This paper proposes structural modification of the Clarke and Hollingsworth (2002) Interconnected Model of Teacher Professional Growth (IMTPG) based on results from doctoral research that studied the changes in mathematical knowledge and beliefs of two Year 5/6 teachers as they implemented a four-week, innovative curriculum unit. These inclusions…

Young children spend a much greater amount of time on practicing multiplication facts compared to understanding the concept of multiplication. When students have long-term, foundational concepts rather than a series of fragmented algorithms or facts, they are more likely to understand and generalize the mathematics. Using generalized models that…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

Competence with fractions is foundational to acquiring more advanced mathematical skills. However, achieving competency with fractions is challenging for many students, especially for those with mathematics learning difficulties who often lack foundational skill with whole numbers. Teaching fractions is also challenging for many teachers as they…

Research findings in the field of Mathematics Education emphasize that storytelling is an effective instructional tool in the teaching of mathematics, as it provides a meaningful context that attracts students' interest and makes learning a pleasant process. The use of stories and fairy tales in the teaching of mathematics motivates students to…

Recent data from a cross-national assessment, the Programme for International Student Assessment (PISA), place the United States performance in mathematics at 38 out of 71 countries (OECD, 2016)--one clear indication of the ongoing need for the improvement of mathematics education. This improvement relies, in part, on improving undergraduate…

This dissertation reports three studies of students' and teachers' meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual's schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is…

In this review, we attempt to integrate two crucial aspects of numerical development: learning the magnitudes of individual numbers and learning arithmetic. Numerical magnitude development involves gaining increasingly precise knowledge of increasing ranges and types of numbers: from non-symbolic to small symbolic numbers, from smaller to larger…

This study begins by connecting semantic elaboration with conceptual understanding and syntactic elaboration with procedural understanding in the context of fractions. Through case studies and discourse analysis, the work and communication of students in fourth through sixth grade is analyzed to determine the extent of their semantic and syntactic…

The study of primary teacher students' knowledge of fractions is very important because fractions present a principal and highly complex set of concepts and skills within mathematics. The present study examines primary teacher students' knowledge of fraction representations in Slovenia and Kosovo. According to research, there are five…

Mathematics teacher professional-development (PD) programs based on Cognitively Guided Instruction (CGI) have been developed and implemented with tens of thousands of elementary mathematics teachers worldwide since the 1980s. Starting with a focus on addition and subtraction on whole numbers in the first CGI PD program, the content of these…

This report provides evidence of the substantive and structural validity of the Knowledge for Teaching Elementary Fractions Test. Field-test data were gathered with a sample of 277 elementary educators, including teachers, administrators, and instructional support personnel, in fall 2016, as part of a larger study involving a multisite…

In Vietnam, primary school students explicitly learn the concept of fraction in Grade 4 and 5. Because this concept is introduced to them intuitionally, it is difficult for them to understand and apply it. Base on this point, we believe that the students will commit many errors when solving exercises related to this concept. The survey of 478…

The importance of the knowledge of fractions in mathematical learning, coupled with the difficulties students have with them, has prompted researchers to focus on this particular area of mathematics. The term "fraction proficiency" used in this article refers to a person's conceptual comprehension, procedural skills and the ability to…

Most students can follow this simple procedure for division of fractions: "Ours is not to reason why, just invert and multiply." But how many really understand what division of fractions means--especially fraction division with respect to the meaning of the remainder. The purpose of this article is to provide an instructional method as a…