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KET introduces mathematics to township and rural preschools

The NUMICON mathematics programme was successfully customised and piloted within 4 preschools during 2013. In January 2014 KET introduced the Numicon Mathematics programme to 31 affiliated preschools in Knysna and Sedgefield. Numicon was developed to teach children new ways of learning mathematics and is based on 16 years of research done in the UK. The programme uses methodologies that are suitable for young children and provides the sensory, hands-on experiences that enable children to build concepts and gain knowledge through their senses. To date the Trust has trained 77 practitioners and 11 volunteers. The feedback from the preschools has been extremely positive. The teachers are finding the programme easy to administer and the children are thoroughly enjoying working with it. When asked to pack away one reluctant group begged for more time “nog net een keer juffrou-asseblief!” This is extremely gratifying and makes the effort that has been put into this amazing programme worthwhile. Foreword  In 2010, The Western Cape Education Department and the Western Cape Provincial Treasury requested the University of Stellenbosch to conduct a large scale study of teaching and learning in the Foundation Phase. In order to obtain a broad picture of what was taking place in different classrooms, a study involving 135 full days of observations and interviews with teachers and principals was undertaken. It was hoped that the results of these findings would identify the strengths and weaknesses regarding the teaching and learning of language and mathematics, improve the quality in these areas of the curriculum and provide appropriate support for those teaching learners in the Foundation Phase. While the overall organisation, procedures, functions and resources were generally adequate, the study found that not enough was done to ensure that ‘substantive and sufficient learning’ was taking place in the Foundation Phase. Furthermore, the study found that there was not enough ‘cognitive demand’ being made on the children. Learners often did not grasp the fundamentals in language and mathematics because not enough reading, writing and mathematical calculation was taking place. This had led to poor learner performance and did not provide adequate foundations on which to build positive outcomes in these areas. Teachers expressed feelings of inadequacy in teaching the subject and reported that the curriculum and assessment standards were confusing. The Knysna Education Trust was particularly interested to see that the study was critical of the amount of time learners spent ‘actually doing’ mathematics. Investing in a suitable mathematics programme  The Trust was also aware of the results of the Annual National Assessments written by six million learners throughout South Africa in 2011. These showed that a high percentage of learners (some in the Foundation Phase) had not reached the expected basic skill levels in literacy and numeracy particularly in ‘rural’ and disadvantaged schools. A great deal at this time was being written about the funding, resources and teacher training being ploughed into the senior high school phase. The Trust’s Education Mentors (with over sixty years of Foundation Phase teaching and remedial training behind them) felt that if children at the grass roots level were better prepared to meet these challenges results in these areas would improve substantially, even in the senior high school phase. After researching various possibilities, the Trust took a decision to be proactive in terms of literacy and numeracy at our affiliated preschools using methodologies that are suitable for young children. While the Souns Literacy programme has been running since the end of 2008, the Trust felt that suitable mathematics programmes needed to be investigated that could run parallel with what was being done in literacy. Why mathematics is important  As society has grown more complex, the ability to use basic mathematics in everyday situations has become even more crucial. Because of its abstract nature, many young children find this subject very difficult. Research by Piaget, Vygotsky and Montessori have shown that because children think differently to adults and because they are not developmentally ready to work at an abstract level, they struggle tremendously with mathematics. Even older children, when working with these abstract concepts become discouraged and lose confidence in their abilities. Their lack of understanding often causes them to resort to just learning the rules. As the concepts become more taxing, they just give up. With this in mind, and in our search for an ideal programme suited to the disadvantage preschoolers in our community, it was obvious that certain important criteria needed to be met. The teaching programme we hoped to implement would need to:
  • be appealing in order to pique the interest of the children
  • be ‘hands on’ and multi-sensory
  • help develop a thorough understanding of number
  • lead children to working independently and with enthusiasm
  • encourage them to calculate and solve problems with confidence
  • be easy for teachers to implement
  • provide guidelines for assessment
  • support the new Curriculum Assessment Policy Statement (CAPS) developed by the Department of Basic Education
  • and finally to provide an element of FUN for the children while they learnt basic mathematical concepts.
