JayChesser

     The foundation for this book centers around the constructivist viewpoint.  This viewpoint emphasizes the fact that all people construct their own knowledge.  The author states "As you read these words, you are giving meaning to them.  You are constructing ideas."  Basically we use ideas we already have to construct new ideas thus developing in the process a network of connections between ideas.  In my undergraduate work, this viewpoint was strongly supported by the college that I attended.  In my short number of years teaching, I have found this viewpoint to be true.

     As teachers we can support this type of teaching in our classrooms by providing an environment that is conducive to the constructivist viewpoint.  They recommend that students be allowed to use manipulatives, symbolism, and even computers as models or tools for learning.  Social interaction with other students is encouraged.  And students should have a set time for reflective thinking and writing.  In the last few math workshops this has been strongly recommended as a way to see if our students truly understand the concepts we are introducing in math.  Students need to realize that there is more than one correct answer.  The writing and social interaction allows for others to see that there is more than one answer.

     This book encourages teachers to make math more meaningful for students.  Problems should be presented in such a fashion that they are within the students' zone of proximal development.  The problems should be concerned primarily with making sense of the math involved in solving the problem.  Students should be able to understand that the responsibility for determining if they are correct or not rests with them.  Students should be able to explain themselves.

      Chapter 2 deals with number sense, a relational understanding of numbers, and operation sense which is a complete and flexible understanding of the operations.  Many activities were included to give the teacher ideas of how to teach from this viewpoint.  I am not sure that I understood all of the fuss about remainders when you are dividing.  "Students should not just think of remainders as 'R 3' or 'left over.'  Remainders should be put in context and dealt with accordingly." 

     Chapter 3 focuses on helping children master the facts.  According to the authors "Mastery of basic facts means that a child can give a quick response (in about 3 seconds) without resorting to nonefficient means, such as counting.  Children simply need to construct effecient mental tools that will help them."  This chapter is full of strategies to help teachers.  Some of these strategies we have implemented before.  Others we will try when we get to that set of facts.

     Chapter 4 presents strategies to help children with whole number computation.  The traditional algorithms that we use in math may not be the most efficient or useful methods of computing.  Flexible methods and invented strategies are encouraged to help children with whole number computation.  Flexible methods involve taking apart and combining numbers in a variety of ways.  Children need a good knowledge of the properties and the operations such as addition to subtraction, addition to multiplication, and multiplication to division.  Invented strategies are those strategies constructed by students.  Success of these strategies requires that the strategy be understood by the one who is using them.  The chapter talks about each of these areas and provides examples of how to use the strategy/method.