Metacognitive monitoring and regulation play an essential role in mathematical problem solving. Therefore, it is important for researchers and practitioners to assess students' metacognition. One proven valid, but time consuming, method to assess metacognition is by using think-aloud protocols. Although valuable, practical drawbacks of this method…

The ability to retrieve basic arithmetic facts from long-term memory contributes to individual and perhaps sex differences in mathematics achievement. The current study tracked the codevelopment of preference for using retrieval over other strategies to solve single-digit addition problems, independent of accuracy, and skilled use of retrieval…

Justification is a core mathematics practice. Although the purposes of justification in the mathematician community have been studied extensively, we know relatively little about its role in K-12 classrooms. This paper documents the range of purposes identified by 12 middle grades teachers who were working actively to incorporate justification…

Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…

Given a growing digital economy with complex problems, demands are being made for education to address computational thinking (CT)--an approach to problem solving that draws on the tenets of computer science. We conducted a comprehensive content analysis of the Ontario elementary school curriculum documents for 44 CT-related terms to examine the…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…

I am a volunteer reader at the Princeton unit of "Learning Ally" (formerly "Recording for the Blind & Dyslexic") and I recently discovered that high school students are introduced to the concept of quantization well before they take chemistry and physics. For the past few months I have been reading onto computer files a…

The technique of bump drafting, also known as two-car drafting in motorsports, is analysed in the framework of Newtonian mechanics and simple aerodynamic drag forces. As an apparent unnatural effect that often pleases the enthusiasts of car racing, bump drafting provides a unique pedagogical opportunity for students to gain insights into the…

The purpose of this study was to determine how the study of number theory might affect high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics. The study utilized questionnaire and/or interview responses of seven high school students from New York City and 33 high school students from Dalian,…

The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…

We describe a modelling activity for students in a course in which modelling with differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a linear, first-order, ordinary differential equation. The activity…

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

Social promotion is defined as the practice of allowing students who failed to meet performance standards and academic requirements the opportunity to pass on to the next grade with their peers. Although the A+ Educational Reform Act abolished the use of the practice, social promotion continues to occur in numerous school districts across one…

Although the Common Core State Standards call on parents to support professional educators' efforts for improving student academic achievement, we have yet to examine how to best support parents in achieving this goal. The present study addresses this need by examining a five-month mathematics intervention which aimed to increase awareness of the…

There are relatively few studies in Australia and South-East Asian region that combine investigating models of math growth trajectories with predictors such as reasoning ability and reading comprehension skills. Math achievement is one of the major components of overall academic achievement and it is important to determine what factors (especially…