It has always been the job of the educator to put abstract number relations into a concrete form which is adapted to the child’s interest and mental capacities. But while we adjust our teaching to fit the inner nature of the child, we must do so without damaging the inner nature of mathematics. Modern teaching attempts have so overdone the adjusting that the arithmetic itself is camouflaged and consequently poorly learned. (Dr Catherine Stern). Is this still true in today’s education climate? Is this because we are not following a child’s natural development? Why are children still struggling to learn number and arithmetic in schools today?
Stern Structural Arithmetic has been described as a bridge into knowing and understanding number (Bristow et al 1999). Stern’s method takes its start in activities natural to all young children, never artificially confronting them with adult conventions. These children discover number relations themselves as they must if relations are to serve them with full power and richness. They learn with delight; they continually show their teacher things they feel s/he must not miss. More than that, the number notions they acquire are not only adequate for the handling of ordinary experience, but are so sound logically, according to the best mathematical knowledge of our day that, as these children advance, they need never discard their early formulations as inadequate or deceptively simple, but can carry them forward as the building blocks of algebra. (Marguerite Lehr. Bryn Mawr College).
This blog gives examples of three pupils, one has severe autism, and two of the pupils have global discrimination delay. All of the pupils have specific processing deficits and have been seen to benefit significantly from being immersed within the Stern programme. Stimulating and encouraging a child’s information processing systems are a very important part of the pedagogy and maths devices within the Stern programme.
At a training course the maths coordinator of a school in Kent came to me and said “There’s no doubt about it Vikki, Stern is more than a maths tool.” This was a superb observation. His school began to use Stern with their Year 6 and 7 classes (within 6 months, they began to use Stern throughout the school). One year 7 pupil in particular held his interest.
specific number structure - Pattern Boards 1-10
The Counting Board - ordinal, cardinal aspects, and number relationships
“In the year 7 class I have been focussing attention on the evident support that the apparatus can give to one child who has severe spatial and visual discrimination delay. Initially he was unable to place the blocks in the correct ‘channels’ and was unable to copy the pattern boards and certainly not with left/right completion. “
“When the materials were first used with this pupil, I asked his art teacher to also monitor his progress in this subject in order to see if any changes were noted. Over the course of the term he was able to sort the blocks into their correct ‘channels’ and also master left/right sequencing and accurate copying up to the ’6′ pattern.”
An improvement in other curricula areas has been demonstrated through the development of this particular child’s cognitive learning systems.
“This pupil’s art work has shown considerable progress so much so that he won the end of term Senior Art Award for the most progress shown during the spring term. Progress is also being shown with his reading, for obvious reasons, and he is currently doing much to overcome ‘on/no’ reversals.”
“This I think is part of the benefit of the materials and the activities namely their cross curricula support because as this pupil’s global discriminatory skills increase these will feed back into supporting his mathematic abilities.”
“As for the year 6 class they have been using the materials at a ‘higher’ level to support 2 digit place value and staff have been very pleased with the children’s enjoyment of the equipment and progress it has brought.” Maths Co-ordinator – Special School Kent
Adding tens in the Dual Board
Sensory experience is essential in forming the imagery needed for internalisation of learning. While we are already familiar with VAK input (visual, auditory and kinaesthetic) as separate learning styles, Prof. Usha Goswami’s (Cambridge University), research has shown that creating a learning environment incorporating all three produces the optimum impact for learners.
Impact Learning – four routes to transfer information from working memory to long term memory
o Visual elaboration route
o Auditory route
o Kinaesthetic route
o Repetition route
Stern’s structural apparatus provides unforgettable imagery, therefore has visual impact. There is also sensory-motor impact through manipulation. The activities provide progressive repetition. There is opportunity for auditory and visual input through the teacher’s explanation; modelling; the child’s own commentary to peers; the incorporation of role play. This strengthens the child’s own developing mental strategies providing multi-sensory experience from the formation of imagery, building concepts and enhancing memory storage and recall.
A further reason for limited progress is the inability to work with the abstract nature of our number system thus many children are unable to access the maths curriculum when moved away from concrete experiences too soon.
The next two examples are a 9 year old boy who has severe global delay and also very little expressive language, and the other boy who is 8, is severely autistic.
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“Previously both boys would join in number rote counts and join in number rhymes with help but had no basic understanding of abstract mathematical concepts.” “Since the introduction of the Stern scheme there has been a marked improvement in both boys understanding. In the first case the boy is able to manipulate the blocks and place them vertically in their assigned place (At first he would place them horizontally and it took a good month to teach him to do it correctly). Now he recognizes the order they should be in and can match them to their twins.”
“With the autistic child who is a visual learner, he has moved very quickly through the first level (Stern) and has developed an understanding of ‘before’, ‘after’, ‘bigger’, ‘smaller’, ‘ordering’, ‘patterns’ and using blocks to make 10’s. He has now put number names to the blocks and has developed an idea of addition to 5. Modelling activities to learn the language, which for him is particularly difficult, and through his actions rather than the use of language, we can monitor his progress.”
“Both boys are developing a fundamental understanding of arithmetic concepts, which were lacking previously. It has also helped with their fine-motor and thinking skills.”
Special Needs teacher Primary School London
Stern has proved to be effective at any age, or stage of development. It has the ability to engage the learner’s interest, adding to long term memory storage effectiveness. It has the intrinsic capacity to display relationships between numbers clearly. The built-in, self-checking element of the apparatus automatically reinforces learning.
What is Structural Arithmetic?
Stern’s multi-sensory maths system was designed to develop a child’s emergent number sense by building-up number knowledge and number facts and by facilitating the understanding and use of the four number operations. Since the system is based on two tangible sets of number representations, the blocks and patterns promote a clear image of number in the concrete enabling pupil’s to discover for themselves all of the attributes on a physical level. When numerals are introduced they correspond to the blocks and patterns by embodying the intrinsic qualities and values of those numerals.
With our memory games we can move children away from the concrete support to practising and further embedding facts and concepts in long term memory, also to speed up recall of facts.
Stern is an inclusive system with proven success in early years and AEN. It aids the development of spatial thinking and reasoning, whether children are measuring blocks or working with patterns of cubes, they are applying spatial thinking to help them reason. Each experiment leaves a mental picture to turn around in their minds to explore new relationships.
Hand-eye coordination and one-to-one correspondence increases; unfamiliar maths vocabulary can be clarified by the practitioner through concrete demonstrations and further reinforced by the child’s actions with the apparatus; by following spoken directions children are able to develop receptive language; this is a means of assessing the child’s receptive language acquisition and auditory memory; a system of errorless learning where misconceptions in the child’s understanding will be seen immediately and acted upon through further demonstration and practice.
Catherine Stern had the vision to develop a maths system ahead of its time through tasks designed specifically to be SMART.
o Specific progressive steps which strengthens learning
o Measurable progress intrinsic to the teaching methodology
o Achievable with built in elements for success
- actively engages the child as a learner
- promotes the interest of the learner
- encourages expressive and receptive language
- enhances short and long-term memory
- develops opportunities for speaking and listening
o Realistic concrete small stepped programme incorporating scaffolded learning
o Time related – level of progress determined by individual
The ease with which practitioners are able to administer Stern’s system and speed of results, coupled with the immediate engagement and genuine enjoyment experienced by children is testament to the effectiveness of this maths programme.
