This article reports on an investigation of how teachers of geometry perceived an episode of instruction presented to them as a case of engaging students in proving. Confirming what was hypothesized, participants found it remarkable that a teacher would allow a student to make an assumption while proving. But they perceived this episode in various…

Students enter the geometry classroom with a strong concept of fairness and a sense of what it means to "play by the rules," yet many students have difficulty understanding the postulates, or rules, of geometry and their implications. Although they may never have articulated the properties of an axiomatic system, they have gained a practical…

In recent years, significant numbers of academics from the science and health disciplines at our institution have found that their students lack the appropriate "mathematical" background to cope with first-year science subjects. Consequently, failure rates are on the increase in these subjects. The mathematical background of students…

In Clark and Lovric ("Suggestion for a theoretical model for secondary-tertiary transition in mathematics", "Math. Educ. Res. J." 20(2) (2008), pp. 25-37) we began developing a model for the secondary-tertiary transition in mathematics, based on the anthropological notion of a rite of passage. We articulated several reasons why we believe that the…

Encouraging students to share their ideas, design mechanisms for testing ideas, and make conclusions about the validity of their ideas on the basis of evidence collected can enhance teaching about friction. The authors focus on teaching science content and science processes in a holistic manner so that students develop enduring understandings of…

(Purpose) As schools scramble to restructure in the hope of thwarting failure, administrators often appropriate money for outside experts who counsel on professional development as well as outside magic-pill programs for student achievement. High-stakes testing remains the arbiter. Perhaps the use of the best practice of inquiry, or classroom…

Student achievement in mathematics has been a focal concern in the United States for many years. The National Research Council's 2001 report and the recent report of the National Mathematics Advisory Panel (2008) both called attention to student achievement in mathematics, and both called for all students to learn algebra by the end of eighth…

Although current reform movements have stressed the importance of developing prospective middle school mathematics teachers' subject matter knowledge and understandings, there is a dearth of research studies with regard to prospective middle school teachers' confidence and knowledge with respect to quadratic functions. This study was intended to…

Two experts on education offer a rich and diverse selection of children's literature and teaching strategies for the K-8 mathematics classroom. To date, a vast majority of classrooms continue to fall short in the implementation and direction of NCTM Principles and Standards for School Mathematics (PSSM), in part because most of these classrooms…

Formal requests were recently introduced for integration of ICT in secondary school mathematics. As the main issue, students must develop competence to decide when and how it is appropriate to use available ICT tools and to use them. These new requests put demands on those teachers who have not developed corresponding competencies themselves.…

Teacher played an important role in ascertaining effective teaching of mathematics. The objective of this paper was to investigate the pedagogical usability of a digital module prototype that integrated a dynamic geometry software, Geometer's Sketchpad (GSP) in mathematics teaching. The prototype was developed based on Reiser's and Dick's…

Technology use in mathematics often involves either exploratory or expressive modeling. When using exploratory models, students use technology to investigate a premade expert model of some phenomena. When creating expressive models, students have greater flexibility for constructing their own model for investigation using objects and mechanisms…

After carrying out a project over several years in eight upper secondary schools in Thuringia on the effects the use of a handheld CAS (Computer Algebra System) has on the students' skills in mathematics, the former ban on the use of such technology in mathematics education was revoked. Late in the project (2002) a survey of all students in the…

In this paper we try to characterize the pedagogical approaches that mathematics teachers are developing to meet the challenges posed by education reforms. A key aspect is the identification of the perspectives that underlie those pedagogical approaches, using the term perspective to include a broad pedagogical structure composed of multiple…

A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are…