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…

Area models are an important strategy for representing and solving multiplication problems under the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010). The hands-on task presented in this article, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around…

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…

Improving children's "number sense" has been a core component of recent mathematics curricular and instructional reforms (CCSS, 2010; NCTM, 2000, 2014) in the United States. Students with mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient…

Facilitating meaningful discourse directly supports what students should be able to do with respect to the third of the eight Standards for Mathematical Practice (SMP 3) in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010): "Construct viable arguments and critique the reasoning of others" (p. 6). Following best…

The benefits of content writing are widely recognized, yet there are still few studies that evaluate the benefits and challenges of mathematical writing (MW) for students. The National Council of Teachers of Mathematics and the Common Core State Standards for Mathematics have an emphasis on written communication of mathematical reasoning as an…

In conjunction with the Council of Chief State School Officers (CCSSO) and governors across the nation, the initial drafts of the Common Core State Standards (CCSS) were introduced in 2009 with the final draft being released in 2010. With a goal of eliminating stagnant academic progress, the Standards were written to outline precisely what…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

The twenty-first century has seen an increased call to train students to craft mathematical arguments. The third of the Common Core's (CCSS) Standards for Mathematical Practice (SMP 3) (CCSSI 2010) calls for all mathematically proficient students to "construct viable arguments" to support the truth of their ideas and to "critique…

The article uses vignettes to illustrate a small group of of grade 5 students who worked on different types of temperature problems (Wessman-Enzinger and Tobias 2015). The Common Core State Standards for Mathematics (CCSSM) recommends including contexts, such as temperature, paired with the introduction to integers in grade 6 and integer…

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…