With the advancement of new technologies, this author has in 2010 started to engineer an online learning environment for investigating the nature and development of spatial abilities, and the teaching and learning of geometry. This paper documents how this new digital learning environment can afford the opportunity to integrate the learning about…

The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

Because of the impact that mathematical beliefs have on an individual's behaviour, they are generally well researched. However, little mathematical belief research has taken place in the field of adult education. This paper presents preliminary results from a study conducted in this field in Switzerland. It is based on Ernest's (1989) description…

Noticing children's mathematical thinking is an important aspect of what teachers need to know. This study explores the role of videocases in supporting preservice elementary teachers' noticing of children's mathematical thinking. Findings from a quasi-experimental study of preservice teachers' engagement with videocases indicate no significant…

Knowing number facts up to 10 become crucial if we want students to solve addition and subtraction problems using more abbreviated strategies. Otherwise, students will keep counting one-by-one until they get an answer. One of important number facts is number pairs that make ten because it is an important "benchmark" that students will…

We introduce playing games on the shadows of knots and demonstrate two novel games, namely, "To Knot or Not to Knot" and "Much Ado about Knotting." We discuss winning strategies for these games on certain families of knot shadows and go on to suggest variations of these games for further study.

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…

As an extension to various sponsored summer undergraduate research programs, academic year research for undergraduate students is becoming popular. Mathematics faculty around the country are getting involved with this type of research and administrators are encouraging this effort. Since 2007, we have been conducting academic year research at…

This study offers an examination of two primary-grades teachers as they learn to transfer knowledge from professional development into their classrooms. I engaged in planning sessions with each teacher to help plan tasks of high cognitive demand, including anticipating and planning for classroom discourse that would occur around the task. A…

This is a study about the didactical organization of a research based group of activities designed using APOS theory to help university students make constructions, needed to understand and graph two-variable functions, but found to be lacking in previous studies. The model of the "moments of study" of the Anthropological Theory of…

This article points out a simple connection between related rates and differential equations. The connection can be used for in-class examples or homework exercises, and it is accessible to students who are familiar with separation of variables.

The emergence of non-Euclidean geometries in the 19th century rocked the foundations of mathematical knowledge and certainty. The tremors can still be felt in undergraduate mathematics today where encounters with non-Euclidean geometry are novel and often shocking to students. Because of its divergence from ordinary and comfortable notions of…

This study looks at a mixed ability group of 21 Year 5 primary students (aged 9-10 years old) who had previously never had formal instruction using letters to stand for unknowns or variables in a mathematics context; nor had they been introduced to formal algebraic notation. Three lessons were taught using the computer software "Grid Algebra"…

The relationship between adolescent extra-curricular activities and choice of graduate-education field was examined among students from three fields of study, science (n = 12), art (n = 12), and education (n = 14), using qualitative and quantitative methods. Results of profile analysis indicated that the different majors participated in…