Understanding negative numbers can be challenging for many students, as these concepts may seem less tangible than counting objects, which are commonly represented by positive numbers. In addition, the multiplication of two negative numbers resulting in a positive might appear inconsistent and puzzling to young learners who are used to seeing the…

In this qualitative study, the researchers investigated the types of K-6th grade lessons 16 preservice elementary teachers created based on mathematics-themed children's books. Lessons were analyzed using Stein et al.'s (2017) Task Analysis Guide (TAG), as well as grouped based on grade level and covered Common Core State Standards Mathematical…

In their commentary, "Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice," Bartell et al. (2017) provide a stepping-stone into the challenge of clarifying the interface between equity and standards setting in mathematics education by devising a framework that relates the "Common…

The Common Core State Standards in Mathematics and Next Generation Science Standards encourage substantial shifts in teaching, but how to enact change is not specified. This mixed-methods exploratory study shows how different implementation supports were related to teachers' use of standards-aligned instructional practices in the Chicago Public…

The Common Core State Standards in Mathematics and Next Generation Science Standards encourage substantial shifts in teaching, but how to enact change is not specified. This mixed-methods exploratory study shows how different implementation supports were related to teachers' use of standards-aligned instructional practices in the Chicago Public…

With the implementation of the "Common Core State Standards for Mathematics," school administrators expect teachers to teach students on grade-level while preparing them to be college and career-ready. The purpose of this qualitative case study was to understand how secondary mathematics teachers prepare mathematics students from…

This article details a high school classroom activity in which algebra tiles are used to help students gain a conceptual understanding of completing the square. The activity utilises the eight elements of effective mathematics education suggested in the National Council of Teacher of Mathematics' (NCTM's) "Principles to action: Ensuring…

In the U.S., state adopted or developed college- and career-ready mathematics standards, including the Common Core State Standards for Mathematics, not only impact districts, students, and their teachers, but also university teacher preparation programs. In order to attain and sustain Common Core's vision of developing mathematically competent…

Problem solving has long been a priority in mathematics education, and the first Common Core mathematical practice (SMP1) focuses on this priority through the language of "Make sense of problems and persevere in solving them." We present findings from a survey about how prospective elementary teachers' (PTs) make sense of potential…

Do your students say that one object is "bigger" than another without attending more precisely to the attribute they are comparing? Do they have difficulty naming numbers from 11 to 19? Do some students still count all while their classmates are counting on or counting by tens? What tasks can you offer--what questions can you ask--to…

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

Math and English language arts seem such disparate content areas but the Common Core State Standards actually draw out their similarities in the teaching and learning process. Both require students to learn grit and perseverance; both ask students to use reasons or evidence to support arguments; both require precision; both require structures to…

This report presents findings from a 2016 American Teacher Panel survey, which gathered information about teachers' instructional materials for mathematics, their understanding of their mathematics standards, and their standards-aligned practices. The authors also consider how teachers' instructional materials might support their understanding of…

The adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) has caused a shift in the expectations for student learning, with implications for teaching. It has also introduced a new kind of standard focused on the way that students think about content in the form of the Standards for Mathematical Practice (SMP). The SMP…

Geometric transformations have long been topics of middle school mathematics. Generations of middle school students have learned to reflect, rotate, and translate geometric objects. Historically, though, the mathematics of "movement" might have been considered a departure from other more central middle-grades geometric content areas,…