involved with reading and writing of two 5. The children with poor auditory digit numbers can make some aspects of discrimination and perception who find it Dyslexia and Mathematics maths confusing. The Stern 10-Box and difficult to discriminate and perceive the blocks help children to gain experience difference between the ‘ teen’ numbers Can Stern’s Structural with the commutativity principle by and the ‘ ty’ numbers, will find it easier seeing two sets of like blocks that can when the numbers are built in the Dual- be switched around and so discover that Board or located in the Number Track. Arithmetic Materials Help? the order of the addends can be changed 6. Stern can make concepts and procedures without changing the sum, thus grasping Since the system is based on two tangible sets more explicit for children with poor visual Cognitive learning systems and the interchangeable of number representations, the blocks and perception as part of their non- difficulties with maths: nature of addition patterns promote a clear image of number in verbal learning difficulties. The (and later with Children with dyslexia may have all or some of the concrete enabling pupils to discover for Dual Board makes the concept of multiplication). the following difficulties. themselves all of the attributes on a physical place value explicit for two digit 1. Oral language weaknesses level. When numerals are introduced they 3. Sequencing errors numbers. Children gain insight into correspond to the blocks and patterns by are reduced through the relationship between the role 2. Sequencing difficulties including left/right embodying the intrinsic qualities and values of working with different and the position of each numeral. orientation those numbers. arrangements The size of the two compartments 3. Memory limitations: short term, long term of equipment to guide the children when building Each piece of Stern apparatus has a unique and working memory strengthen learning. numbers and are easily placed function, as well as contributing collectively, They learn about size correctly. 10 ones equal 1 ten is 4. Auditory and visual processing vulnerabilities and shows the child familiar aspects of number relationships and seen clearly when filling up the in a different light. The strength of this system 5. Slow processing speed measuring with the ‘ones’ compartment with unit is the maintenance of subliminal stimulation number blocks in cubes. A 10-block can be laid on 6. Weak conceptual knowledge of number relationships in the form of images, the Counting Board. They ‘see’ and ‘feel’ top to show they are the same. 7. Weak non-verbal spatial abilities whilst keeping them in the child’s view on a that each length is one unit longer in the concrete level. 7. Children with slow processing speeds Many of the underlying difficulties of dyslexia sequence from 1 to 10, or one unit shorter who work at a slower pace than the oral could also be the core factors affecting progress It is necessary to look at some of the main in the reverse order. Children can ‘see’ presentation by a teacher may find it in maths and a significant proportion of underlying difficulties of dyslexia in order to where each block ‘lives’ in the sequence hard to follow. Stern materials enable dyslexic children have difficulty learning maths. consider if Stern materials can help. as well as the relationships they have with the child to grasp the verbal meaning Many of these children have difficulties with each other. 1. Most dyslexic children have some oral while experiencing the visual and tactile the surface aspects of numeracy rather than language weaknesses, especially when it 4. Auditory and visual memory limitations associations that the materials provide. an intrinsic lack of number sense which is now comes to learning new vocabulary. The that are characteristic of many dyslexic This leads to some children understanding often referred to as dyscalculia. This article language of maths can pose a problem. learning patterns are supported by Stern maths lessons more easily. intends to address these surface aspects rather The Stern programme is particularly materials. These limitations may be in than the profound difficulties in having a feel 8. Children may not have developed much thorough in the way it teaches maths short term, working and in long term for numbers that characterise the dyscalculic conceptual knowledge about numbers vocabulary in a multi-sensory way to and/or visual memory and respond well child. It can however be mentioned that Stern due to their dyslexic learning difficulties, facilitate the child hearing and using the to the multi-sensory approach of the materials can also help dyscalculic children but or may have other problems that could be maths words in a meaningful context. Stern programme. It also helps the child’s they would need to spend longer on certain investigated by an educational psychologist memory to be able to stay focused on aspects of the Stern programme to equip them 2. Sequencing and left–right orientation using a test such as the WISC IV. They could the exact numbers whilst performing with a ‘toolkit’ for numeracy before moving on weaknesses that interfere with the learning also be screened for Dyscalculia on the calculations with those numbers. The child to other areas of the programme involving the Butterworth screener. may be able to build up a more explicit beginnings of basic calculations. mental image by using the materials 9. With explicit multi-sensory teaching, these What is Stern’s regularly so that they can remember them children may also be able to build up their Structural Arithmetic? even when they are not present. conceptual understanding in due course. If this conceptual Stern’s multi-sensory maths system was understanding designed to develop a child’s emergent fails to occur number sense by building-up number easily, then knowledge and number facts in a logical and it may be structured manner thus enabling children to advisable think logically and reason mathematically. to consider Stern facilitates the understanding and a deeper application of the four number operations.

