Our math tutoring fills in the gaps. Many children come to us with a weak number sense. We use online manipulatives to move from the visual to the abstract and learn about place value, number bonds, the four operations and fractions. Meaning is constructed by children over a period of time, through exploring the tools and connecting them directly to mental and recorded calculation.
We encourage students to talk about math. The quality of the talk is important. It is not simply children sharing how they did a particular calculation, but describing why and how it worked. Students solve problems in a variety of ways and using different tools before being confronted with algorithms.