The Department of Basic Education, in its Numeracy Handbook for Foundation Phase Teachers (2009) stated: Critical to being able to ‘do mathematics’ is the development of a strong sense of number. Children who leave the Foundation Phase with a poorly developed sense of number are almost certainly unable to every make sense of mathematics.  A further incentive was research by Jeremy Kilpatrick, Jane Swafford, Bradford Findell (2001) in Adding It Up: Helping Children Learn Mathematics, (Washington, DC: The National Academies Press). The researchers maintain that in order to ensure that children become proficient in mathematics they need:
  • to understand what they are doing
  • to be able to apply what they have learnt
  • to be able to reason about what they have done
  • to be able to engage with a problem in order to solve it
  • be able to calculate or compute with confidence
Numicon, a mathematics programme developed from a classroom-based research project carried out between 1996 and 1998 by three UK authors seemed to fit the Trust’s bill. The project set out to find why so many children failed in arithmetic where they were successful in all other areas of the curriculum. They also wanted to find out whether visual imagery could support mathematical understanding. The following comment seemed to sum it up. ‘Numicon is a highly visual resource which can be used to explain abstract concepts in a clear way.’ – Jayne Evans The aim of the programme Numicon was developed to teach children new ways to learn about number and calculation. According to Dr Tony Wing, one of the developers of the programme: Numicon aims to help children understand numbers through their natural ability and strengths when working with pattern. The pattern plates provided represent different numbers in their number patterns. The multisensory approach makes learning numbers ‘real’. Children can see the numbers, touch, feel and move them. In doing so, they gain confidence in their abilities and are more inclined to persist in their efforts when problem solving. By getting to know numbers, it is felt that there will be a better understanding of them. While we were certain that the right choice was being made, funding might have proved an obstacle. A Rotary matching grant received from New Mexico in the USA, however, allowed the Trust to invest in this revolutionary programme. Sixty First Foundation kits were purchased allowing each preschool to have two sets. Having been successfully piloted in four preschools since 2012, the Trust knew it was on the right track and launched Numicon in twenty eight disadvantaged preschools this year. The programme is integrated into the daily maths activities at the preschools and is not ‘taught’ in isolation. Teaching and learning takes place in the two main home languages in our area, Xhosa and Afrikaans. Teaching manuals have been translated into both Afrikaans and Xhosa in a simplified form for ease of use. Matching Numicon with CAPS (Curriculum Assessment Policy Statement)  The Trust was aware that the children currently at local preschools and crèches in the Knysna community would find themselves, sooner or later, at Government Primary Schools where they will begin their formal education. We felt sure that those that had firm foundations in literacy and mathematics would be at a distinct advantage, so it was important that their experiences in these subjects matched those that set out in the CAPS curriculum. In its introduction to the CAPS curriculum it is stressed that: The acquisition of emergent mathematics and related mathematical concepts should, like all good teaching, adhere to the following learning principles where children move through three stages of learning. These are:
  • the kinaesthetic stage (experiencing concepts with the body and senses)
  • the concrete stage (3-D, using a variety of different objects such as blocks, bottle tops, pebbles and other objects in the environment)
  • semi-concrete stage: (2-D representations using drawings, pictures, matching cards etc.)
The Numicon programme provides opportunities for all the above. For example:
  • Kinaesthetic stage: A teacher holds up a Numicon Shape. The children jump, hop or clap to the number shown, they identify a Numicon Shape using the Feely Bag, or they match the correct number of beanbags to Numicon Shapes in hoola-hoops in outside games and team races.
  • Three-dimensional stage: The children experiment with the shapes using play dough. This allows for sensory experiences and can be used for one-to-one matching. Estimation is also covered. The children can be challenged to guess how many pegs or other small items fit into a cup or shoe. Patterning activities using pegs on the Baseboard or while threading ‘necklaces’ with the hollow Numicon pegs reinforce logical thinking and planning.
