Students were pretested, then 27 first graders were trained using a highly verbal procedure emphasizing class addition activities. On posttests, trained subjects significantly improved their class inclusion and number conservation scores, but no effects were found for substance conservation or transitivity. (DT)

An explanation is given for the development of the Roman numeral system in terms of the smallest number of marks required to enumerate items. (RM)

Six units of instruction, each including a variety of activities involving ratios, are presented. (DT)

Ways of combining mathematics and coding are discussed, with a wide variety of applications given. (DT)

A simple model that portrays both addition and subtraction of positive and negative numbers is explained. (DT)

Paper folding and coloring activities are presented which involve the use of rectangular and square regions as models for basic fraction concepts. Rules for a fraction game also are included. (DT)

This paper describes the Rational Number Project (RNP), teaching experiments concerned with the teaching and learning of fractions among 4th and 5th grade students. Interviews with 4th grade students who used the RNP curriculum and with students who used a traditional curriculum were conducted by RNP staff as well as classroom teachers. This paper…

The development of proportional reasoning is a major focus of the middle grades curriculum. The challenge for educators is to find contexts that engage students and that facilitate the study of proportional reasoning. This chapter explores proportional thinking with students in grades 3-8 by using a number of books in which the underlying stories…

This yearbook contains articles that give insight into students' thinking about factions, ratios, and proportions. Suggestions are offered on how to develop the concepts and skills associated with these topics. The book is divided into elementary, middle school, and professional development sections. Chapters include: (1) "The Development of…

Noting that current research on childrens mathematical development does not adequately detail how toddlers represent small numbers and the role that number words play in the development of number understanding, this study used a combination of methods to examine mathematical development in one toddler. Underlying the study was an Integrated Model…

Seventh and eighth grade students identified as holding an incomplete fraction conception of decimals were tested on related fraction knowledge. Most of these students (78%) had a problem in coordinating the size of the parts and the number of parts in comparing fractions. These students underwent several instructional sessions. Half of them…

This book features a collection of 54 decimal number puzzles designed to provide experiences in problem solving and mathematical reasoning for middle and high school students. Each puzzle consists of a sequence of 10 clues about an unknown decimal number. The clues, when revealed one at a time, lead students through deductive reasoning to the…

This study involved examining the nature and scope of numeracy, distilling out the important features, and representing these features in sample numeracy materials. The paper examines the precise nature of numeracy and its scope in enhancing the educational experiences of adult learners. It is intended to discuss the characteristics of the adult…

This paper describes an action research project that investigated issues concerning the teaching and learning of numeracy in the middle years. Building on research concerning the middle years of schooling, and their own experience of teaching mathematics in years 5-8, a group of teachers, drawn from four schools, trialed strategies intended to…

This report describes a classroom observation study in Korean primary mathematics classrooms. What was discovered in Korean classrooms was children, through higher level questioning, were being led to conceptualize the constructs and operations. The textbook was focused on the concepts in a concise, coherent and systematic manner similar to what…