The Primary Mathematics

This textbook shows how young people can master the mathematics curriculum in half the allotted time by learning algebra before arithmetic. The book is in three parts. In learning to learn mathematics we give examples of children¿s work with Gattegnös Cui materials. We follow them as they encounter Cuisenaire® rods, and play games that lead to the discovery of key insights: the mathematics of sorting and naming. We illustrate their experience with commutative diagrams ¿ the ¿equations¿ of sorting and naming ¿ and diagrams of brix¿, analogues of the rods, taken from their web diaries. In the second part, formative assessment, we discuss what is wrong with the traditional Piagetian unfolding of state and national curricula. We apply conceptual mathematical ideas to show how Cui can help teachers rapidly to overcome traditional shortcomings. In the third part of the book and linked web materials, we set out 200 questions that parents and teachers can use in working with young people to plan and implement whole school adoption of algebraFirst¿