  • Semi-concrete stage: matching pictures and numerals to Numicon Shapes or playing games such as dominoes where numerals are also included.
The CAPS curriculum sets down specific skills that learners need to know. These are:
  • The development of the correct use of the language of mathematics
    The Numicon Teacher’s Manual suggests that every opportunity is used to introduce and reinforce mathematical language such as: number names, how many, more, less, enough, not enough, match, find, next, before, after, too many, too few, same size, same shape, on top, next to, underneath, big, bigger, biggest, small, smaller, smallest, first, next, after, last, before, in front of and in between etc.
  • The development of number vocabulary, number concept and calculation 
  • Numicon allows children to recognise the number shapes and they soon learn how many each shape represents. They learn the number names, and count kinaesthetically. They learn about one-to-one correspondence, sequencing, matching pegs to a number line to get the cardinal number, putting numbers in order (forwards and backwards), the number patterns, one more, one less, odd and even numbers and later, moving beyond counting to calculating.
  • Listening to instructions, communicating, thinking, logical reasoning, applying the mathematical knowledge gained 
  • Numicon provides opportunities for sorting colours and shapes, comparing and ordering, listening to instructions such as “Can you find me a shape that is bigger/smaller, one bigger, one smaller than this one….?”. Children are encouraged in their free play to use the Numicon Shapes and pegs in fantasy corners. Another activity is in identifying which Numicon Shape or numeral has been swopped in an array of shapes that have been placed in order.
  • Learn to investigate, analyse, represent and interpret information 
  • We suggest teaching the concept of ‘odd’ and ‘even’ numbers using socks. Questions are extended once the concepts have been understood. “Which Numicon Shapes have odd/even numbers?” “Which shape can I add to the five shape to make the another or next even number?” The children use the concept of subtraction by playing with play dough balls placed in Numicon Shapes. By placing two Numicon Shapes together they learn the commutative law in addition and subtraction. Similarly, if the learners know that 3+4=7 it is easy to see that 7-4=3 and 7-3=4 which again draws on pattern.
The Curriculum Assessment Policy Statement and the five content areas  Mathematics in the Foundation Phase covers five content areas. Each of these contributes to the acquisition of specific skills. They are: • Numbers, operations and relationships • Patterns, functions and algebra 5 • Space and shape • Measurement • Data handling
  1. Numbers, operations and relationships relates to the development of number sense 
  2. The Numicon programme provides opportunities to understand the meaning of different kinds of numbers; the relationships between different kinds of numbers; the relative size of different numbers; representation of numbers in various ways and the effect of operating with numbers in interesting, threedimensional games using dice and domino games. They are encouraged to match the Numicon Shapes to the large number line that is provided in the kit. The children work as far as ten in the preschool phase. Once children understand the patterns of number in the Numicon Shapes and have had many opportunities to work with the apparatus during play, the next level (the symbolic level) is introduced with numerals. Children learn to match these to the Numicon Shapes. While shape and number swop games provide interest and consolidation they also provide opportunities for assessment.
  3. Patterns, functions and algebra 
  4. Pattern forms a huge part of understanding number. Whether counting in twos, fives and tens or counting on from 274. Children need to understand and build patterns with three-dimensional apparatus, shapes or two-dimensional pictures. Copying or making their own patterns develops the children’s logic and this lays the basis for later algebraic thinking skills. Patterns should first be introduced kinaesthetically ‘clap, clap, jump; clap, clap, jump. Children can then be encouraged to copy patterns using pegs on the Baseboard, or by placing Numicon Shapes in a pattern on a table. During free choice activities, children can be encouraged to construct patterns using potato prints, items from nature, collages or drawing their own patterns in creative activities.
  5. Space and shape 
  6. An interesting inclusion in the Numicon Firm Foundations Kit is the Numicon spinners. The Trust saw the potential of these and developed further spinner overlays, which are used in circle games using 3-D coloured shapes (such as Logiblocks), which children pick up according to the shape and colour shown on the spinners. These also work well in small groups in posting games, Bingo, either on a 3-D using shapes in the Feely Bag or a 2-D level as shown. Symmetry can also be introduced by experimenting with Numicon Shapes on the Numicon Baseboard.
