithmetic skills are in fact,

more of a handicap in the workplace than poor literacy skills (Bynner and Parsons, 1997). Struggling

with mathematics can be common amongst children without specific learning difficulties, so is an

important area for attention. Despite this, there has also been little in the way of recent design

developments specifically targeted at children struggling with mathematics during the early school

years.

1.1 Cross cultural transfer of teaching methods

The literature indicates there is limited cross-cultural transfer of teaching methods from East to West

(Bishop, 1988). Fuson (1992) suggests that there is a need to develop and test new ways of teaching

mathematics and specifically to test and adapt approaches from cultures that seem to be more

successful in mathematics teaching.

Research findings reveal enormous discrepancies in young children’s levels of mathematics

competencies, and these discrepancies appear to be larger in Western countries than they are in some

other countries in the Far East (Starkey & Klein, 2008). Although no formal research been undertaken

regarding the prevalence of mathematics difficulties in the Far East, in general, pupils in the Far East

perform well in international comparisons of mathematics achievement (Geary, 1996; Wang and Lin,

2005; D’Ailly, 1992).

One mathematics tool widely used in the Far East, but rarely seen in use in the UK is the abacus (Fuson

et al., 1988). The abacus is a device used to perform operations in mathematics, mainly addition and

subtraction. At a more complex level of operation it can also be used for multiplication and division. It

does not require pen and paper to perform calculations, but is solely based on the visual representation

on the counting board or frame. It can be used for any base number system (Young, 2004). There are

various formats of the abacus from the ancient counting table, to a frame with strung beads (bead

frame). There are 3 main forms of abacus still in use today; the Chinese abacus (Suan-Pan), the

Japanese abacus (Soroban), and the School abacus (originated from the Russian Schoty) (Pullan, 1968).

The Japanese abacus is pictured in use in Figure 1.

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Figure 1. School children in the Far East performing calculations using an

abacus.

The validity of the abacus as a mathematics teaching tool has been demonstrated for ‘normal’ students

in the Far East (Chen et al., 2006). Chen et al (2006) demonstrated that changes to the brain occur with

intensive training and practice on the abacus. This study used fMRI brain scanning to explore the brain

activation differences between abacus experts and non-expert subjects. They found that solving

computation-based problems involved more visuo-motor imagery processing, and very low level use of

executive function in a group of expert abacus users compared to a group of non-experts. They also

demonstrated that abacus experts tended to use fewer and more effective strategies in mental

computation, which may account for the outstanding computational skills of abacus experts.

The evidence suggests that as a teaching aid, the abacus does not result in high levels of dependence. In

fact, skilled abacus users are able to visualise a mental image of the abacus, and performing rapid

mental calculation by manipulating imaginary beads in their brains (Stigler, 1984). As a result the users

develop effective mental calculation ability.

In Sudan, Irwing et al. (2008) have shown the abacus to improve mental arithmetic and reduce

dependence on rote learning and memorisation. They showed that abacus-based training supports

mental arithmetic and provides benefits to working memory which are advantageous to the

performance of other mental processes. As a result they believe that the abacus can provide a greater

emphasis on problem solving skills which may lead to an increase in general intelligence.

Cotter (1996) reports findings that show using the AL abacus may help children develop a mental

abacus as well as to develop arithmetic concepts such as place value and mental computations. AL

abacus is a physical plastic frame that introduces simple number representation. The visual

representation of an AL abacus such as the arrangement and colour help children understand the

structure of numbers in an easy and effective way and avoid a reliance on counting.

Furthermore, a Japanese study showed that given the right circumstances, abacus-based learning can

promote motivation and achievement in school mathematics, and general attitudes towards the subject

(Shwalb et al., 2004). The research on use of the Japanese abacus explored its influence on

mathematics learning and motivation in formal school settings. It was found to have a positive

influence on mathematics education. The existence of the mental abacus was supported by the reports

of many children, and was seen to be related to motivation towards mathematics and calculation skills.

Despite the emerging evidence of the benefits of the abacus, we are not aware of any existing research

demonstrating use of the abacus for children with mathematical learning difficulties, or indicating

extensive adoption within the UK. It is likely to be an appropriate tool to support children with

learning difficulties because it conforms to the principles of tactile learning; provides a visual aid; and

enables left to right reading avoiding confusion (Shen, 2006).

