This article discusses an approach designed for mathematics educators. Maria Montessori intended this knowledge to be shared with other teachers, increasing the Montessori community's understanding of children's thinking. A group of Montessorians has even tried to formalize this process with a program called Teachers' Research Network. Similarly,…

This research focuses on eliciting bilingual students' problem-solving reasoning by providing mathematical tasks designed to involve the students in the action described in the problem by making connections to contexts familiar to them. Results showed these tasks allowed children to articulate their mathematical reasoning through gestures and…

Compared with standard arithmetic word problems demanding only the direct use of number operations and computations, realistic problems are harder to solve because children need to incorporate "real-world" knowledge into their solutions. Using the realistic word problem testing materials developed by Verschaffel, De Corte, and Lasure…

This study focuses on the nature of preservice elementary school teachers' understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called "Number Worlds". In particular, the focus is on the concepts of factor, multiple and prime number. The notion of "thickness" is examined with respect to…

Traditional assessment methods are not always suitable for diagnosing learners' knowledge structures at different levels of their expertise. This paper describes an alternative schema-based rapid assessment technique and its application in the area of arithmetic word problem solving. The technique is based on an assessment of the extent to which…

Background and aims: In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between…

This publication offers excerpts from the National Courses of Study revised by the Ministry of Education in Japan. The first section discusses curriculum for kindergarten. It states that lessons must be presented at least 39 weeks a year and the standard number of class periods per day should occupy four hours. Content is classified into four…

This instructional guide and set of three companion workbooks are intended for use in an arithmetic course based on the Tic Tac Toe method of addition and multiplication, which is an alternative means of learning to add and multiply that was developed for students whose learning disabilities (including difficulty in distinguishing left from right…

The development of the place value system and its universal use demonstrate the elegance and efficiency of mathematics. This paper examines the concept of place value by: (1) presenting the historical development of the concept of place value in the Hindu-Arabic system; (2) considering the evolution of the number zero and its role in place value;…

This instructor's guide contains materials for a 20-30 hour course designed to address essential math skills in the workplace. The course description lists target audience, general objective, and typical results observed. The next section gives instructors basic information related to providing successful educational programs in a workplace…

This book describes how parents can develop a mathematical environment for children in the home. Four major areas are emphasized: whole numbers, fractions, decimals, and basic geometry. Section 1 "'Shoebox' Activities," provides activities to teach specific concepts within a manageable time period. Materials are listed and diagrams…

The report lists competencies for teachers in every day interactions with learning disabled students. Developed by a task force, the competencies are intended to serve as general guidelines. Information is presented on the goal, assessment competencies, and instructional competencies for the following areas: classroom management, spoken language,…

This guide contains six sections which offer suggested sequential steps for teaching addition, subtraction, multiplication, division, fraction concepts and algorithms, and decimal fractions. Based on the manipulative approach, the guide offers activities and teaching methods which give students many opportunities to work with models. This approach…

This research was concerned with the clarification of the role that the external representation process (e.g. drawing) plays in children's solving of complex arithmetic problems. Fourteen children in the 10- to 12-year-old age range were asked to represent and solve five complex arithmetic problems (three with temporal organization of data, two…

This book was written to help teachers to plan and implement an effective addition-subtraction basic fact program. When it is determined that children have gained an adequate concept for an operation, the next long-range goal is fact memorization. Children need to respond quickly and correctly to number facts and retain this learning over time. To…