The purpose of this three-paper manuscript dissertation is to add value to the limited knowledge base of research surrounding the quality of teacher-child interactions in pre-k mathematics contexts. The first paper, based on an extensive review of literature, presents a theoretical basis for using five-frames to support children's development of…

The purpose of this qualitative case study was to determine the effect of lesson study on teachers' mathematical understanding. This study reviewed a three year program called SEISMIC which implemented lesson study within a school district. The goal was to increase teacher and student understanding of mathematics' Teacher understanding of…

This article is the third in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation". In this article the author focuses on what learners have to understand and learn in order to do secondary mathematics well in general terms. She is assuming a…

The goal of this longitudinal study is to examine the relationships between early child factors (i.e., age at identification, enrollment in early intervention, oral language skills) and school readiness skills (i.e., conceptual knowledge) in a group of young children with hearing loss (HL). Standardized language, cognition, and conceptual…

Not knowing multiplication facts creates a gap in a student's mathematics development and undermines confidence and disposition toward further mathematical learning. Learning multiplication facts is a first step in proportional reasoning, "the capstone of elementary arithmetic and the gateway to higher mathematics" (NRC 2001, p. 242). Proportional…

Fifty-two exceptional education pre-service teachers getting a K-6 endorsement were involved in this study that investigated the changes in levels of mathematics anxiety before and after a mathematics methods course for education majors. The changes were measured with respect to the use of manipulatives and other activities to make mathematics…

This study examines presentations of the distributive property (DP) in two widely used U.S. elementary text series and one main Chinese text series along three dimensions: problem contexts, typical problem types within each problem context, and variability in using the DP. In general, the two U.S. texts were found to resemble each other but to…

Action research (AR) is defined by Macintyre to be: "an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a problem,or a topic or an issue which needs to be explained, and on the basis of information, plans, implements, then evaluates an action then draws conclusions on the basis of…

Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

Contributions of domain-general and domain-specific numerical competencies were assessed on first graders' number combination skill (NC) and word-problem skill (WP). Students (n = 205) between 5 and 7 years of age were assessed on 2 aspects of numerosity, 8 domain-general abilities, NC, and WP. Both aspects of numerosity predicted NC when…

A concept inventory is a standardized assessment tool intended to evaluate a student's understanding of the core concepts of a topic. In order to create a concept inventory it is necessary to accurately identify these core concepts. A Delphi process is a structured multi-step process that uses a group of experts to achieve a consensus opinion. We…

Previous research on children's conceptual and procedural understanding of fractions, and other arithmetic skills, has led to contradictory conclusions. Some research suggests that children learn conceptual knowledge before procedural knowledge, some suggests that they learn procedural knowledge before conceptual knowledge, and other research…

To focus on mathematical reasoning and what makes a good argument, the authors developed an assignment that requires college students to submit a book of mathematical reasoning as an assessment during the semester. To begin, the authors looked for questions and tasks that lend themselves to developing mathematical arguments and justifications and…

Aerial imagery has a great capacity to engage and maintain student interest while providing a contextual setting to strengthen their ability to reason proportionally. Free, on-demand, high-resolution, large-scale aerial photography provides both a bird's eye view of the world and a new perspective on one's own community. This article presents an…

Middle school mathematics classrooms are changing. The curriculum has changed as well. Instead of an annual return to previously encountered topics, many middle school students encounter mathematics of a varying nature, characterized in "Principles and Standards for School Mathematics" (NCTM 2000) as the five Content Standards of Number and…