1.2 Computers and mathematics education

The use of computer-based learning or ICT (Information and Communication Technologies) is

widespread in the UK (BESA, 2008) and strongly recommended within the National Curriculum

(2009). The availability of ICT impacts how children learn mathematics (Yelland, 2001). It can enable

experimentation, logical thinking and problem-solving. It can help children observe, explore and

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explain patterns in numbers, shape and data, and develop mathematical vocabulary and language

(National Curriculum, 2009).

It has extended benefits of motivating and engaging children and encouraging confidence and

independence in learning (Higgins, 2003; Yelland, 2001; Valentine et al., 2002). However, there are

few available programmes aimed specifically at mathematics and specifically dyscalculia

(Parliamentary Office of Science and Technology, 2004). It is proposed that an ICT-based abacus

could offer significant advantages to children with mathematics difficulties in the UK.

1.3 Aims

The literature indicates that mathematics difficulties are a significant problem in the UK. However

there has been limited attention to research and development in this area. Here, we suggest a novel way

of supporting UK children through the development and introduction of a Far Eastern teaching tool. A

computer (or ICT) based abacus is proposed as a way of capitalising upon, and updating this traditional

mathematics aid.

Through this study it is aimed to explore user needs for an ICT-based abacus through a user-centred

design process (Stanton et al., 2005) and determine the feasibility of the concept for teaching children

with mathematics difficulties. Here, the initial user requirements research stage is described. We then

go on to describe current design work and future evaluation.

2 METHODOLOGY

A user-centred design process involves extensive consideration of the needs, wants, and limitations of

the end user at each stage of the design process. This methodology adopted involved the collection of

teacher and child needs in the design of a novel teaching aid for mathematics difficulties. This was

undertaken through a review of existing products, observation in the classroom, and 1:1 interviews

with teachers. Classroom observation was carried out to gain an understanding of mathematics

difficulties and see current teaching methods in use. Interviews were used to follow up the observation

sessions and gain a more in depth understanding. Ethical approval for this element of the research was

obtained from Coventry University Ethics Committee.

2.1 Participants

Observation of 14 teaching sessions with 7 different teachers was observed. Group teaching was

observed in 3 main stream schools (7 sessions). This included classes of 11-25 pupils, at least 2-5

pupils per class experienced mathematics difficulties, some of which were severe. Small group

teaching, of up to 5 children per class was observed in 1 special education school (2 sessions). Five,

one to one teaching sessions were observed at a dyslexia centre. The length of each teaching session

lasted between 45 and 90 minutes.

Interviews were undertaken with 8 dyslexia teachers in the UK (with 5-15 years experience), 7 of

which had been observed teaching. A further interview was undertaken with a Malaysian teacher with

experience of running her own learning support and intervention service in Malaysia. All of the

teachers were female.

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2.2 Procedure

Informed consent was gained from the teachers, the children and their parents involved in the research.

A protocol was developed for structuring the observation. This included focussing on pupil difficulties,

the teaching methods employed, physical or computer-based tools in use, and students’ responses to the

teaching (e.g. motivation and attention). The observation sessions lasted between 45 and 90 minutes.

Interviews with the teachers were held following the observation sessions. A semi-structured interview

format was followed, this comprised of questions relating to problems and strengths of children

experiencing mathematics difficulties, teaching materials and methods they employ, and their views on

current product/tools that are available. The interviews were taped and written notes taken.

The observation and interviews enabled identification of the teaching tools and techniques available for

children with learning difficulties. This process was supplemented with a literature and web search.

These tools were reviewed by three of the teachers and the first author based on criteria such as ease of

installation, use and control, sound and graphics quality, learning objectives, teaching methodology

appropriateness for children with mathematics difficulties.

3 RESULTS

The findings from the research reported in this paper highlight pupil difficulties, teaching methods and

tools currently in use, as well as pupil responses to these. The research focused on Key stage 1 in the

UK education system (typically age 5-7 years) as the literature about early child development indicated

that this was the time during which a basic foundation should be developed to enable later building of

more abstract concepts of number and arithmetic.

