Mathematics for Elementary Teachers: An Activity Approach, 5/e; Preface

Preface

The primary purpose of Mathematics for Elementary Teachers: An Activity Approach is to engage prospective elementary and middle school teachers in mathematical activities that will enhance their conceptual knowledge, introduce them to important manipulatives, and model the kind of mathematical learning experiences that they will be expected to provide for their students.

The National Council of Teachers of Mathematics' Principles and Standards for School Mathematics ("Standards 2000") and its predecessor, Curriculum and Evaluation Standards for School Mathematics, strongly assert that students learn mathematics well only when they construct their own mathematical thinking. Information can be transmitted from one person to another but mathematical understanding and knowledge come from within the learner as that individual explores, discovers, and makes connections.

The National Council of Teachers of Mathematics' Professional Standards for Teaching Mathematics presents a vision of mathematics teaching that "redirects mathematics instruction from a focus on presenting content through lecture and demonstration to a focus on active participation and involvement. Mathematics instructors do not simply deliver content; rather, they facilitate learners' construction of their own knowledge of mathematics."

This book provides instructors with activities and materials to actively engage students in mathematical explorations. It provides prospective elementary and middle school teachers the opportunity to examine and learn mathematics in a meaningful way.

Reasons for Mathematical Activities

Current views about the learning of mathematics are summarized in Everybody Counts: A Report to the Nation on the Future of Mathematics Education (National Research Council, pp. 58-59):

Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding. To understand what they learn, they must enact for themselves verbs that permeate the mathematics curriculum: "examine," "represent," "transform," "solve," "apply," "prove," "communicate." This happens most readily when students work in groups, engage in discussion, make presentations, and in other ways take charge of their own learning.

Mathematics for Elementary Teachers: An Activity Approach is a book of inductive activities for prospective teachers. It provides the instructor with the resources to make students' mathematical activity the focus of attention. The instructor is then free to interact with small groups, pose questions, and encourage reflective thinking and class discussions. The book enables students to experience mathematics directly by using models that embody concepts and promote mathematical thinking.

This book reflects the beliefs that:

Students who learn mathematics constructively through the appropriate use of manipulatives, models, and diagrams are more likely to develop a solid conceptual basis.

A concrete approach diminishes the mathematical anxiety often accompanying a more abstract approach.

Tactile and visual approaches provide mental images that can be more easily retained than symbols and called forth as needed in mathematical thinking.

Prospective teachers who learn mathematics by being actively involved in doing mathematics will be more likely to teach in the same manner.

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