Mathematical modeling has taken on increasing curricular importance in the past decade due in no small measure to the Common Core State Standards in Mathematics (CCSSM) identifying modeling as one of the Standards for Mathematical Practice (SMP 4, CCSSI 2010, p. 7). Although researchers have worked on mathematical modeling (Lesh and Doerr 2003;…

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…

The Common Core State Standards for Mathematical Practice (CCSSI 2010) elevate the ways of thinking used to create mathematical results to the same level of importance as the results themselves. These mathematical habits of mind (MHoM), or "specialized ways of approaching mathematical problems and thinking about mathematical concepts that…

The recent focus on computational thinking as a key 21st century skill for all students has led to a number of curriculum initiatives to embed it in K-12 classrooms. In this paper, we discuss the key computational thinking constructs, including algorithms, abstraction, and automation. We further discuss how these ideas are related to current…

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…

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…

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

Surveys were used to examine mathematics teachers (15) on their ability to solve similarity problems and on their likely implementation of lesson objectives for teaching similarity. All correctly solved a similarity problem requiring a traditional static perspective, but 7 out of 15 failed to correctly solve a problem that required a more…

In recent years, learning progressions (LPs) have captured the interest of educators and policy makers. There have been numerous efforts to develop LPs aligned to college and career readiness standards, to unpack these standards, and to provide more clarity on the pathways students follow to reach them. There is great variation, however, in the…

Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

With the June 2, 2010, release of the Common Core State Standards, state-led education standards developed for K-12 English Language Arts and Mathematics, Pearson Learning Assessments and content experts conducted an in-depth study to analyze how the "Stanford 10 Achievement Test Series," Tenth Edition (Stanford 10) and Stanford 10…