The purpose of this work is to explore alternative geometric pedagogical perspectives concerning justifications to 'fast' multiplication algorithms in a way that fosters opportunities for skill and understanding within younger, or less algebraically inclined, learners. Drawing on a visual strategy to justify these algorithms creates pedagogical…

Our article aims to show how illuminating mathematical work as a concept from didactics of mathematics is useful in understanding issues relating to proving and learning of proof, with or without technology. After posing our hypotheses on the relationship of proof with mathematical work, the pedagogical intent of historical elements of geometry…

As classrooms begin to adopt a greater number of digital technologies such as computers and tablets, it is important for educators to understand how effective such tools can be in aiding in the delivery of instruction to students who struggle in mathematics, such as those identified with a learning disability in mathematics. One digital-based…

As a component of the ongoing development of the mathematics curriculum in China, we compare the country's high school mathematics textbooks with those of several other countries. We base our analysis on the assumption that textbooks, as primary printed teaching resources, are key tools for interpreting educational policy. In this paper, we…

This study compares American and Korean curriculum standards, textbooks, and geometry items to help explain the consistent differences that have been found between the achievement levels of U.S. and Korean students in the Program for International Student Assessment (PISA) mathematics. Since PISA measures the mathematical proficiency of…

Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…

Much of the work on teacher knowledge suggests that content knowledge shapes pedagogical content knowledge, and in fact is primary in the relationship between the two forms of knowledge. In this paper we challenge this view, arguing from a situated perspective on knowledge and learning, that pedagogical content knowledge strongly shapes content…

This paper presents findings from a comparative analysis of three similar secondary geometry texts, one critical unit, one standards-based reform unit, and one specialist chapter. I developed the critical unit as I took the tenets of critical mathematics (CM) and substantiated them in printed curricular materials in which to teach as part of a…

The Finnish National Board of Education has been publishing guidelines for the evaluation of student learning in the comprehensive school since the 1970s. This evaluation is two-fold: 1) during school it guides and supports students along their academic paths and 2) at the conclusion of the comprehensive school it expresses each student's level of…

It is widely accepted that learning becomes more enduring and deeper if geometric concepts are presented in various orientations and dimensions in textbooks. The purpose of this study was to examine how geometric concepts are presented in the Turkish elementary mathematics curriculum and the textbooks in terms of sizes and orientations. For this…

This study investigates the effect on student performance in drawing their attention to relevant task variables, focusing on accuracy of responses and reaction times. We chose this methodology in order to better understand how such interventions affect the reasoning process. The study employs a geometry task in which the irrelevant salient…

Last year the United States unveiled the Common Core State Standards (CCSS) in English and Mathematics for grades K-12. In particular, the authors included two possible sequences of 8-12 mathematics courses that would fulfill the standards. Most notably, the courses titled "3a" and "3b" in these two sequences have become…

Early in development, there is a transition in spatial working memory (SWM). When remembering a location in a homogeneous space (e.g., in a sandbox), young children are biased toward the midline symmetry axis of the space. Over development, a transition occurs that leads to older children being biased away from midline. The dynamic field theory…

This Annual Measurable Objective (AMO) is designed to keep Florida moving forward toward national and international competitiveness. Florida will compare its National Assessment of Educational Progress (NAEP) scores to those of the top five states and its Trends in International Mathematics and Science Study (TIMSS), Progress in International…

In this experiment, physical science students measured the mass of several soda cans, measured the mass and volume of water displaced when these cans were placed in water, and determined whether these cans sank or floated in water. Then, the students plotted graphs of the mass of displaced water versus the volume of displaced water, the mass of…