This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…

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…

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach…

Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in…

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.…

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…

Measurement is an important component of K-grade 12 mathematics curricula. The concepts of area and perimeter of polygons are first introduced in third grade and serve as the basis for teaching in the upper grades. Without a strong understanding of measurement, students will struggle to meaningfully grasp three-dimensional measurement concepts…

With the adoption of the National Common Core State Standards in Mathematics (CCSSM) in many states and the lack of understanding and strategies to implement the new standards by classroom teachers, implementing effective professional development is vital. The focus of this qualitative case study was to provide insight into elementary school…

Prospective elementary teachers at three universities engaged in online modules called the Virtual Field Experience, created by the Math Forum. The prospective teachers learned about problem solving and mentoring elementary students in composing solutions and explanations to nonroutine challenge problems. Finally, through an asynchronous online…

The Common Core State Standards (CCSS) have been developed in response to the criticism that students in the U.S. are graduating from high school without being college and career ready and that they are falling behind their counterparts in other countries in key subject areas. In this work, the authors report the results of an efficacy study that…