Generations have been inspired by Edwin A. Abbott's profound tour of the dimensions in his novella "Flatland: A Romance of Many Dimensions" (1884). This well-known satire is the story of a flat land inhabited by geometric shapes trying to navigate the subtleties of their geometric, social, and political positions. In this article, the authors…

Fay and Sam go for a walk. Sam walks along the left side of the street while Fay, who walks faster, starts with Sam but walks to a point on the right side of the street and then returns to meet Sam to complete one segment of their journey. We determine Fay's optimal path minimizing segment length, and thus maximizing the number of times they meet…

We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.

This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered to be at the trans level of development of the derivative schema (action-process-object-schema). The derivative schema is characterized in terms of the students' ability to explicitly transfer the relationship between…

We generalize a standard example from precalculus and calculus texts to give a simple description in polar coordinates of any circle that passes through the origin. We discuss an occurrence of this formula in the context of medical imaging. (Contains 1 figure.)

The authors used an alternating treatments design to compare the effects of a worksheet condition and an iPad condition on math fluency and active academic engagement during a high school math class in an alternative school setting. Following group instruction, the three participants engaged in independent seatwork either by completing problems on…

The present study examined the potential relationship between 1st and 5th year secondary school pre-service mathematics teachers' skills in understanding, method, modelling, verification, and extension dimensions of problem solving and their learning style characteristics. The data consisted of the skills pre-service teachers demonstrated in the…

Most students love to play games. Ernest (1986) believed that games could be used to teach mathematics effectively in four areas: motivation, concept development, reinforcement of skills, and practice of problem-solving strategies. Fifteen is an interesting and thought-provoking game that helps students learn mathematics at the same time. Playing…

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

Though the No Child Left Behind Act of 2001 requires secondary students with Asperger's syndrome (AS) to take high-stakes mathematical tests, many students with AS exhibit weaknesses in mathematical and executive functioning skills. The purpose of this mixed-methods case study was to explore the use of differentiated mathematical strategies with…

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…

The purpose of this study was to investigate the effect of a computer-based story on sixth grade students' mathematics word problem solving achievement. Problems were embedded in a story presented on a computer, and then compared to a paper-based story and to a condition that presented the problems as typical, isolated words problems. One hundred…

This paper explores how curriculum and classroom conceptual and procedural emphases affect the learning of algebra for students of color. Using data from a longitudinal study of the Connected Mathematics Program (CMP), we apply cross-sectional HLM to lend explanatory power to the longitudinal analysis afforded by Growth Curve Modeling that we have…

This submission contains the Proceedings of the 2011 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Memorial University of Newfoundland in St. John's, Newfoundland. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

The purpose of this article is to identify the order of significance of the variables that affect science and mathematics achievement in middle school students. For this aim, the study deals with the relationship between science and math in terms of different angles using the perspectives of multiple causes-single effect and of multiple…