... discover mathematics for themselves with the teacher only being there to facilitate and encourage discovery. The opposing view to this was that the teacher was there to drill particular methods and routines into the children regardless of whether the children knew or understood what was happening this meant that, while children could recite number facts without error, when it came to solving problems they did not necessarily know what methods to apply to derive the correct solution. Research has shown that children respond individually to experiences and that while some are able to 'discover' mathematics for themselves (often these children have access to other ideas at home) others need more direct instruction. It would seem then that a 'connectionist' approach where both teacher and children work together to develop a deeper understanding of mathematics is needed. This approach gives children the necessary broad and balanced experiences for them to succeed, ...

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