DJohnston

Teaching Student-Centered Mathematics: Chapters 1 through 4

The underlying premise of the book is that students learn best by creating their own knowledge and understandings by being able to manipulate objects and  models to build withing their mind a concept of the world around them, most specifically in this case, mathematics. Van de Walle and Lovin base their text on the constructivist method. One only has to teach in an elementary classroom to see that students constantly comment, "Can I see that?" "Can I hold that?" "Can we make one?" To a child and many adults as well, learning comes best with we can hold an object and turn over and around not only in our hands but our minds as well.

Chapter 2 expounds on developing number and operation sense, the foundation for all mathematics. Without a child being able to grasp that a numeral has a quanity or value attached, there is little on wich to develop concepts of one more, some, all, less than and greater than, half, etc. Number sense used to come in part when children played board games, were engaged in pretend play, and in the magical world of Kindergarten with sand and rice tables and centers filled with a myriad of physical objects to be counted, stacked, and manipulated. Many children now have little opportunity to "play" with simple toys that have to be handled and positioned. I see more and more students who have had 4 to 5 years of school and no sense. How then does opertaion sense emerge? There are several activities in this first chapter that will be immediately implemented in math class to reach those students who are significantly deficit in this area.

Chapter 3 adheres to the concept that all math facts are related and that by building this concept in a physical way through manipulatives helps a child see that math goes beyond symbols and cooresponding rules that must be memorized and time tested. By learning how facts of addition/subtraction and mulitplication/division are related at a basic level, then the understanding and manipulation of larger numbers can be made by taking large numbers apart and solving problems in smaller chunks. The strategies for multiplication facts were taught to us in a math workshop earlier this year. I have already begun to use "doubles" for times two and am working on the "clock facts" for times five.

Chapter 4 presented challenges for those of us who religiously learned our algorithms just as our teachers presented them. If you were lucky, you had a teacher that presented more than one way to do a problem. I learned exactly one way to do each operation and thankfully master more the required ones to get me through high school. I t was not until college that I learned there is more than one way to solve most any problem. The idea of grounding mathematics in everyday life is not new. Math was invented in ever increasing complexity to solve the problems of life encountered everyday. This chapter is rich with expanding concepts of invented strategies that are constructed by the learner and is reliable. the underlying basis is a well developed number and operation sense. Practice by the teacher must be done ahead of time to be able to provide guidance and encourage students to step away from looking at the teacher for the "right" way of performing an operation.