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…

"Where Mathematics Comes From" (Lakoff & Núñez 2000) proposed that mathematical concepts such as arithmetic and counting are constructed cognitively from embodied metaphors of actions on physical objects, and four actions, or 'grounding metaphors' in particular: collecting, stepping, constructing and measuring. This article argues…

This study examined the pedagogical content knowledge of pre-service preschool teachers on quantity concepts in terms of children's mistakes. A total of 94 pre-service teachers who were attending a teacher training program at a state university, in Turkey, participated this study. 52 of them were second-year, and 42 of them were third-year…

Conceptualizing numbers as discursive constructs generated in, and for the sake of, communication, we investigated the development of the numerical discourse of Milo, a boy who was 2 years and 8 months old when we first met him and whom we then followed for 18 months. Our analyses of the child's evolving responses to the question "Where is…

A lack of numerical knowledge early on can impede a child's academic development. In past research, playing linear board games improved children's understanding of numerical relations, which the authors theorised could extend to children with autism spectrum disorder. For this pilot study, 10 children played a board game where they moved tokens…

Understanding place value is a critical and foundational competency for elementary mathematics. Classroom teachers who endeavor to promote place-value development adopt a variety of established practices to varying degrees of effectiveness. In parallel, researchers have validated models of how young children acquire place-value understanding.…

The ability to count has traditionally been considered an important milestone in children's development of number sense. However, using counting (e.g., counting on, counting all) strategies to solve addition problems is not the best way for children to achieve their full mathematical potential and to prepare them to develop more complex and…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

Many students encounter difficulty in their transition to advanced mathematical thinking. Such difficulty may be explained by a lack of understanding of many concepts taught in early school years, especially multiplicative reasoning. Advanced mathematical thinking depends on the development of multiplicative reasoning. The purpose of this study…

Students with special needs require unique intervention strategies as they enter infant care and preschool environments. The techniques and materials discussed in this paper are designed especially for the child's unique abilities and disabilities. This paper will also focus on the skills needed for infants who have been identified as requiring…

Field experience during teacher preparation enables the prospective teacher to observe children as they develop -- emotionally, socially, intellectually, and physically. Children, at different stages of development, exhibit characteristics of behavior which may or may not affect how and what they learn in the formal classroom environment. Thus,…

This article elaborates on three principles which are the foundation of the developmental approach to early childhood education. These principles are multiage grouping, nongraded curricular materials, and interactive teaching. (IAH)

A project conducted several years ago to develop informal mathematical learning experiences at kindergarten level is compared with the results of the work-book type (formal) program being used at that time. It is hypothesized that kindergarten pupils who study mathematical concepts in a planned, sequential, systematic, but non-workbook (informal)…

This document was developed to provide some perspectives on the use of case studies and other clinical approaches in mathematics education. A large portion of the paper contrasts several research strategies, discussing in detail some of the procedures and results of three distinctive types of clinical studies. The perspectives and the premises of…