26 27 involved with reading and writing of two 5. The children with poor auditory digit numbers can make some aspects of discrimination and perception who find it Dyslexia and Mathematics maths confusing. The Stern 10-Box and difficult to discriminate and perceive the blocks help children to gain experience difference between the ‘ teen’ numbers Can Stern’s Structural with the commutativity principle by and the ‘ ty’ numbers, will find it easier seeing two sets of like blocks that can when the numbers are built in the Dual- be switched around and so discover that Board or located in the Number Track. Arithmetic Materials Help? the order of the addends can be changed 6. Stern can make concepts and procedures without changing the sum, thus grasping Since the system is based on two tangible sets more explicit for children with poor visual Cognitive learning systems and the interchangeable of number representations, the blocks and perception as part of their non- difficulties with maths: nature of addition patterns promote a clear image of number in verbal learning difficulties. The (and later with Children with dyslexia may have all or some of the concrete enabling pupils to discover for Dual Board makes the concept of multiplication). the following difficulties. themselves all of the attributes on a physical place value explicit for two digit 1. Oral language weaknesses level. When numerals are introduced they 3. Sequencing errors numbers. Children gain insight into correspond to the blocks and patterns by are reduced through the relationship between the role 2. Sequencing difficulties including left/right embodying the intrinsic qualities and values of working with different and the position of each numeral. orientation those numbers. arrangements The size of the two compartments 3. Memory limitations: short term, long term of equipment to guide the children when building Each piece of Stern apparatus has a unique and working memory strengthen learning. numbers and are easily placed function, as well as contributing collectively, They learn about size correctly. 10 ones equal 1 ten is 4. Auditory and visual processing vulnerabilities and shows the child familiar aspects of number relationships and seen clearly when filling up the in a different light. The strength of this system 5. Slow processing speed measuring with the ‘ones’ compartment with unit is the maintenance of subliminal stimulation number blocks in cubes. A 10-block can be laid on 6. Weak conceptual knowledge of number relationships in the form of images, the Counting Board. They ‘see’ and ‘feel’ top to show they are the same. 7. Weak non-verbal spatial abilities whilst keeping them in the child’s view on a that each length is one unit longer in the concrete level. 7. Children with slow processing speeds Many of the underlying difficulties of dyslexia sequence from 1 to 10, or one unit shorter who work at a slower pace than the oral could also be the core factors affecting progress It is necessary to look at some of the main in the reverse order. Children can ‘see’ presentation by a teacher may find it in maths and a significant proportion of underlying difficulties of dyslexia in order to where each block ‘lives’ in the sequence hard to follow. Stern materials enable dyslexic children have difficulty learning maths. consider if Stern materials can help. as well as the relationships they have with the child to grasp the verbal meaning Many of these children have difficulties with each other. 1. Most dyslexic children have some oral while experiencing the visual and tactile the surface aspects of numeracy rather than language weaknesses, especially when it 4. Auditory and visual memory limitations associations that the materials provide. an intrinsic lack of number sense which is now comes to learning new vocabulary. The that are characteristic of many dyslexic This leads to some children understanding often referred to as dyscalculia. This article language of maths can pose a problem. learning patterns are supported by Stern maths lessons more easily. intends to address these surface aspects rather The Stern programme is particularly materials. These limitations may be in than the profound difficulties in having a feel 8. Children may not have developed much thorough in the way it teaches maths short term, working and in long term for numbers that characterise the dyscalculic conceptual knowledge about numbers vocabulary in a multi-sensory way to and/or visual memory and respond well child. It can however be mentioned that Stern due to their dyslexic learning difficulties, facilitate the child hearing and using the to the multi-sensory approach of the materials can also help dyscalculic children but or may have other problems that could be maths words in a meaningful context. Stern programme. It also helps the child’s they would need to spend longer on certain investigated by an educational psychologist memory to be able to stay focused on aspects of the Stern programme to equip them 2. Sequencing and left–right orientation using a test such as the WISC IV. They could the exact numbers whilst performing with a ‘toolkit’ for numeracy before moving on weaknesses that interfere with the learning also be screened for Dyscalculia on the calculations with those numbers. The child to other areas of the programme involving the Butterworth screener. may be able to build up a more explicit beginnings of basic calculations. mental image by using the materials 9. With explicit multi-sensory teaching, these What is Stern’s regularly so that they can remember them children may also be able to build up their Structural Arithmetic? even when they are not present. conceptual understanding in due course. If this conceptual Stern’s multi-sensory maths system was understanding designed to develop a child’s emergent fails to occur number sense by building-up number easily, then knowledge and number facts in a logical and it may be structured manner thus enabling children to advisable think logically and reason mathematically. to consider Stern facilitates the understanding and a deeper application of the four number operations.

