Grades 4 and 8 students had shown slow but steady improvement in scores on the National Assessment of Educational Progress (NAEP) mathematics assessment from 1990 until 2013, but performance since then has been lower despite the introduction of the Common Core State Standards for Mathematics (CCSSM) in the early 2010s. This study examined 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…

The Common Core State Standards for Mathematics emphasize the importance of developing students' conceptual understanding, mathematical reasoning, and problem solving skills. This is a shift from the traditional approach to teaching mathematics and many teachers rely on curriculum resources to help them meet these new standards and expectations.…

The Common Core State Standards in Mathematics outline both the content and practices students must engage in at each grade level to become mathematically proficient. Mathematical processes include problem solving, reasoning and proof, communication, and procedural fluency, which includes flexible thinking. The purpose of this study was to…

Science, Technology, Engineering, and Mathematics (STEM) education initiatives have placed pressure on teachers to bring technology tools into classroom, including three-dimensional (3D) printing. Yet, little research has examined what specific math skills are required for 3D printing technology. This article describes a follow-up analysis of…

Statistics standards found in the Common Core (CCSSI 2010) and other state standards require considerable instructional time and focus for students to develop the depth and breadth of understanding necessary. In this article, the authors offer an approach to teaching a statistics unit that combines student choice with authentic and sustained…

The current project, Exploring Math Education Relations by Analyzing Large Data Sets (EMERALDS) II, is an attempt to identify specific Common Core State Standards procedural, conceptual, and problem-solving competencies in earlier grades that best predict success in algebraic areas in later grades. The data for this study include two cohorts of…

Long before the release of the Common Core State Standards (CCSSI 2010), the Mathematical Tug-of-War was engaging students in the type of reasoning and problem solving described by the Standards for Mathematical Practice (SMP). In this updated version of a Marilyn Burns task, students use algebraic reasoning to determine the outcome of a contest…

The year students take Algebra I historically determines how far they progress in secondary mathematics, creating complex equity issues around access to this course. By examining a case study of one large, urban school district adjusting to the Common Core State Standards in Mathematics (CCSS-M), we demonstrate how district leaders' interactions,…

In this article, the authors begin this inquiry by describing their research with a class of middle school writers who played "Quandary," a free online educational game designed to teach argumentation, as part of a unit on writing arguments for environmental action. Regarding the subject area of English language arts (ELA), research has…

Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

This article describes a type of professional development focused on students' thinking that occurs in middle school mathematics classrooms. This type of professional development is called "Classroom Embedded" and occurs over one or two days in a classroom with middle school students and their teacher. Teachers actively participate in…

Students engage in proportional reasoning when they use covariance and multiple comparisons. Without rich connections to proportional reasoning, students may develop inadequate understandings of linear relationships and the equations that model them. Teachers can improve students' understanding of linear relationships by focusing on realistic…

The Common Core's Standards for Mathematical Practice encourage teachers to develop their students' ability to reason abstractly and quantitatively by helping students make sense of quantities and their relationships within problem situations. The seventh-grade content standards include objectives pertaining to developing linear equations in…

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…