Three diagnostic questions are presented and discussed to help locate a child's difficulty in problem solving. (JT)

The authors describe a series of magic tricks based on computation which they use in elementary and secondary school mathematics classes to motivate and challenge students. (SD)

Investigated was the effect of prior experiences on the acquisition of number conservation by 10 mildly and 10 moderately retarded students (7-16 years old). (CL)

In the study of mathematics instruction the focus has changed from the outcomes of learning to the cognitive processes involved in mathematics learning. This new emphasis presents a serious challenge for curriculum design, but it may also lead to more success for students in learning mathematics. (Author/VM)

Describes the characteristics of progressive schematization with regard to column multiplication and column division. Contrasts this with column arithmetic based on progressive complexity. Presents a summary of research data concerning column arithmetic. (TW)

Discusses the use of the Rhind Mathematical Papyrus to motivate classroom activities related to computation and place value using the Egyptian number system. (PK)

This study showed that Oksapmin children not only spontaneously use the indigenous numerical system of their nontechnical culture but also have created new forms of numerical symbolization and calculation to deal with schooling arithmetic problems. Novel conceptual developments, factors mediating the schools effect, and the influence of prior…

Discusses procedures used throughout history to solve fractional and decimal divisor problems. Early rules and definitions, approaches in mathematics and methods books, "new math" approaches, research findings, and recent textbook procedures are included. Concludes by presenting nine recommendations for teaching the operation. (DH)

Reports that microcomputer use will help six year-old children solve some types of problems better but will not improve their general learning and thinking abilities. Logo programing resulted in higher creativity scores and in children's ability to monitor their own thinking, but revolutionary changes in cognitive development were not found. (DH)

Three lessons are outlined which employ "scholar dollars," pretend bills and coins of different denominations that students can make and use to help solve subtraction, division, and decimal problems. The technique clarifies difficult mathematical concepts by making them less abstract. (PP)

A longitudinal study of students' developing understanding of decimal notation has been conducted by testing over 3000 students in Grades 4 to 10 up to 7 times. A pencil-and-paper test based on a carefully designed set of decimal comparison items enabled students' responses to be classified into 11 codes and tracked over time. The paper reports on…

This book features a comprehensive review of the Math Sense series and is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include whole numbers;…

This paper considers whether or not curriculum initiatives within England are in fact leading to qualitatively improved levels of thinking among children identified as lower achievers in arithmetic. Revisiting data from two earlier studies and introducing current data, the paper draws comparisons in the strategies that 8-year-old children use to…

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

This book sets out a constructivist, inquiry-based approach to instruction. The approach builds on clear understandings of children's current levels of knowledge, where their learning should progress to, and the means by which children learn early numeracy topics. The methods presented in this book have been used extensively by practitioners in…