The following chapters main aim is to make a teacher comfortable with mathematical content and feel free in front of a class (Van de Walle, Karp and Bay-Williams 1). The first chapter discusses ideas of leadership which NCTM provides for education in this sphere. It reveals some historical dates of the development of standards of teaching. This chapter also outlines main principles for school mathematics. They are equity, curriculum, teaching, learning, assessment and technology principles. The main sense of each principle is covered. The chapter also enumerates five common standards which are very important for the teaching process and should be implemented. These standards should be applied across all grades. Five process standards are also given. The chapter speculates on the main qualities of a mathematics teacher and professional standards for him.
Knowledge obtained from this chapter can be useful while planning a lesson. It is obvious that a teacher should consider all standards which were described here and add them to his lessons. Moreover, he should build a teaching process based on the main principles for School Mathematics, for his lessons to be effective and informative. The list of professional standards can give a teacher the possibility to look on himself from another perspective and determine whether he has them or not in order to develop these standards.
Chapter 2 centers around the issue of knowing mathematics. It describes it as a science of pattern and order. The chapter stresses role of mathematics in discovering solutions to certain problems. It also reveals some facts about the environment in class for better understanding of mathematics. Students should not just copy teacher’s actions, but to be stimulated to think and do something by themselves. There is also a list which describes ways to support students in their study. It enumerates some main ideas which can make students be more involved in the process and show better results. There is also a section which engages the reader to submerge in mathematics. It names some problems and their possible solutions. The chapter describes benefits of developing mathematical proficiency and how people can better understand and learn this science.
Main ideas from this chapter can also be very useful. It is possible to use them in motivating students and stimulating their own independent work. For example, it is possible to stimulate students to share theoretical ideas, for them to develop collective and critical thinking. Trying to use them, students will develop their mathematical skills, even if ideas are false.
Chapter 20 discusses main ideas connected with geometry. It outlines the importance of combining knowledge of geometry and algebra for better view and some ways of improving geometric thinking.It suggests the idea of developing visual thinking among students to see how shapes and forms fit together.
Chapter 21 centers around the importance of data analysis and the best ways to become familiar with it. Main ideas about statistics, which also reveal some certain data are given. It is also added that this science is not just set of numbers and it is very important to ask concrete questions to get better vision.
Information obtained from these two chapters is very important for developing skills among students. It will help them in their further life and of course it can help to understand mathematics better.
One lesson can be devoted to developing analysis skills among students. It can be easily done in terms of geometry for them to analyze shapes of objects. With the further development of their skills they will be able to work without models, having the image of the figure in their heads and making deep analysis of these figures. This skill can also influence development of analytical thinking.
Chapter 19 speculates about the idea of developing measurement concepts. It underlines the fact that measurement is one of the most important notions in the course of mathematics. It deals with comparison of peculiarities of one object with peculiarities of another one, looking for some similarities. The chapter suggests some concepts and skills which are connected with this notion. It also gives some prompts for a teacher to make students involved in the process and develop their skills. Some estimation activities and their main peculiarities are also discussed in this chapter.
There are some important measurement concepts, mentioned it this part of the book. They can be very useful in the process of study mathematics. That is why it is important to include them to lesson.
First of all, it is the concept of time as it is a very important thing to develop visual thinking. It cannot be seen or felt that is why its perception is rather subjective. It is vital for students to understand main peculiarities of its measurement for them to be oriented in this dimension. The second one is length, as usually it is the first attribute people draw their attention to and students also learn it at the beginning of the course. The last one is area, as its determination develops students visual thinking and eye sight measurement, making them estimate objects size better.
Works Cited
Van de Walle, John, Karen Karp, and Jenifer Bay-Williams. Elementary and Middle School Mathematics: Teaching Developmentally, Student Value Edition (8th Edition). Pearson: London, 2012. Print.