conceptual vs procedural

When supporting a learner with a large skill deficit in mathematics it is tempting to skip the foundations and spend the lion's share of therapy time on getting them a passing grade. This of course is the reason why your family has sought my help - your child is failing maths and you want me to solve this problem. There is lots of pressure to work to the curriculum rather than to the child's individual needs and unique level of understanding. The reality is of course much more complex than that. We have to start with the reasons why we use mathematics in our daily lives - functional numeracy should always be the goal. What use is the trigonometric mnemonic SOH-CAH-TOA, if one cannot work out which item represents the best buy in the supermarket? Or how long it will take to travel to one's intended destination and how much to budget for fuel costs? So I like to start with real life maths - what do you already know about numbers, how do you use numbers in your everyday life, and how can I support you to extend this understanding? 

The remediation of mathematics deficits requires a solid plan and the plan I follow is the CRA approach. 

C = concrete, this is Using the Maths

R = representational, this is Making Sense of the Maths

A = abstract, this is Doing the Maths

Did you know that it requires four times more repetition at the Concrete level than the Representational level, for conceptual understanding to develop?  And that the Representational level should in turn be used for as long as the learner needs it? And that if we allow the learner to choose the level, then they will automatically choose the most appropriate one for their needs (if we have not messed up their internal feedback loop)? 

Start where it counts. Real life, applicable, everyday numeracy. Then focus on building the concepts that support that numeracy. Then explicitly teach the procedural skills that lead to fluency.