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PrefaceThe 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 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 (“Standards 1989”), strongly assert that students learn mathematics well 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.” In this vision, “mathematics instructors do not simply deliver content; rather, they facilitate learners’ construction of their own knowledge of mathematics.” This book contains 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. It also provides instructors with a variety of resources for making an interactive approach to mathematics the focus of their teaching.Our PhilosophyMathematics for Elementary Teachers: An Activity Approach is a collection of activities for prospective teachers that involves and develops inductive and deductive reasoning. The activities enable students to think deeply about how manipulatives and visual models contribute to understanding mathematical concepts. Students experience mathematics directly by using models that embody concepts and promote mathematical thinking. This book reflects the beliefs that:
• Prospective teachers who learn mathematics through appropriate use of manipulatives, models, and diagrams are more likely to develop a solid conceptual basis and a deeper understanding of the mathematics they will teach.
• Prospective teachers who learn mathematics by being actively involved in doing mathematics will be more likely to teach in the same manner.
• Prospective teachers who use manipulatives effectively in their learning will experience how manipulatives assist understanding and will be more likely to use them effectively in their teaching.
• Becoming familiar with manipulatives and models in structured activities will give prospective teachers confidence to develop lessons that use manipulatives and models.
• A concrete approach diminishes the mathematical anxiety that often accompanies a more abstract approach.
• Tactile and visual approaches provide mental images that, for some students, can be easily retained to provide understanding for symbolic representations. Cooperative Learning and Using Manipulatives
Each Activity Set can be done individually or in small groups. Small group instruction provides opportunities for discussion and for listening to others explain their reasoning. Guidelines for cooperative learning in small groups are outlined in Activity Set 2.3.
It is well known that effective teachers have a good understanding of the mathematics they teach and are skillful in choosing and using a variety of appropriate instructional techniques. The importance of using manipulatives in mathematics teaching and learning is well documented and amply illustrated in the pages of NCTM’s Standards and Expectations 2000. Research has shown that the appropriate use of manipulative materials has a significant positive effect on students’attitudes to learning and potential for achievement in mathematics.
Interviews with teachers successfully using manipulatives in classrooms revealed the following commonalities: the teachers had all received training for using manipulatives; they designed their own lessons and worked through them using manipulatives themselves; and they prepared for classroom use of the manipulatives by anticipating how the class would react to each activity.Course Formats
Many of the Activity Sets in Mathematics for Elementary Teachers: An Activity Approach are independent of each other and can be covered out of sequence (see the Instructor’s Resource Manual for information on the Activity Set dependencies). The flexible coverage of the Activity Approach makes it possible for the book to be used effectively in a variety of course formats:
• A lab course based on the Activity Sets and supplemented with outside readings from a reference text or journals, with the Follow-Up Questions and Activities used for assignments
• A combination lab and recitation course in which the Activity Sets are integrated with discussions or lectures extending the ideas raised in the Activity Sets and developed further in Mathematics for Elementary Teachers: A Conceptual Approach
• A traditional lecture/recitation course in which the Activity Sets and Follow-Up Questions and Activities in the Activity Approach are used to supplement Mathematics for Elementary Teachers: A Conceptual Approach.  <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0077237501/97854/acrologo.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (2.0K)</a>]]> | Click on the link below to view the Preface in its entirety for Mathematics for Elementary Teachers: An Activity Approach, 8e in Adobe Acrobat PDF.  Preface
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