26 27 difficulty which could then be described as in the child’s understanding will be seen When adding 2 or subtracting 2, using the Economy of learning – dyscalculia. The Stern materials could still immediately and acted upon through patterns, it is visually very clear that this results in the result of transfer help the dyscalculic child but the materials further exploration and practice. the next even or odd number, depending on the might be used more selectively in an even By making the structure of the number system Dr Catherine Stern, mathematician, child starting point. For example, by direct experience, more structured and controlled way which visual, Stern materials make it possible for psychologist and Montessorian, (Children the child sees that if 2 cubes are added to 4 then is dealt with in a further article. children to transfer a newly learned fact to other Discover Arithmetic) introduced us to a specific the next even number is the result. areas. For instance, if they know that 3+5=8, 10. Stern develops concepts by measuring, pattern structure to encourage cognitive Number facts they can discover that this fact holds true in not by counting. There is opportunity development such as left/right orientation. any decade by measuring in the Number Track: There is greater impact and opportunity for for visual and auditory input through 13+5=18, 23+5=28, or 63+5=68. the teacher’s explanation; modelling; the successful learning of number facts to 10, child’s own commentary to peers and the (and 20), developing strategies that lead to incorporation of role play. The activities internalisation of facts and speedier recall. provide progressive repetition through Through structured, small-step activities and kinaesthetic input. All these factors games, pupils work with combinations of blocks strengthen the child’s own developing in number boxes to acquire the basic addition mental strategies providing multi-sensory and subtraction facts with numbers up to and experience from the formation of imagery, including 10. Beginning with the 10-Box, (see building concepts and enhancing storage fig 1) children fit pairs of blocks into this self- and recall. checking device like a puzzle. The materials By working with cubes and 10-blocks in the 11. Weak spatial knowledge could be encourage children to think and reason for Dual Board, children can see that what is true strengthened through regular use of Stern themselves, if a block is too big or too small for the ‘ones’ as in 3 ones and 5 ones equal 8 blocks and patterns of cubes. Children they can ‘see’ and ‘feel’ in which way it doesn’t ones or 3+5=8, is also true for the ‘tens’ as in 3 learn to recognise patterns of cubes at fit and try others until they are successful. tens and 5 tens equal 8 tens or 30+50=80. The a glance and then check their patterns Pupils are able to name the combinations of result is an immense economy in the number by placing the cubes into the empty the blocks that go together to fill the 10-Box facts that have to be learned. Therefore, it can insets in the boards to verify their visual be seen that Stern is a very appropriate resource Whilst the blocks facilitate much of the and express them orally as equations - Telling perceptions against their motor and tactile to help dyslexic children over-come their learning, the Pattern Boards and cubes provide the story of 10. They will also understand the senses. The process of recognising and surface difficulties with maths and would be an more opportunities to develop concepts based concept and language of the missing addend. constructing number patterns also calls for invaluable addition to any classroom. on the characteristics of odd and even numbers. This becomes a useful strategy when working spatial thinking, and will be reinforcing with subtraction facts not readily internalised. Jane Emerson and Vikki Horner already developing abilities such as left/ It is easy to teach children the quality of You will find that the language of mathematics right orientation, sequencing; hand-eye evenness and oddness with this specific pattern is used naturally by children since it fits the A more comprehensive version of this article can coordination, one-to-one correspondence, structure. The even patterns all have ‘partners’ facts they have discovered and links their be found on www.mathsextra.com as well as estimation of quantities, and the and the odd patterns have an ‘odd man’ or a concepts of too many and too few. actions with the Structural Arithmetic materials. ‘driver’. References: 12. Stern impacts on learning by aiding the Making sense of numbers The Pattern Boards Children Discover Arithmetic by Dr Catherine development of spatial thinking and Visualisation skills are crucial in acquiring the Stern: Harpers & Row reasoning. Whether children are measuring Once number names have been