Reflection on Chapter 1 and 2

Before I read the textbook, I did not know that there are principles and process standards that teachers need to understand and use the process standard to teach mathematics to children. After reading the two chapters, I have come to realise and understand the importance of using the right standards/ways to teach mathematics to young children helps to lay the foundations for their future learning. At the same time, using the process standards to teach children learn mathematics will assist children to develop thinking skills that is crucial for learning. 

The six principles and five process standards mentioned in the textbook are important information for people who design the curriculum for the preschool. It is also important for teachers who are teaching mathematical knowledge to read and understand the six principles and five standards for school mathematics. Personally, I agree with the points mentioned  and  I feel that it is important to give all children the equal opportunity to learn mathematics through active learning. Children must be active learners when they are learning mathematics concept.

One way for children to learn mathematics concept is through problem solving. When children are solving mathematics problem, they are able to  reason and proof that their answer make sense through logical thinking. When they talk about and describe or explain the mathematical ideas, they are exploring the different ideas and making connections to mathematical ideas. Through the process of brain storming for solution to their problem, children can also use charts, graphs, diagrams, symbols and manipulative to express mathematical ideas and relationships. However, the classroom environment must be well equipped with learning centers in which technology is used to enhance learning and understanding of mathematics concept.   

As Piaget suggested, assimilation occurs when a new concept "fits" with prior knowledge and the new information expands an existing network. Accommodation takes place when the new concept does not "fit" with the existing network, so the brain revamps or replaces the existing schema. (Walle, Karp & Bay-Williams, 2009, p. 20) Therefore, as we build on our existing knowledge with newer ideas about mathematics knowledge, we are able to make better connections between prior knowledge and new knowledge so as to achieve a maximized understanding of mathematics concept.