  7. Measurement 
  8. Although Numicon has been developed primarily to reinforce number and pattern, it can also be extended to teaching and learning the concept of measurement. A balance scale is useful for finding the equivalent mass of two numbers. The balancing scale is not included in the Firm Foundations kit but can be purchased separately. In this activity children need to find out for themselves that a four shape and a two shape on one side will balance with a six shape on the other. Multiplication and division also come into play informally – “how many three shapes will make the nine shape balance?” By covering the Baseboard, the children are learning about area. This activity can be extended to cover bigger or smaller areas such as a tray. Length is one of the first attributes discovered by children. Numicon also provides opportunities for measuring in arbitrary units. The height of a child, the length of a shoe or box can be measured in arbitrary units using Numicon Shapes.
  9. Data handling 
  10. Numicon lends itself to data handling. Venn diagrams can be used to organize and sort information into categories. Graphing is a wonderful tool for promoting basic math concepts, vocabulary and mathematical thinking. Using a small container full of pegs, the children sort the colours and then represent the number of each using simple graphs.
Training of facilitators  The ‘hands-on’ training of facilitators takes place in two-hour sessions during the week at the KET offices. The Trust prefers to work with small language groups where those present experiment and play with the Numicon apparatus. Planning and group work is discussed, and comprehensive notes handed out. Demonstrations also show the attendees how to prepare their own mathematics games and activities. Our two Education Assistants are on hand to translate where necessary. We suggest that an inviting area to encourage mathematics, is set aside in every classroom but space is often limited in small preschool establishments, so this often proves a challenge. Working in pairs  The Trust suggests that the children have many opportunities to work in pairs or small groups to encourage language, co-operation, the exchange of ideas and problem solving. Children also learn concepts such as ‘counting on’ using simple path games and teacher made games such as snakes and ladders which provide interest and challenge. Our experience has shown that these activities must be preceded by kinesthetic experiences in games such as hopscotch using the Numicon Shapes outdoors. Assessment  The Trust has suggested that teacher initiated learning and assessment takes place in group work sessions. It encourages the preschool facilitators to prepare five mathematical activities weekly, which are placed in prepared beer boxes. These might include play dough and play dough mats, path games, games using the overlays on the spinners, shapes collages or sorting out which shapes in the prepared box are able to roll. Pictures can be created with Numicon rubbings or on the Numicon Baseboard using elastics. These activities help to develop fine motor skills. Provided that the children understand each activity they will be able to work independently and keep themselves occupied. At the same time a small group works with the facilitator who introduces new concepts or undertakes informal assessment. The beer boxes are then rotated every day of the week so that each group has access to a different activity. The Numicon manual provided in each Firm Foundations kit is extremely comprehensive but too advanced for many of our preschool facilitators to use, especially as English is often their third language. The Trust has a developed a simplified year plan and assessment tools to meet these needs. A tracking sheet, similar to the one used by volunteers for the Souns literacy programme has also been designed. These enthusiastic ladies (and one gentleman) have been trained in the use of the Numicon programme and their report backs to KET identify problems and difficulties being experienced. The Trust is gratified to note that the introduction of the Numicon programme has been extremely well received by teachers and children alike. The preschoolers love working with the apparatus and are seldom at a loss for something to do if the kit is always available. We are confident that the early introduction of Numicon at our affiliated preschools will provide the firm foundations and concepts necessary in order to develop a love of, and understanding of, mathematics. The road to success is still under construction although we expect that this initiative will make a huge contribution in uplifting teaching and learning in this subject. We feel confident that the Numicon programme will provide the stimulus and interest to allow children to persevere and enjoy the challenges that come with number and problem solving. Note: After extensive additional research and feedback from teachers and through monitoring the children’s progress, this programme has been updated and extended, known as the Numba mathematics programme.