This qualitative case study aims to address the ways that pre-service mathematics teachers (PSTs) used a rope in a daylong research meeting for cognitive development of children's understanding of counting numbers in Tanzanian elementary schools. Three university mathematics pre-service teachers volunteered participating in this study. Collective…

Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…

The need for global competence in mathematics is apparent. Algebra is considered a gateway course to prepare students for the demands of a competitive global market. Many students demonstrate low performance in algebra; this is especially true for students with disabilities. Effective algebra instruction is essential to increase algebra…

An exploratory investigation designed to gain insights into children's mathematical formulation of observed actions upon objects is presented. Eight episodes in which first and second graders were asked to interpret, in terms of number sentences, a sequence of actions with unifix cubes are also presented. Results of analysis of the videotaped…

Some possible uses of math lab materials and activities that are natural and appropriate to the development of process skills are explored through a discussion of a geoboard activity. (MP)

Investigated what effects two instructional strategies (related to student use of manipulative materials) would have on second-grade students' (N=96) development of logical structures. Also examined the effects of sex on logical development. Results indicate that supplying manipulative materials alone is not adequate in promoting development of…

Discusses how teachers can help students make the transition from using manipulative materials to abstract mathematical symbols. Includes: (1) a definition of the transition state; (2) ways to bridge the gap (by asking questions and by using activities); and (3) a specific example (teaching place value). (JN)

Presents activities that have been used successfully in leading students from concrete experiences through pictorial and symbolic representations of important numeration concepts and patterns, including place value, multiples, and rounding. Each activity includes concept or skill fostered, list of materials needed, recommended grade level, and…

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;…

Applies the Lesh Translation Model to develop conceptual understanding by showing relationships between five modes of representation proposed by Lesh to learn multiplication of fractions. Presents five teaching activities based on the translation model. (MDH)

This paper describes an educational program developed on the basis that the use of blocks and other manipulatives can be useful both for initial teaching of exchange operations in arithmetic and for remediation of the faulty strategies which very commonly arise during acquisition of written calculation algorithms. This computer program is a…

Investigates issues of conceptual understanding in teaching and learning mathematics provided conceptually based instruction on place value and two-digit addition and subtraction without regrouping in four first grade classrooms. Conventional textbook-based instruction was provided in two first grade classrooms. Experimental-group students scored…

Concrete experience should be a first step in the development of new abstract concepts and their symbolization. Presents concrete activities based on Hyde and Nelson's work with egg cartons and Steiner's work with money to develop students' understanding of partitive division when using fractions. (MDH)

Traditional methods of teaching addition include algorithms that involve right-to-left procedures. This article describes efficient procedures for left-to-right addition and subtraction involving computation and computational estimation that reflect children's natural behaviors observed during activities with unifix cubes. (MDH)