While contemplating ways to extend the author's ninth-grade honors geometry students' thinking and knowledge about area and perimeter, he discovered an interesting type of problem based on Erickson's (2001) rectangle problem, which he had been using for ten years. Erickson's original problem involves creating random rectangles with lengths and…

The authors investigated benefits of digital technology compared with traditional manipulatives in relation to preschoolers' development and learning of computational skills. The sample consisted of twenty four 4-and 5-year old children who attended a half-day prekindergarten program five times a week in a university laboratory school in the…

The level of interest in mobile technology for teaching and learning was analyzed according to the responses of 70 pre-teachers. Some pre-teachers (27%) were interested enough to find out what teaching with mobile devices involved. (Level One Engagement). The same students (27%) attended an informative workshop about the new methodology and…

Virtual manipulatives as cognitive tools, dynamic/interactive, Web-based representations and/or technology-based renditions, allow users to engage in mathematical meaning making. This research investigated teacher candidates' perceptions of the mathematical, cognitive, and pedagogical fidelity of Fill and Pour virtual manipulative. Findings…

This submission contains the Proceedings of the 2016 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Queen's University in Kingston, Ontario. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study…

Traditionally, the difficulties associated with mathematics were largely seen as coming from the cognitive demands of mathematics itself. It is now accepted that language and mathematics are connected in mathematics learning and teaching, and, the potential challenges of language in mathematics have been investigated by a number of researchers.…

Doug Williams presented the opening address at Conference 2012 on the theme of "Enigmas". Here he continues storytelling about the learning and teaching of mathematics at its best. The descriptions are of real classrooms with real teachers, and real learners. As with many good stories this is the narrative of a journey. A journey that…

Getting students to think about the relationships between area and perimeter beyond the formulas for these measurements is never easy. An interesting, nonroutine, and accessible problem that will stimulate such thoughts is the Lattice Octagon problem. A "lattice polygon" is a polygon whose vertices are points of a regularly spaced array.…

Teaching computer concepts to individuals with visual impairments (that is, those who are blind or visually impaired) presents some unique challenges. Students often have difficulty remembering to perform certain steps or have difficulty remembering specific keystrokes when using computers. Many cannot visualize the way in which complex computing…

If we want to make something concrete in mathematics education, we are inclined introduce, what we call, "manipulatives", in the form of tactile objects or visual representations. If we want to make something concrete in a everyday-life conversation, we look for an example. In the former, we try to make a concrete model of our own,…

We describe a set of manipulatives developed to help students learn three-dimensional Cartesian, cylindrical, and spherical coordinate systems. (Contains 6 figures.)

This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

A picture is worth a thousand words. This statement is especially true in mathematics teaching and learning. Visual representations such as pictures, diagrams, charts, and tables can illuminate ideas that can be elusive when displayed in symbolic form only. The prevalence of representation as a mathematical process in such documents as…

This design-based research study was conducted to identify what importance of a tangible user interface (TUI) can add to teaching and learning. Over a 2-year period, teachers ("n"?=?39) and students ("n"?=?145) participated in the study. The identified problem for investigation was how students, including those with low fine…

This study reports findings from a teaching experiment in which 4th grade children engaged in solving multiplication tasks with rectangular arrays in a computer environment. The environment provided flexible task-solving through dynamic virtual manipulatives (VMs) so children could use their existing knowledge of multiplication to complete array…