GJones

Chapters 9-12 discuss the presentation of mathematical conceptual knowledge to be implemented in a student-centered environment.  Most of the examples given are accompanied by an array of strategies, i.e. in Chapter 9 a general plan of instruction is allocated for the instruction of measurement comprehension.  I find the three summarized in this chapter to be true.  Students do need to use comparisons when measuring to make the measurement relative.  Using model units to portray measurements is also imperative for a visual representation of the conceptual knowledge.  This provides an appropriate amount of duality to mathematical perspectives needed in developing successful students.

The most important of the lessons proposed in these chapters is application.  Students need to utilize these concepts and apply the attained skills authentically. Chapter 12 was my favorite because it dealt with probablity.  The 12.4 activity was one I will use in my class.  I enjoy implementing hands-on learning experiences.  There are many creative activities dispersed throughout the chapters that seem very simplistic in pedagogic approach.  This book would be a good classroom resource if we could keep a copy in our room.  However, once we turn this book over to the media center I fear it will be a resource not many will check out. 

Is there any way we could keep this book indefinitely, as a temporarily-permanent fixture (oxymoron) in our repetoirre of resources.  At least until I become accustom to some of the best activities proposed.

Chapters 5-8 proposes to allow students to come up with their own methods of solving mathematical problems using self-generated algorithms.  They propose that it is okay for the student to manifest algoritms and prove these algorithms successful via trial and effort.  The use of formal algorithms are not a ulitmate priority, but they are to be only aids to the students autonomous methods.  There are several examples of how to allow this process to flourish in each of the chapters.  I already am a proponent of informal algorithms in mathematics.  The Saxxon style of math seems somewhat an antithesis to what is being proposed.  Saxxon is very strong on adherring to formally taught algorithms and does not allocate time for the type of authentic self-discovery that is presented within Student-Centered Math.  I however, I agree with the methods professed in the chapters of this book. They seem to mirror those set by the NCTM (National Council of Teachers of Mathematics).

Student-centered mathematics is the way mathematics should be taught on a daily basis.  This book is a proponent of constructivism in the presentation of mathematic education.  Comprehending math means students must be engaged in authentic mathematics, with cognatively appropriate instruction.  Teachers must present the conceptual and applicable nature of mathematics to fully faciliate student mathematical comprehension. 

The schema children acquire prior to entering a teacher's class should act as catalysts to new mathematical endeavors.  Numbers are an important part of a child's life before they enter a classoroom.  Students use numbers constantly and need to build new schema upon their existing foundation of numeral sense.  Teachers need to facilitate the encounters of new mathematical concepts via authentic, applicable activities.

The main goal of mathematical education is application.  Children should be able to implement their knowledge of mathematical operations in authentic situations.  Proficient students show mastery of the basic functions of mathematical operations. Some children have several ineffective strategies to compensate for a lack of mastery of these basic operations.  Teachers can help all children develop effective means of acquiring a mastery level of all the basic mathematical operations and functions.  It can be done.