Tape diagrams, also known as strip diagrams, bar models, fraction strips, or length models, are linear representations that can be used to effectively model quantitative relationships during problem solving. Tape diagrams are a powerful model recommended by the Common Core, but they are relatively new to teachers and students in the United States.…

Effective use of mathematical representation is key to supporting student learning. In "Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014), "use and connect mathematical representations" is one of the effective Mathematics Teaching Practices. By using different representations, students examine concepts…

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

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;…

The Common Core State Standards (CCSS) began to take form when dozens of educators from across the country were led by governors and chief state school officers in gathering and reviewing the academic standards of states that had the best outcomes. Their goal was to determine what the current best academic standards were in the country and then…

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…

With rigor outlined in state and Common Core standards and the addition of constructed-response test items to most state tests, math constructed-response questions have become increasingly popular in today's classroom. Although constructed-response problems can present a challenge for students, they do offer a glimpse of students' learning through…

To support elementary school students in finding a solution to an engineering problem, the authors developed a series of five lessons using the 5E Instructional Model (Bybee 2014). The lessons align with the "Next Generation Science Standards" and the "Common Core State Standards" and integrate the teaching and learning of…

In the last several years a good deal of public discourse was devoted to describing the effects that more than two decades of education reforms, the last iteration of which was known as the Every Student Succeeds Act (ESSA), has had on teaching and learning. It is widely argued that coupling teacher evaluations with students' test scores, enforced…

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…

This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

Many students with and/or at risk for emotional and behavioral disorders have academic deficits that affect their performance in mathematics. In addition, these students' behavioral issues may interfere with their academic achievement. For these students, it makes sense for teachers to consider implementing research- and/or evidence-based…

Preservice teachers (PSTs) must be able to link content, effective teaching practices, and student learning; thus, it is critical for teacher educators to emphasize connections between research and practice in methods courses. Reflection plays an important role in this process. In this article, the authors discuss and illustrate a vignette…

Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…