In response to claims that the quality (and in particular linearity) of children's mental representation of number acts as a constraint on number development, we carried out a longitudinal assessment of the relationships between number line estimation, counting, and mathematical abilities. Ninety-nine 5-year-olds were tested on 4 occasions at 3…

Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions…

The purpose of this study was to evaluate the effectiveness of School Improvement Grants (SIGs) in the state of California (CA) in increasing student achievement using the turnaround implementation model. The American Recovery and Reinvestment Act of 2009 (ARRA) included educational priorities focused on fixing America's lowest achieving schools.…

"enVisionMATH," published by Pearson Education, Inc., is a core curriculum for students in kindergarten through grade 6. The program seeks to help students develop an understanding of math concepts through problem-based instruction, small-group interaction, and visual learning with a focus on reasoning and modeling. Differentiated…

Although there is growing interest in implementation fidelity, little research has been reported on the sustainability over time of faithful implementations of learning innovations. This study examined the sustainability of teachers' implementation fidelity to the components of a prekindergarten mathematics intervention two full years after…

This paper discusses what being involved in a mathematical inquiry project looks like from two classroom teachers' perspectives, gained throughout six years spent in a longitudinal study. Collaboration amongst all stakeholders has resulted in a deeper understanding of the thinking and reasoning required in the inquiry process and has led to…

In this paper, we propose and describe in some detail a framework for helping low achievers in mathematics that attends to the following areas: Mathematical content resources, Problem Solving disposition, Feelings towards the learning of mathematics, and Study habits.

Early number sense knowledge is highly predictive of later math achievement (Herbers et al., in press; Jordan, Kaplan, Ramineni, & Locuniak, 2009; Obradovic i et al., 2009). However, research suggests that variables beyond number competencies contribute to students' mathematics achievement, most notably, executive function (Blair & Razza,…

Minority and low-income students are less likely to have access to, enroll in and succeed in higher-level math courses in high school than their more advantaged peers. Under these circumstances, higher-level math courses function not as the intellectual and practical boost they should be, but as a filter that screens students out of the pathway to…

This module assumes that the information presented in previous modules is well known to the learner. Module 6 is the third of three modules (4, 5, and 6) designed to provide an in-depth look at the Standards of Mathematical Practice which are part of the Common Core State Standards for Mathematics. Module 6 focuses on strategies for implementing…

Previous research has demonstrated the effectiveness of particular instructional practices that support students' constructions of the partitive unit fraction scheme and measurement concepts for fractions. Another body of research has demonstrated the power of a particular mental operation--the splitting operation--in supporting students'…

Purpose: The paper aims to explore the academic performance (measured by quality points (QP)) of undergraduate business students in introductory courses of quantitative methods at a private university in the United Arab Emirates (UAE). It also examines the impact of a number of academic and demographic factors pertinent to the performance of the…

"Saxon Math," published by Houghton Mifflin Harcourt, is a core curriculum for students in grades K-5. A distinguishing feature of the curriculum is its use of an incremental approach for instruction and assessment. This approach limits the amount of new math content delivered to students each day and allows time for daily practice. New…

Computer assisted learning (CAL) programs have been shown to be effective in improving educational outcomes. However, the existing studies on CAL have almost all been conducted over a short period of time. There is very little evidence on how the impact evolves over time. In response, we conducted a clustered randomized experiment involving 2741…

This article focuses on "the unexpected" in relation to teacher change. We take an enactivist approach to charting the parallel development of one teacher (Hannah) as she learnt to value and plan for unexpected events in her mathematics classroom, and one of her students as he learnt to notice and trust mathematical patterns. Shifts are…