3.1 Challenges to pupils

The research revealed that many students struggle with elements of mathematics, particularly

numeracy concepts, and practical mathematics skills needed to function in everyday life. Other

common challenges included:

• counting

• properties of numbers and number sequences (e.g. counting numbers reliably forward and

backward up to 100; knowing the number names and reciting them

• place value and ordering (read and write numerals up to 100; understand 23 is made up of 2-

tens and 3-units etc.)

• estimating

• simple calculations (to solve problems using counting, addition, subtraction, doubling and

halving)

• using mathematical language (read, write and order numbers)

• remembering times table

It was observed that the answers to mathematic problems often seem more important to children than

the working steps of calculation. This makes it difficult to determine whether they understand the

rationale of the calculations, and hold knowledge that can be built upon.

3.2 Teaching methods

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The teaching tools and techniques currently employed in the UK have been identified and analysed.

Many different teaching methods are used to deliver numeracy concepts. Most of these tools are

physical artefacts, rather than ICT products.

The existing methods can prove impractical for problems with high values, or for use in formal exams

(e.g. counting fingers and objects). Some of the teaching aids can lead to reliance, so that children

reach the correct answer without understanding the rationale (e.g. Number-line & 100-square).

Some teaching methods were reported to be confusing, requiring students to perform many steps to

complete the task (for example see Figure 2.). This is challenging for students with short term memory

deficits, as is often the case for children with learning difficulties.

Figure 2. Complicated calculation steps may lead to confusion.

The teachers interviewed were willing to try new and varied methods to suit individual children, and

specifically developments for children with dyscalculia. They all felt that they do not currently have

adequate tools for improving mental arithmetic. As a result, some had developed their own methods to

help pupils grasp numeracy.

The abacus is not widely used in the UK for teaching mathematics, and has not been explored for

children with learning difficulties. Only 3 teachers had used a western abacus in teaching, and just for

counting numbers. They were not fully utilising the functions of an abacus and were unaware of how it

could further facilitate early numeracy. They were, however keen to explore this further.

3.3 ICT

The literature indicates that computer-based learning is attractive and motivating to students (Rieber,

1996). The classroom observation and interviews with teachers indicated that the graphics, animation

and independent working are engaging and motivate child participation. This is important to raise

confidence and self-esteem, which often dyslexic children are lacking.

Despite the advantages offered by this format, most of the tools used are physical artefacts. The

available computer programmes (e.g. NumberShark®), are mainly game based and dyslexic children

can be distracted by the colourful graphics and sound effects (McFarlane & Latorella, 2002).

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4 DEVELOPMENT OF A COMPUTER-BASED ABACUS

In the Far East the abacus is widely used as a teaching tool. It has been shown to improve mental

arithmetic and reduce dependence on the calculator. It conforms to the principles of tactile learning;

provides a visual aid; and enables left to right like reading avoiding confusion and so may provide

benefits to children with learning difficulties (Shen, 2006).

The area most commonly found to create difficulties for pupils with dyscalculia is developing an

understanding of fundamental numeracy concepts and the relationships between numbers (Dowker,

2004). Mathematics and numeracy is a sequential subject which builds upon early knowledge and

skills. Therefore remembering the fundamental numeracy concepts are essential and a tool for

supporting this would be of value.

4.1 Rationale

It is proposed that in an ICT format, the abacus could add to the advantages offered by the physical

abacus by offering an engaging and motivating learning experience. Therefore a computer-based

abacus for supporting pupils with mathematical learning difficulties is being developed.

The tool will be directed at Key stage 1 in the UK education system (typically children aged 5-7 years).

At this stage it will enable building of mental arithmetic, and most children are able to follow rules and

methods.

4.2 Software development

The abacus is being designed using Macromedia Flash software. It will run on both Microsoft

Windows and Apple Macintosh machines. This will enable interaction using a mouse, touch screen and

keyboard.

This platform will enable use in class for demonstration, and practice on a smart board, or at home by

the pupil.

