Teaching Correct Number Formation: Implications for Maths.

When it comes to handwriting, we always talk about children needing to have automatic handwriting so they can think about WHAT to write, not HOW to write.  And that holds true so much more for maths.  Automaticity in number formation is essential for achievement in maths, making teaching correct number formation a critical foundation skill we need to consider.

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Some children are naturals when it comes to maths, while for others there is no getting away from the fact that is difficult.  It is something they need to work at and work on all through their schooling.  And those children, more than any others, need to have soundly established number formation.  They cannot afford for their working memory resources to be consumed with thinking about how to write a number – it just has to be there without them having to think about it.

In addition, poorly formed numbers can easily be mis-read.  Poor number formations can be carried through a child’s entire schooling experience and are very hard to remediate once habits have been formed.  Teaching correct number formation is not optional.

CAPS maths curriculum and number formation

The Grade 1 CAPS mathematics guidelines simply states in the overview that the child should be able to form numerals correctly.  The more in-depth guidelines mention that the child should be able to write the number symbols from 1 – 10 in Grade 1, and up to 20 in Grade 2.  However, there appears to be no emphasis on the teaching of number formation, its critical foundation to maths, or how it should be taught.

Forming numbers correctly

“When a child with fine motor problems must copy math problems out of a textbook before even beginning to solve them, she may not physically be able to do enough problems to get the necessary practice, thus her achievement in math may be affected. 

Another child may not be able to demonstrate that he knows how to do long division if he cannot write legibly enough to read back to himself correctly the numbers he has written. This situation may lead the teacher to assume that the child does not know how to do long division, thus illustrating the effect of fine motor skills on assessment for instruction. 

A third child who writes very slowly may not be able to complete many math problems on the annual timed test that determines math group placement. He may then be placed in an inappropriate math group.”                                                                                                                           McHale & Cermak

In order to progress with maths, children learn times tables.  And they drill them until they know them automatically.  This is so that when they are confronted with multiplication or division, they don’t have to work out the answer by counting in 5’s on their fingers – they just know.

And it needs to be the same with the ability to form numbers – our children must “just know.”

What is number formation

Number formation is the direction the pencil follows when a child writes a number.  If a child has to think which way a number 7 faces, they simply cannot focus on the calculation.  There just aren’t enough working memory resources available.  What a tragedy it would be if the teacher were to believe that the child was weak in maths, simply because they have never achieved automaticity in writing numerals.

The quality of written numbers is critically important.  If either the child or the teacher are unable to decipher what the number is, the child may be penalized for their answer, when the problem is not their mathematical ability – the problem is their pencil control and their ability to form their numbers so they can be accurately read.

Teaching number formation requires certain foundations to be in place

Number formation requires certain foundations to be be in place before children are ready to learn to form them.  The child needs to be able to reproduce a vertical, horizontal and diagonal line.  It is not enough that they can copy one while they watched you draw it.  While this is a precursor to being able to do it independently, they need the next step – they need it to be automatically internalized.  They need to be able to reproduce these lines when presented with an already completed line.  And then, they can go ahead and learn to put those lines and shapes together to form the numbers.

Number formation is established as the neural pathways are used over and over again, and a “motor map” or set of instructions on how to form them is laid down in the brain. This is achieved through repetition.

But what if the repetition is in the incorrect pattern?  What if your child practises a number 7 backwards over and over again?  The “motor map” is going to be laid down in the reversed pattern, and that pattern is going to become hardwired.  And we may work on improving the shaky foundations of directionality and spatial perception which may have resulted in the reversal in the first place, but the “motor map” for the number 7 remains in the reversed pattern.  And that is difficult to change.

Number formation: numbers are not like letters

Numbers are not like letters where you can learn a different handwriting style, or transition to cursive handwriting to deal with reversals.  It is also not so easy to use accommodations like a computer for maths as it is for writing an essay.  Numbers are numbers, and laying down a poor “motor map” is a real problem.

I feel passionately about the importance of number formation.  It needs to have it rightful place.  We cannot simply leave number formation to chance!  The implications for children who develop illegible numbers is simply too great a risk.

Number formation teaching order

 

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We teach the numbers by grouping them according to their starting positions.  The numbers are divided into blue starters which start on the blue side; red starters which start on the red side; and middle starters which start in the middle.  We start with the blue starters, namely 2, 3, 5 and 7.  The middle starters come next and start in the middle of the boundary box.  They are 4, 1 and 6.  Last come the Red Starters, namely 8, 9 and 0 which start on the red or right-hand side of the box.  We start with this in Grade R and continue into Grade 1 where we also learn how to position the letters on the lines – and you know how I love lines!

Teaching correct number formation: how to teach numbers to pre-schoolers

Just like we do with writing letters, here at The Happy Handwriter we use a multisensory number formation strategy.

  1. Build the number.  But don’t just use pieces of play dough to create it, it must be built in the correct formation pattern.  A number 5 must be made up of the down and round,” with a hat added on top.
  2. Sing the formation pattern.  Research has shown that when comparing a group of children who used the “watch and copy” approach; to those where the formation directions are verbalised; the group for whom the directions were verbalised, showed significant improvements compared to the other group which showed no improvement over the same time period, with the same amount of input.  Many strategies use rhymes to teach writing numbers.  However, The Happy Handwriter has taken this a step further by developing number formation songs.
  3. Always practise numbers in the correct formation pattern.  As we have said before, it is of little use to be practicing in the incorrect pattern, and laying down a “motor map” which is going to be difficult to remediate later on. That is why at The Happy Handwriter we always introduce the number with a correct number form that the child is going to work on top of: either by building, tracing, or adding sensory input.
  4. Touch input. Using the touch input by tracing over the texture board, together with singing the formation song is going to give extra input to the brain on the formation pattern, and is going to establish it better.
  5. Rainbow Numbers.  Formation patterns are developed through repetition.  Tracing all the letters in one colour, then all in the next, and the next, allows for multiple repetition in the correct formation pattern.
  6. Boundary boxes limit the tendency for number reversals.  We place the numbers in a boundary box with a blue line on the left.  If a number starts on the blue side, the child will have to leave the box in order to reverse the number which limits this tendency.

Don’t compromise your child’s maths skills with poorly established number formation. Teaching correct number formation is as critical as learning to read or learning number bonds.  Children cannot do maths without this critical foundation in place.  It is our responsibility to ensure we make the time and provide the opportunity for our children to master this skill of automaticity in number formation.

©Bunty McDougall
Occupational Therapist

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