Oral language weaknesses – will impact on maths learning. Remembering or interpreting directions. Expressive language may result in difficulties explaining how well a concept is understood. Difficulty with maths vocabulary on the surface may seem like a lack of maths understanding or ability when in fact is stems from a problem with language.
The best way to teach the meaning of spoken language is to provide opportunities to see and feel what the words describe.
The Counting Board
 Early vocabulary taught with the Counting Board
The Counting Board
“Which is the smallest?” “Which comes next?” “Which comes after this one?” “…and the biggest?” “Which is the next biggest?” Each request is followed by a pointing prompt, so that the meaning is grasped. “Which number comes between 4 and 6?” “Show me 4, good! Cover it with your hand. Show me 6, good! Cover it with your other hand.” The 5 remains in view. This action, together with the visual image, describes the meaning of between and is then understood. Working in this way with other numbers provides the repetition and the practice required, encouraging reasoning ability, leading to greater understanding.
At the same time we can incorporate memory stimulation. By placing blocks on a table nearby, a child is instructed to go to the table and bring back 5 and the block one bigger than 5. The words can be verified immediately. By placing the 6-block after the 5-block, we can see and feel that it is one unit bigger. Language comes alive with meaning from the very beginning. Such insights are not easily gained when children use the piecemeal approach of counting or depend on printed number symbols that do not show the meaning of “one bigger than,”
Language confusion with ‘TEEN’ and ‘TY’ numbers is another example of confusion children experience. We have multiple ways of learning about teen numbers which are simple and effective.
Physically build component parts of teen numbers in the 20-Tray
More practice with teen numbers, introducing place value; see the structure and position in the Dual Board
More practice with teen numbers, measuring size of a number by stretching it out in the Number Track.
 ‘TY’ numbers – simply practice placing 10-blocks into the Dual Board as well as the Number Track. First we make the 2-digit ten numbers (ty), 10, 20, 30, 40, and so on, next try adding and subtracting whole tens; 3 tens and 2 tens equal 5 tens: 30+20=50. 50–20=30
 Reversing numbers can be problematic – Using the full Number Track, first ask the pupil to make 18 (see track above) then reverse the number (81) ask the pupil to make this. He puts 8 lots of 10-blocks into the track followed by 1 unit. Next, place the blocks for 18 along the top of the track for comparison. The pupil will have an unforgettable image of the size difference between the two numbers. This will provide both tactile and visual information about the size of 81, as well as the position and value of each digit.
Differences between two numbers are overcome in the same way from support with the blocks and maths devices.
The Counting Board
Sequencing difficulties,  Left/right orientation - sequencing errors can be overcome through working with different arrangements of equipment. From the onset, a child’s sequencing ability and left/right directionality is being developed in the Counting Board whilst working on ‘size’ or ‘length’ and ‘position’ of numbers in the series. The sequencing image here is that each block gets longer. In contrast, the sequencing in the 10-Box shows the vertical stair.
 The 10-Box - ordering numbers to 10 is being reinforced. 
From here it is easy to locate the partner for each block 1 to 10 to begin work with the combinations to 10.
 
Sequencing number patterns and Left/right directionality – experienced with the Pattern Boards and cubes. This specific number pattern, first advocated by Dr Catherine Stern, draws on powerful visual imagery to show quantity/amount of a number, based on the characteristics of odd and even numbers.
This gives an indication of the broad based learning through hands-on manipulation, practice and reinforcement using a range of specific equipment in which to develop and strengthen processing systems and sound understanding.
The 10-Box
The 10-Box
Memory limitation, short term, long term and working memory
Having a strong memory is crucial for mathematics. Difficulties with memory – working, short or long-term storage impedes maths learning. Limitations with memory are characteristic of many dyslexic pupils learning patterns. To pass information to the long-term memory, it has to be meaningful. It often needs frequent repetition. Links between old and new information also facilitate the process. The ability to visualise a maths question helps support the working memory process to a very significant degree. Pupils have to acquire long-term memory of, or have efficient access to, maths facts and also to remember important concepts and procedures. Despite limitations in working memory, recall from long-term memory can release more time and space for ongoing cognitive operations, therefore it is important to begin work with the 10-Box (and smaller boxes for facts less than 10) so that the number facts can be thoroughly learnt and internalised.
An example is with a subtraction calculation. A pupil begins a procedure which involves a subtraction fact, because the fact invariably is not known, the child has to stop to figure out the fact, usually falling back on a counting procedure. This takes up more space in working memory resulting in the loss of earlier information being held. Consequently the pupil has to start again, which can be demoralising.
 With Stern equipment, children have positive experiences with subtraction and all the support they need to acquire real understanding. Note, earlier in the programme children will have worked with all ten patterns and internalised the pattern structures. Thus now they can draw on this STORED imagery. With this example 10-3=7, the overall pattern is seen (10) and is the number we are subtracting from, the empty cube inserts (3) represent the part that has been subtracted, the remaining cube pattern (7) represents the answer. After completing the hands-on task, the pupil has all the parts of the procedure still in place to enable recap or recording.
No counting is involved; pupils see the whole number at a glance.
Visual and auditory processing
Visual and auditory memory limitations are characteristic of many dyslexic learning patterns and are supported by Stern’s materials. Pupils respond well to the strong visual imagery and Stern’s multi-sensory approach to learning. The example above shows how pupils are able to stay focused on the exact numbers whilst performing calculations with those numbers. Regular use enables more storage of explicit images which they remember even when the apparatus is not present.
Visual aspect - Stern’s apparatus strengthens visual memory, by providing a clear image of numbers and concepts.
Auditory aspect – following directions provides practitioners with a means of seeing a child’s developing receptive language and auditory memory.
Kinaesthetic aspect – handling the materials is an important part of the learning because information is absorbed through touch, active participation and engenders motivation in the learning process.
Slow processing speed
Children with slow processing speeds working at a slower pace may find it hard to follow or keep up with the oral presentation by a teacher. The Stern materials enable the child to grasp the verbal meaning whilst experiencing the visual and tactile associations that the materials provide. This can have a positive impact on a child understanding maths lessons more easily.
Weak conceptual knowledge
Many children do not develop conceptual understanding due to heavy reliance on counting procedures or through rote learning. However, Stern’s approach offers a greater opportunity to develop conceptual understanding through measurement.
To begin to understand the difference let’s take a look at what is taking place in the child’s mind.
When children hear an example such as 6 + 3 = ? and do not know the answer, they often respond by counting …. 7, 8, 9. Then there is an assumption that encouraging children to count, count, count, will on day result in their stopping counting and saying 9.
However, every time they see + 3 as in 6 + 3, or 9 + 3 they automatically practice counting. The numbers themselves have no meaning. For the counting child, 6 plus 3 does not equal 9, it makes 9 by counting. No picture in the child’s mind makes that number fact unforgettable. Further, what if the child counts the total incorrectly as 10? He/she would have no certain way to check that result except by another uncertain counting procedure.
In contrast Dr Stern believed that by working with whole numbers (blocks) at a much earlier stage, children will be able to move on to calculation earlier. Using the specific devices then, the two addends (6) and (3) actually measure 9 in the number track, and exactly fit into the 9-Box opposite.
There are two big points about the measurement approach as opposed to the counting approach.
- Measurement makes obvious the relationships between numbers and number patterns, whereas the counting approach does not.
- Relationships, particularly number facts, are processed as ‘recall from long-term memory’ rather than counting on or counting back. This saves time and space in working memory for on-going processes. It makes for more efficient calculating, and lowers the likelihood of errors.
Children need to access both routes to learning. |