4.3 Abacus design and layout

The interviews indicated that the Chinese and Japanese abaci formats were not familiar to teachers and

were complex to learn in the West. The beads represent different values (e.g. upper deck beads

representing values of 5, lower deck beads representing values of 1) (see Figure 3.). This requires a

certain amount of basic mathematical knowledge (i.e. the relative worth of 1 and 5, and the ability to

count in 5s). Operation is also dependent on the capacity to hold information in the working memory

when performing calculations which involve carrying and borrowing. These would present specific

challenges to young children and those with mathematic difficulties.

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Figure 3. Eastern abacus (left) vs. Western abacus (right)

Therefore the software abacus has been developed based on the Western model. This is more

straightforward, as each bead represents a value of 1, arranged in blocks of 10. This facilitates simple

counting strategies reinforcing the properties of numbers as discrete units. Simple sums are readily

visualised, and the concepts of tens and units and borrowing can be demonstrated.

Whilst it is not used widely in schools, the format is familiar to most children and teachers.

The physical Western abacus however cannot be used in such an advanced manner as has been

demonstrated by the Chinese and Japanese abaci in the East.

4.4 Abacus activities

The advantage of ICT is that the format can be enhanced to enable additional tasks and functionality

built in and it enables a log of performance to be retained. The computer programme will incorporate a

resource of different learning tools designed around the abacus concept.

It will focus on different sub-sections of the curriculum standards set by ‘National Literacy &

Numeracy Strategies: Curriculum Standards’. In particular, the exercises will focus on developing

mental images of quantities, strategies, and mathematical operations and understanding basic sets and

numbers (e.g. ordering, steps of the sequence i.e. every number, every second number, and grouping)

(Department for Education and Skills, 2002).

The programme will offer a combined suite of tools building on existing physical tools used in schools.

It will incorporate abacus-based activities for children to grasp number sense and numeracy concepts.

Figure 4 shows some early paper prototyping to explore the tasks and activities. The final design will

incorporate tasks that focus on the development of early numeracy concepts and arithmetical facts. It

will enable a child to practise counting, place value, recognition of odd and even numbers, addition,

subtraction, multiplication and division.

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Figure 4. Paper prototyping explores the possible abacus activities.

4.5 Learning support

The presentation of multi-sensory information within the abacus programme will meet the needs of

children with varying learning styles and reinforce the learning experience (Orton-Flynn & Richards,

2000). Furthermore, the provision of graphics, sound and tactile interaction (through the touch screen)

will support spatial thinkers and visual and kinaesthetic learners (Doyle & Rutherford, 1984).

The programme can be personalised and therefore set for the different needs of children in regards to

topic, level of difficulty, complexity, visual needs, background knowledge and interest. The activities

undertaken can be saved and performance over time logged for each child. Activities can be flexibly

set in terms of time frame needed, repetition of visual representations, instance feedback, and rewards

in order to support the learning curve.

4.6 Future Work

Evaluation of the ICT abacus in UK schools in due to begin in October 2009. An iterative user-centred

design approach is being adopted (Stanton, 1998). This will involve evaluation of whether the learning

objectives have been met by the programme, and an assessment of the programme’s usability.

Usability evaluation is an essential validation phase that considers the extent to which a product

achieves its specific goals, with effectiveness, efficiency and satisfaction (ISO, 1998). Initially a mock

up will be evaluated informally with teachers in terms of the usability of the system.

Once reliability and usability has been established, a working prototype will be taken into schools and

the impact of the tool on children’s level of understanding, and learning of basic mathematics concepts

will be evaluated. Children at Key stage 1 will take part in the study, as well as children identified to

have specific mathematics learning difficulties. This stage of evaluation will also involve qualitative

feedback on the engagement and motivating qualities of the software and usability assessment, to

ensure ease of use is achieved for both teachers and children.

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5 CONCLUSIONS

This paper has described initial research undertaken in the design of ICT for children with mathematics

difficulties. Based on the transfer of a teaching tool used widely in the Far East, a computer-based

abacus is being developed. A user-centred design approach is being adopted to build in activities based

on National Literacy and Numeracy Strategies to address Key stage 1 learning outcomes. The resulting

tool will cater to the needs of children with learning difficulties and offer the benefits of conforming to

the principles of multi-sensory learning, providing a visual aid allowing tactile exploration, and

enabling left to right reading. Ongoing work involves the iterative design and evaluation of the

resulting software.

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