In a previous study, we posited a link between Chinese sixth grade students' problem solving and problem posing based on a pattern-formation strategy (Cai & Hwang, 2002). A similar parallel structure between problem solving and problem posing did not obtain for the U.S. sixth graders in the study. The present study attempts to locate this type of…

Discusses geometrical reasoning in the framework of the theory of Figural Concepts to highlight the interaction between the figural and conceptual components of geometrical concepts. Examples of students' difficulties and errors in geometrical reasoning are interpreted according to the internal tension that appears in figural concepts resulting…

This paper reviews special considerations in teaching higher order thinking skills to students with mild disabilities, focusing on curriculum implications; principles of instruction (prior knowledge, connections between new and existing knowledge, self-regulated learning, and impact of social setting); the use of an anchored instructional…

Eight teachers were interviewed concerning how students verify conjectures. The study is a sequel to a previous study, "How Students Verify Conjectures" [Bergqvist, T. (2000). "How students verify conjectures." "Research reports in Mathematics Education" 3]. Teachers' expectations of students' reasoning and performance are examined, and also how…

This paper describes Topdown Conceptual Analysis (TCA) and how it can be used to produce the knowledge base for the development of courseware. Some of the prerequisites and basic theories behind TCA are explained. In discussing what is meant by learning and teaching a concept, an explanation is given of how a complex concept can be taught in terms…

This ERIC digest examines recent research about the use of manipulatives to teach mathematics. "Manipulatives" refers to objects that can be touched and moved by students to introduce or reinforce a mathematical concept. The digest also speculates on some of the challenges affecting future use of manipulatives. Since the 19th century,…

This pamphlet reviews five reports that highlight an emerging consensus among researchers about the value of systematically incorporating cognitive instruction into the elementary school curriculum. First is a comprehensive framework by Robert J. Marzano and C. L. Hutchins for an integrated approach to thinking skills that has been developed and…

The papers contained in this document were originally presented at the May 1978 conference on Modeling Mathematical Cognitive Development sponsored by the Models of Learning Mathematics Working Group of the Georgia Center for the Study of Learning and Teaching Mathematics. Most have been revised to reflect comments and suggestions made at the…

Some potential difficulties involved in using "real-life situations" in teaching problem solving are illustrated with a racing car problem. The importance of developing mental images and the ability to abstract in the solution process is indicated. (MP)

An examination of the effects of different types of review questions on the transfer skills of seventh grade math students indicates that relatively difficult review questions can effectively facilitate the retention of these skills. (JD)

This article presents specific instructional approaches and examples to develop the algebraic reasoning skills of middle and secondary students with mild disabilities. Discussion of the National Council of Teachers of Mathematics standards identifies general principles, content standards, and process standards. Discussion of effective instruction…

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

Ten remedial mathematics exercises are provided for children who have failed to integrate or apply their math skills. The exercises provide remediation through systematic experimentation, rather than abstract drills, by using number-configuration distinction with blocks, fractioned candy bars, decimal match sticks, graphed pictures, etc. (JDD)

This study investigated the effects of combining interactive microcomputer simulations and concrete activities on the development of abstract thinking in elementary school mathematics. Students in grades 2-4 were assessed on tasks involving designs and patterns. (MNS)

Concepts from cognitive psychology are presented as an alternative framework to arithmetic instruction for students with disabilities. The approach, which emphasizes reasoning, communication, and problem solving, is applied to addition, division, multiplication, subtraction, and word problems. The purpose of arithmetic instruction is asserted to…