This article presents an exploratory study that gives account of some students' perceptions of the completeness property of the set of real numbers. Students taking three undergraduate correlative courses in Calculus and Analysis answered a written questionnaire; their scripts are analysed trying to understand how operational is the notion of…

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

In this article, we derive one-parameter family of Schroder's method based on Gupta et al.'s (K.C. Gupta, V. Kanwar, and S. Kumar, "A family of ellipse methods for solving non-linear equations", Int. J. Math. Educ. Sci. Technol. 40 (2009), pp. 571-575) family of ellipse methods for the solution of nonlinear equations. Further, we introduce new…

For middle school students who have seen only pictures of dinosaurs in books, in the movies, or on the internet, trying to comprehend the size of these gargantuan animals can be difficult. This lesson provides a way for students to visualize changing scale through studying extinct organisms and to gain a deeper understanding of the history of the…

Standardized tests have been selected as a key assessment factor in expanding the academic achievement of the national student population. However, these tests position immigrant students at the risk of academic failure, leading education experts to search for new strategies and teaching models. The "Handbook of Research on Assessment…

Failure rates in first year calculus courses are high in most post-secondary institutions across North America and other parts of the world. This Inukshuk-funded open education project involved the development of five stand-alone pre-calculus learning modules. The design and revision phases of this project occurred between the fall of 2007 and…

Middle school is a crucial transition period for students as they move from concrete to algebraic ways of thinking. This article describes a sequence of instruction geared toward helping prospective middle school instructors teach the topic of percentages.

The continuous inventions and evolutions in all information technology fields open new channels and opportunities to enhance teaching and educational methods. On one side, these may improve the abilities of educators to present information in interactive and media-enhanced formats relative to traditional methods. This may help students or learners…

Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…

In this study we investigate the conceptions of mathematics bridging courses held by students enrolled in these courses at a major Australian university. We report on the participants' responses to email-interview questions about the mathematics bridging courses to describe a two-dimensional outcome space of variations in awareness about the…

Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…

The need to design teacher preparation programs to ensure that pre-service teachers (PSTs) are prepared and equipped with knowledge, skills and practices to increase the chances that they will become effective novice mathematics teachers is of prime importance. Teacher educators are facing lingering challenges, since teacher education is…

This dissertation tests a dynamic assessment-based cognitive hierarchy model and attempts to identify mathematical concepts that predict student learning potential on more advanced mathematical concepts using the units from ST Math, a self-paced curriculum, for third, fourth, and fifth grade students. The quantitative analyses compared a…

Our study, situated within graduate-level courses for teachers focused on statistics, illustrates work across institutions for making sense of teachers' statistical thinking. Using a common assessment instrument, we identify and discuss four items that indicate strong statistical thinking and two that highlight concepts with which teachers…

While Socrates and Meno are discussing the nature of knowledge through considering the square-root of two with one of Meno's slaves, their wives are discussing the nature of knowledge through considering the square-root of three with one of the slave girls, using a diagram based on Raphael's "The School of Athens" being contemplated by Euclid.