assigned and fundamental building blocks of maths. Pupils Dyslexia Dyspraxia and Mathematics by Dorian blocks or working with patterns of cubes, internalised this frees up space and time within who mostly maintain a ones-based concept Yeo: Wiley Blackwell they are applying spatial thinking, to the limits of working memory to better focus do not see numbers as whole ideas. Nor are on the learning new concepts. Adding 1 to a The Butterworth Dyscalculia Screener published help them reason. Each experiment they able to see that numbers contain many leaves an unforgettable mental picture number in the 10-Box and again with the cube by nferNelson patterns such as the doubles, near doubles or to turn around in their minds to explore patterns shows the different ways Stern helps Dyscalculia Guidance by Brian Butterworth and sub-groups. It is also hard for them to see the new relationships. Unfamiliar maths children to access the same concept. Children Dorian Yeo: David Fulton Publishers structures within numbers. language is clarified by the practitioner are rather amused to see that adding an extra For information and advice regarding Dyslexia, through concrete demonstrations and cube to a number pattern causes the next Stern provides opportunities for children to Dyscalculia, Dyspraxia contact Jane at Emerson further reinforced and linked to the child’s higher number pattern to appear! Equally with see patterns within numbers. Doubles are seen House, London T:0208 741 4554 actions with the apparatus. By following subtraction, that removing one cube gives the clearly with the even pattern structure. Near W: www.emersonhouse.co.uk spoken directions, children are able to next lower number. Also, with the addition of doubles ‘neighbours’ 3+2 will also be seen For more information and advice on Stern develop receptive language and this one cube, children see an odd number become and encourage the strategy double 2, add 1. programmes contact Vikki at Maths Extra is a means of assessing their receptive an even number and an even number become Addition facts for all numbers can be taught T: 01747 861 503 language acquisition. Stern is a system of and odd number. It is easy to show that if you using two different sets of coloured cubes E: [email protected] errorless learning where misconceptions add nothing to a pattern it stays the same. leaving the overall number in view. W: www.mathsextra.com

28 29 difficulty which could then be described as in the child’s understanding will be seen When adding 2 or subtracting 2, using the Economy of learning – dyscalculia. The Stern materials could still immediately and acted upon through patterns, it is visually very clear that this results in the result of transfer help the dyscalculic child but the materials further exploration and practice. the next even or odd number, depending on the might be used more selectively in an even By making the structure of the number system Dr Catherine Stern, mathematician, child starting point. For example, by direct experience, more structured and controlled way which visual, Stern materials make it possible for psychologist and Montessorian, (Children the child sees that if 2 cubes are added to 4 then is dealt with in a further article. children to transfer a newly learned fact to other Discover Arithmetic) introduced us to a specific the next even number is the result. areas. For instance, if they know that 3+5=8, 10. Stern develops concepts by measuring, pattern structure to encourage cognitive Number facts they can discover that this fact holds true in not by counting. There is opportunity development such as left/right orientation. any decade by measuring in the Number Track: There is greater impact and opportunity for for visual and auditory input through 13+5=18, 23+5=28, or 63+5=68. the teacher’s explanation; modelling; the successful learning of number facts to 10, child’s own commentary to peers and the (and 20), developing strategies that lead to incorporation of role play. The activities internalisation of facts and speedier recall. provide progressive repetition through Through structured, small-step activities and kinaesthetic input. All these factors games, pupils work with combinations of blocks strengthen the child’s own developing in number boxes to acquire the basic addition mental strategies providing multi-sensory and subtraction facts with numbers up to and experience from the formation of imagery, including 10. Beginning with the 10-Box, (see building concepts and enhancing storage fig 1) children fit pairs of blocks into this self- and recall. checking device like a puzzle. The materials By working with cubes and 10-blocks in the 11. Weak spatial knowledge could be encourage children to think and reason for Dual Board, children can see that what is true strengthened through regular use of Stern themselves, if a block is