As we anticipate the publishing of the ‘Mathematics Strategy’ we should take heed of Kevin’s challenge. Enjoy!
The Numeracy Project will work in an ideal world because the processes and strategies espoused are logical and clearly without fault. An ideal world would be one in which all children are naturally inclined to mathematical thinking. The real world on the other hand does not match the perfect logical approach to mathematics as advocated by the Numeracy Project.
Children on the whole are definitely not naturally inclined to think in clever ways about mathematics. They are not junior mathematicians as the Numeracy Project proponents would like to believe. Most children when they come to school need to be established in routines and processes that allow them to take the next step.
Being established is a multi-sensory task. They are instructed and guided, and they attempt, practise and master one step at a time aurally, visually, and orally through a range of tactile procedures. The role of the teacher here, keeping the child working in a progressive manner, cannot be overestimated.
Modern educational thinking has turned the focus of education onto the child — the learner - and away from the teacher. This means that the child has been given more say about their learning and the teacher, less. Now the teacher understands the pathway that has to be taken in order for learning to take place. Too much reliance has been put on child capability and choice. In rare cases, this approach will prove valid but for the majority, it is the beginning of disorder in learning.
One of the key purposes of the Numeracy Project is to instruct teachers in mathematical thinking so that they in turn are giving consistent instruction to the learner. The problem is that many teachers, like their pupils, are not mathematically inclined and have the same problem with maths that the child has.
Instead of illuminating their practice and giving them confidence, it rather highlights their confusions and forces them to cling religiously to Numeracy Project practice out of insecurity and their lack of expertise in the subject. Thus, the mathematical practice in a classroom is more often than not at risk of becoming a case of the blind leading the blind.
If teachers were to realise that pure mathematical thought is only necessary for future academics and that processing numbers by a method or a formula is the only necessary pathway for most of us, the development of knowledge in this field would not be so arduous and once grasped would be a pleasure to teach.
If children worked continuously with concrete representations of number and concentrated on recording the processes they are learning through simple equations, did this repeatedly, and talked through what they were doing, they would be developing mathematical knowledge. Once having grasped knowledge in this way, they will be so much more receptive to thinking about what is going on and notice patterns and relations that will simplify processing for them.
For instance, if they are adding 15 and 6, the simple method of counting six more numbers on from 15 to get a sum of 21 will over time ensure their knowledge of this relationship and so they may be more receptive to seeing 15+6 as ( 15+5)+1 and so speeding up the process. However, this is not essential, but learning 5+ 6=11 is — because computing with greater numbers requires basic fact knowledge before learning to see patterns in numbers.
This intellectualising approach may suit the top 5 percent of learners but not the rank and file. It is more beneficial for them to follow a method applying facts learned while recording what they are doing. At the end of the day employing a formula, a calculator or a method is as far as they will ever need to go in mathematics.
The British mathematician and philosopher Bertrand Russell said that mathematics is the science of doing the necessary things in the easiest way.
When we lose sight of the fact that mathematics is only a tool, we are in danger of turning it into an end in itself. The advocates of the Numeracy Project want us to do maths in the hardest possible way by reinventing the wheel.
An astute teacher will know that appreciating how the solution was achieved is of lesser importance than the actual achievement. The learner who has mastered a straightforward method of computing may be more receptive to the underlying thought at a later date.
What is essential for the child learner is knowing the steps that will safely allow them to reach a successful solution. This is why it is more important for them to activate the memory ahead of reasoning. Repetitive exercises to establish number facts will be more useful to the average learner than unwelcome stressful intellectual figuring.
In the early stages, children need to be immersed in number activities such as counting, labelling, matching, joining, etc, often and accompanying these activities with the appropriate recording. This doing should be repetitive and given incentives to be memorised.
It is natural for humans as they learn, to do it step-by-step until you have mastered the process. This is how we learn most things until it becomes second nature. When children can compute readily and confidently then they are in the best position to think about what they are doing in enriching ways, but if they never get to that stage it doesn't matter because they have learned what mathematics is all about: following a process in order to reach a solution.
The Numeracy Project put the cart before the horse in pressurising children to exercise their intelligence in the abstract long before they have the foundation for it let alone readiness for or interest in such activity. If schools are ever to do a service to their pupils in mathematics they have to stop treating them like junior mathematicians and treat them like children. Recognising, memorising, and recalling must be well established before reasoning is relied upon.
