First graders at three different schools were individually interviewed to determine their understanding of missing addend problems. Details of the interview are provided. Behaviors separating successful from unsuccessful students, students' number conservation ability, and the abstractness of missing-number problems are discussed. (DT)

The teaching of different number bases to elementary school children is questioned. (DT)

An ant city is used as the basis for counting and other numerical activities. (DT)

This article shows that the recognition of the dualities in equality (operator-equivalent) of the minus sign (unary-binary) and the zero (nullity-totality) during the transitional process from arithmetic to algebra by 12-13 year-old students constitutes a possible way to achieve the extension of the natural number domain to the integers. (Contains…

This paper provides some guidance as to what to listen for to help students make sense of expressions in ways that connect to their ideas and honestly address the mathematics of rational numbers. It offers a reasonable initial answer to the question, "Where do students' ideas about fractions and ratios come from, and how can we work productively…

The objective of preschool teachers should be to determine the mathematical ability of preschool children and improve their skills using meaningful teaching methods through pictorial demonstration and manipulative models. Children who receive number concept instruction through hands-on play models, activities, and discussion show greater…

Fractions and division are two topics that receive considerable attention in elementary school mathematics, particularly in grade three and beyond. Despite this attention, fraction and division concepts and skills prove difficult for many middle school students to learn and for teachers to teach. This paper reports on part of a larger study…

The rationale of this study is based on the premise that the outcomes of children's learning are specifically shaped by the interaction of their individual cognitive structures with the presentations of curricular content in the classroom. Therefore, since the interpretive tools that children apply to instructional content may vary substantially,…

This textbook is designed for common schools, normal schools, high schools, academies, and other schools. Among the topics covered are: arithmetical language, fundamental operations, prime numbers, fractions, practical measurements, percentages, ratios, and mensuration. A section providing miscellaneous problems is also included. Appendices…

Discusses children's concept of number and number operations and describes activities which help to develop number concepts and skills. (JP)

Examples are presented in which students are able to answer test items requiring manipulation of numbers for such topics as reducing fractions, but lack understanding of the operation. In addition to paper-and-pencil test, interviews are recommended for evaluating a student's understanding. (JP)