too big or too small for the ‘ones’ as in 3 ones and 5 ones equal 8 blocks and patterns of cubes. Children they can ‘see’ and ‘feel’ in which way it doesn’t ones or 3+5=8, is also true for the ‘tens’ as in 3 learn to recognise patterns of cubes at fit and try others until they are successful. tens and 5 tens equal 8 tens or 30+50=80. The a glance and then check their patterns Pupils are able to name the combinations of result is an immense economy in the number by placing the cubes into the empty the blocks that go together to fill the 10-Box facts that have to be learned. Therefore, it can insets in the boards to verify their visual be seen that Stern is a very appropriate resource Whilst the blocks facilitate much of the and express them orally as equations - Telling perceptions against their motor and tactile to help dyslexic children over-come their learning, the Pattern Boards and cubes provide the story of 10. They will also understand the senses. The process of recognising and surface difficulties with maths and would be an more opportunities to develop concepts based concept and language of the missing addend. constructing number patterns also calls for invaluable addition to any classroom. on the characteristics of odd and even numbers. This becomes a useful strategy when working spatial thinking, and will be reinforcing with subtraction facts not readily internalised. Jane Emerson and Vikki Horner already developing abilities such as left/ It is easy to teach children the quality of You will find that the language of mathematics right orientation, sequencing; hand-eye evenness and oddness with this specific pattern is used naturally by children since it fits the A more comprehensive version of this article can coordination, one-to-one correspondence, structure. The even patterns all have ‘partners’ facts they have discovered and links their be found on www.mathsextra.com as well as estimation of quantities, and the and the odd patterns have an ‘odd man’ or a concepts of too many and too few. actions with the Structural Arithmetic materials. ‘driver’. References: 12. Stern impacts on learning by aiding the Making sense of numbers The Pattern Boards Children Discover Arithmetic by Dr Catherine development of spatial thinking and Visualisation skills are crucial in acquiring the Stern: Harpers & Row reasoning. Whether children are measuring Once number names have been assigned and fundamental building blocks of maths. Pupils Dyslexia Dyspraxia and Mathematics by Dorian blocks or working with patterns of cubes, internalised this frees up space and time within who mostly maintain a ones-based concept Yeo: Wiley Blackwell they are applying spatial thinking, to the limits of working memory to better focus do not see numbers as whole ideas. Nor are on the learning new concepts. Adding 1 to a The Butterworth Dyscalculia Screener published help them reason. Each experiment they able to see that numbers contain many leaves an unforgettable mental picture number in the 10-Box and again with the cube by nferNelson patterns such as the doubles, near doubles or to turn around in their minds to explore patterns shows the different ways Stern helps Dyscalculia Guidance by Brian Butterworth and sub-groups. It is also hard for them to see the new relationships. Unfamiliar maths children to access the same concept. Children Dorian Yeo: David Fulton Publishers structures within numbers. language is clarified by the practitioner are rather amused to see that adding an extra For information and advice regarding Dyslexia, through concrete demonstrations and cube to a number pattern causes the next Stern provides opportunities for children to Dyscalculia, Dyspraxia contact Jane at Emerson further reinforced and linked to the child’s higher number pattern to appear! Equally with see patterns within numbers. Doubles are seen House, London T:0208 741 4554 actions with the apparatus. By following subtraction, that removing one cube gives the clearly with the even pattern structure. Near W: www.emersonhouse.co.uk spoken directions, children are able to next lower number. Also, with the addition of doubles ‘neighbours’ 3+2 will also be seen For more information and advice on Stern develop receptive language and this one cube, children see an odd number become and encourage the strategy double 2, add 1. programmes contact Vikki at Maths Extra is a means of assessing their receptive an even number and an even number become Addition facts for all numbers can be taught T: 01747 861 503 language acquisition. Stern is a system of and odd number. It is easy to show that if you using two different sets of coloured cubes E: [email protected] errorless learning where misconceptions add nothing to a pattern it stays the same. leaving the overall number in view. W: www.mathsextra.com

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