The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…

This paper discusses an approach to the study of algorithms which values students' construction of nonstandard algorithms but also emphasizes the essential roles of the teacher and instructional activities in supporting the development of students' numerical reasoning. Episodes are presented from a 3rd grade classroom in which a 9-week teaching…

Three types of arithmetic algorithms are discussed and compared. These are algorithms designed to get the right answer, computer algorithms, and algorithms designed to get the right answer and understand why. (MP)

An attempt is made to establish a link between ordinary arithmetical situations and relevant mathematical concepts by the analyzing of complexity of concepts. (MP)

This classic reprint was first published in 1955. Fehr discusses how to determine what is taught, and makes specific comments on the roles of planning, meaning, practice, learning, and problem solving. (MNS)

Shortcomings of mathematics curricula are described and research on the use of sameness analysis with learning-disabled and at-risk students is outlined. The paper then illustrates how to teach addition-subtraction and multiplication-division relationships and their interrelationships in the context of solving word problems in mathematics.…

Fourth-grade students who participated in a yearlong, whole-class teaching experiment not only reconceptualized natural numbers but also generated flexible solution strategies to perform numerical computations mentally and in writing. Students' reconceptualization of number was mediated by their perceived resemblance between the physical action of…

Elementary notions to (1) clarify meaning of "set , (2) suggest why the notion of set is an important one, and (3) give some hints as to how a teacher might use the word in the classroom. (RP)

This book contains revised versions of the major papers presented at the Research Agenda Project Conference on Number Concepts in the Middle Grades. It is organized into three major sections, along with an introductory chapter and two brief summaries. Part I includes chapters that deal primarily with analyses of subject matter. The four chapters…

This collection of activities demonstrates how the study of elementary mathematics can be extended beyond the school and involve teachers and students in investigative, problem-based experiences. The activities include topics in geometry, concept of number, algebra, measurement, graphing, statistics, and probability, and are organized into five…

This curriculum guide presents a program of 20 open-ended math activities to be used to supplement the math programs in kindergarten, first, or second grade classrooms. The program consists of child-oriented counters and gameboards used to explore the concept of number from counting to making up and solving addition and subtraction equations. Each…

This book contains 15 chapters: (1) "Teaching Problem Solving"; (2) "Using Calculators and Computers in Elementary School Mathematics"; (3) "Organizing for Instruction"; (4) "Teaching Numeration of Whole Numbers"; (5) "Teaching Numeration of Common and Decimal Fractions"; (6) "Teaching Addition and Subtraction of Whole Numbers"; (7) "Teaching…

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…

The "Curriculum and Evaluation Standards for School Mathematics" (1989) provides a vision and a framework for revising and strengthening the K-12 mathematics curriculum in North American schools and for evaluating both the mathematics curriculum and students' progress. The document not only addresses what mathematics students should…