In chapter one, I have comprehended that the five content strands defined by Principles and Standards are number and operation, algebra, geometry, measurement and, data analysis and probability.
According to the authors, these five content strands are emphasized differently in different grade bands. In comparison, in Singapore context, number and operations are very heavily emphasized in primary school and algebra is seen to be taught in secondary school onwards.
According to the Principles and Standards, the five process standards are referred to 'the mathematical processes through which students should acquire and use mathematical knowledge' (p. 3). The five process standards consist of problem solving, reasoning and proof, communication, connections and representation. According to the authors, 'To teach in a way that reflects these process standards is one of the best definitions of what it means to teach 'according to the standards'' (p. 4).
In this chapter, I have learned and perceived that to become a teacher of mathematics, 'She needs to have a very good knowledge of mathematics. She needs to be persistent and have a positive attitude toward the subject of mathematics. She must always be ready for change. Most importantly, she must have a reflective disposition to make time to be self conscious and reflective' (p.10).
In chapter two, according to the authors, this chapter focuses on 'learning theories of teaching developmentally and the knowledge necessary for students to learn mathematics with understanding' (p.13).
I fully agree with the authors in order to help student learn mathematics 'the importance of both words in 'productive struggle'- students must have the tools and prior knowledge to solve problem, and not be given a problem that is out of reach, or they will struggle without being productive' (p.15).
I have also learned that according to the constructivism and sociocultural theories, 'the best learning opportunities takes place when the teacher encourages and engages the students in using their own knowledge and experience to solve problems through social interactions and reflection' (p. 29).
(Walle, J. V., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching
developmentally (8th Edition). New Jersey: Pearson Education.)