The tally system is among the oldest and most widely found methods of counting. Before the first glimmer of arithmetic, prehistoric Cro-Magnon man used a device called a tally bone.
The earliest archaeological evidence dates from the Aurignacian era (35,000 to 20,000 BC) discovered by archaeologists in 1937 in Czechoslovakia. Among these is the radius bone of a wolf, marked with 55 notches in two series of groups of five.
These counting tools made it possible to count even in the absence of adequate words, memory or abstraction. The technique of tallying remains unchanged but largely undervalued as a powerful visual tool for developing early maths skills.
As part of her professional development, Mecky Turner, a special educational needs co-ordinator at St Peter's Church of England Voluntary Controlled Primary School in Sible Hedingham, near Halstead in Essex, conducted an action research project with a DfES Best Practice Research Scholarship to investigate how the use of structured images, such as tally marks and a paper abacus, can help children develop an understanding of the decimal number system and improve their ability to do mental calculations.
Using Vygotskian psychology to inform her ideas, she worked with a group of Year 2 children last year teaching them how to recognise quantities without counting one by one - "ordered arrays".
Mecky Turner began her work by modifying the key objectives from the National Numeracy Strategy for key stage 1 to incorporate visualisation of ordered arrays, and generated a set of materials to help children see quantities in a structured way. Her interventions have been successful with clear progress being made in children's first skills in mental maths.
She argues that children need to acquire a mental image of quantities before they can work with numerals and that a clear distinction between the two is vital. Tallying provides a memorable, reliable and stable image and is a consummate representation of quantities because they can easily be lined up. Bundles of four sticks with one lying across give the perception of five a visual closure and makes five an easy package to scan for.
Grouping into fives is ideal because fives fit neatly into the decimal system. When comparing the tally marks for five and nine, children can instantly see the association, whereas faced with numerals five and nine they may not be able to.
Tally marks can help children learn about odds and evens at the same time as multiples of five. Tally marks up to 20 can help children understand the teens. Teens are difficult because children have to get used to hearing "six" before "teen", but writing the "one" before the six. Teaching tallying would provide the essential stepping stone from practical to theoretical problem solving.
Tally marks can also help children prepare for working with a paper abacus (see figure above). For children with perception difficulties, a paper abacus is more effective than using counters or cubes, because the elements are fixed in relation to each other and can't be lost. Children quickly realise why it is easier to count larger quantities in groups of five because they do not have to start again if they lose count. A paper abacus helps them partition quantities rather than just reading or memorising numbers in a sequence. As Mecky Turner says: "It helps them to see the trees and the wood at the same time. It connects practical thinking with verbal thinking."
A strip of translucent coloured plastic with a step cut out at the top will allow you to reveal any number as rows of 10, plus fives and ones. Move the overlay along each line as if reading the text. The paper abacus could easily be disguised as a bookmark.
There is little doubt that using structured images helps children to boost mental maths skills and that tallying and the paper abacus deserve serious attention throughout KS1. Action research such as Mecky Turner's study is a good example of a classroom-based and sharply focused small-scale study in a priority area directed towards greater understanding and improvement of practice.
Mecky Turner can be contacted at Email: firstname.lastname@example.orgCoursesUsing imagery to support mental mathematics (KS1) is a one-day course from BEAM to support maths development. The course costs pound;120 plus VAT. Tel: 020 7684 3334www.beam.co.uk