In this chapter, I learned that doing mathematics helps children to analyse the pattern, create strategies to problem solve and to understand the relationships between the process and concepts.
According to Piaget, children construct knowledge to generate new ideas which happens in two ways - assimilation and accommodation in a equilibrium. Therefore in mathematics, children uses their prior knowledge to understand the problem and try to 'insert' new knowledge to see if the problem could be solved.
Children uses such representations to translate their knowledge on mathematics. In the early years, I understand that if teachers provide various opportunities to allow children to understand such representations, they are able to translate a concept from one representation to another, thus enables them to problem solve and understand the computations. One example is providing manipulative or counters for children as they are visual learners and it helps them to understand and grasp the concept, such as addition or subtraction, better.