The National Assessment of Educational Progress (NAEP) provides data about what children know and can do with the goal of using this information to improve education. This book contains interpretive reports based on results from the mathematics assessments conducted by the NAEP regarding: (1) the cognitive performance of students at grades 4, 8,…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features that present book and software reviews and math problems. The first of two issues of volume 9…

Students can learn to solve problems of qualitative integration and differentiation independently of their study of formal calculus or algebra. This exploratory study investigated the basic intuitions that elementary school children construct in their daily experience with physical and symbolic change. Elementary school children (n=18) were…

This study was designed to: (1) outline briefly the meaning and importance of the family of concepts stemming from the ideas of estimation, approximation, checking, and precision; (2) survey the present place of such concepts in the curriculum; and (3) relate the teaching and learning of these concepts to the availability of the calculator as an…

A model for multiplication is described and used to discuss the properties of division. (SD)

It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of…

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

This document contains teaching modules based on 17 objectives for grade 3 mathematics. The modules may be used for program evaluation and curricular planning as well as detailed outlines for classroom activities. Each module has eight sections: (1) "Objective"; (2) "Explanation of Objective"; (3) "Prerequisite…

This document contains teaching modules based on 20 objectives in grade 5 mathematics. The modules may be used for program evaluation and curricular planning as well as detailed outlines for classroom activities. Each module has eight section: (1) "Objective"; (2) "Explanation of Objective"; (3) "Prerequisite Skills";…

Every child who enters a school system brings a different level of language mastery with which to recognize and express a different background of experience. This study examined the development of mathematical understanding and tested the efficacy of direct teaching to the target concepts. Two very similar districts in rural Idaho were selected.…

This material describes curriculum specifications for grade 3 mathematics in Alberta. Emphases are: (1) subject matter (60%); (2) problem-solving skills (20%); (3) psychomotor skills (10%); and (4) attitudes (10%). Priorities within each category are identified and suggested problem solving strategies are listed. (YP)

This study was designed to investigate whether the implementation and integration of the use of the Explorer Calculator into the curriculum influenced students in grades three through six. The sample consisted of approximately 440 students who were assigned to the treatment group or the control group. Achievement scores from the Iowa Test of Basic…

Independent neighborhood schools in inner-city areas serve primarily minority students. They are in a position to assist American educators in understanding the best methods of teaching minorities who usually do not reach their full academic potential in public schools. Teachers in independent schools use culture and sometimes religion as a basis…

Two central concepts in probability theory are those of independence and mutually exclusive events. This document is intended to provide suggestions to teachers that can be used to equip students with an intuitive, comprehensive understanding of these basic concepts in probability. The first section of the paper delineates mutually exclusive and…