This article describes students learning to build their own numbering system by recognizing and identifying patterns with interlocking cubes in different place values. The students used the Egyptian hieroglyphic numeral system in conjunction with this activity to connect learning in other subjects. Students used prior knowledge of place value to…

In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not…

This report delineates the outcomes of an intervention conducted with in-service high school educators, focusing on elucidating three distinct scenarios within geometric and arithmetic domains: the infinitely large, infinitely numerous, and infinitesimally close. Grounded in the theoretical framework of conceptual change, it is posited that when…

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively,…

Early measures of mathematics skill and development have focused on early numeracy skills like counting, number identification, and sequencing of numbers. This study attempted to expand early mathematics assessment. Six new measures of early mathematics skill competence were developed and evaluated. Four existing measures also were examined.…

This article describes how first graders' sense of number can be developed through the perspective of measurement. (Contains 5 figures.)

A solid understanding of equivalent fractions is considered a steppingstone towards a better understanding of operations with fractions. In this article, 55 rural Australian students' conceptions of equivalent fractions are presented. Data collected included students' responses to a short written test and follow-up interviews with three students…

The use of a multiple approach using both geometric and algebraic contexts is suggested in teaching concepts. Several examples are given including area and multiplication, length and number, and functions and power. (MP)

Multi-shaped blocks can be used to help young children develop many mathematical concepts and abilities. Several suggestions for using these blocks to create problem situations through which children develop concepts are offered. (SD)

This workbook for children was prepared especially to accompany the level 1 Micronesian Mathematics Program Teacher's Guide. It is to be used to check whether children have learned concepts taught by activities and activity cards. Work is provided for such concepts as color recognition, categorizing, counting, ordering, numeration, contrasting,…

This booklet develops the theme that young children best learn mathematics through exploration of their environment. Several activities designed to promote the learning of concepts about space, numbers, and measurement are illustrated. Also discussed is the role of the teacher in sequencing instruction, selecting materials, and maintaining the…

Numerous mathematical examples are presented which illustrate and raise questions about students' tendencies to overgeneralize. (BB)

An outline of practical experiences from which the concept of length measurement may be learned. (MM)

Investigated children's preferred learning styles when exploring spatial concepts. Found that young children first develop the spatial concept of topology, which supports Piaget's theory, followed by the concepts of position. The two separate groups of children appeared to exhibit different learning styles when exploring space concepts. (AP)

Using case studies that are functionalist in orientation and computational in technique, the role of control knowledge in developing constructive thinking is illustrated. Further, the integration of related knowledge structures, emanating from diverse sensory modes and pertaining to both place value in addition and angle relationships in geometry,…