This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

This study aimed to determine the impact of the Math Matters Program on student achievement in third- and fourth-grade math and to understand leaders' perceptions of the Math Matters Program. Researchers analyzed end-of-year or spring Northwest Evaluation Association and Measures of Academic Preparation math results across treatment and control…

This study aimed to determine the impact of the Math Matters Program on student achievement in third- and fourth-grade math and to understand leaders' perceptions of the Math Matters Program. Researchers analyzed end-of-year or spring Northwest Evaluation Association and Measures of Academic Preparation math results across treatment and control…

Teachers across the United States have implemented the Common Core State Standards (CCSS) in math since their release in 2010. These standards were created for all students, both in general education and special education settings; yet, the findings of this study showed one set of standards for every student does not make every student…

We respond to a call to analyze issues of curriculum standards and to present alternative storylines by addressing criticisms of the Common Core State Standards in early childhood. We describe a storyline from multiple media and evaluate this storyline's criticisms, focusing on the criticism that the standards are developmentally inappropriate. We…

Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific…

The Common Core State Standards for Mathematics (CCSS-M) aim to engage students in complex mathematical practices, including modeling, reasoning, and argumentation. Currently, little is known about how teachers' daily instruction supports these practices. This study draws upon data from daily logs completed by third-, fourth-, and fifth-grade…

Using the method of educational criticism and connoisseurship, this study examined third grade teachers' pedagogical choices made to prepare their students for high stakes testing under the Common Core Standards. Three teachers in three different suburban school settings within a large district in one of the states of the Rocky Mountain West…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) outlines ambitious goals for fraction learning, starting in third grade, that include the use of the number line model. Understanding and constructing fractions on a number line are particularly complex tasks. The current work of the authors centers on ways to successfully…

International rankings show children in the United States perform well below average in mathematics. There are also large mathematics achievement gaps between children of lower- and higher-socioeconomic status. As today's teachers face these challenges, they are also faced with the pressures of sweeping educational reforms that arrived with the…

A fundamental claim for Common Core State Standards (CCSS)-aligned assessments is that they will lead to better teaching practices. The purpose of this study is to seek evidence in support of this claim by surveying teachers about their instructional practices, test preparation strategies, and test score use both before and after the introduction…

During the past few years, several of the authors have incorporated student problem posing as a regular instructional feature in their classrooms. When they offer their students the opportunity to construct their own problems, particularly during the course of an entire school year, they create many novel tasks. Student-created tasks not only…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

A "repeating pattern" is a cyclical repetition of an identifiable core. Children in the primary grades usually begin pattern work with fairly simple patterns, such as AB, ABC, or ABB patterns. The unique letters represent unique elements, whereas the sequence of letters represents the core that is repeated. Based on color, shape,…

Students' development of conceptual understandings is a central goal of mathematics education (CCSS-Mathematics, 2010). Such a challenging, yet ambiguous, goal cannot be achieved without empowering teachers with the knowledge and tools critical for their ability to adequately convey the content, and assess and interpret students' performance. This…