This study was an investigation of the effectiveness of mathematics instruction using the interactive whiteboard (IWB) for 1, 2, and 3 years. Guided by Gagne's conditions of learning theory, this program evaluation study investigated the impact of receiving 1, 2, or 3 years of mathematics instruction using the IWB on mathematics scores on the…

Over the course of two years, data was collected focused on preservice elementary teachers' engagement with mathematics textbooks and curriculum materials in two contexts: (1) a university mathematics education course, and (2) student teaching. To frame the results and suggest opportunities for learning, Feiman-Nemser and Buchmann's (1985)…

A Mathematics course for elementary school teachers (MFET) is required in North America in most teacher education programs. Our study investigates the perceptions of prospective elementary school teachers with respect to the contributions of such a course to their teaching. The results show that acquiring an understanding of concepts from the…

Nowadays, many technological means are available to support teaching, such as the interactive whiteboard, class sets of laptop or netbook computers, and high speed internet access. For mathematics education there are advanced software packages for geometry, algebra, calculus, and statistics, which in many cases are available on line at no cost.…

This article is based on a study that documented the daily work practice of an eighth-grade mathematics teacher and her colleagues at a secondary school in Shanghai when they taught the unit on geometric proofs. Four interrelated work activities were identified to highlight a pedagogy around homework errors. They form an activity system…

A common activity--having students collect data to measure the radius and circumference of circular objects--can be given a new twist. These data can be viewed virtually using technology. A dynamic geometry environment coupled with the powerful capabilities of a spreadsheet can greatly enhance student learning. The activity in this article…

Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to which secondary school teachers recognise the conflicting paradigms and how they handle the geometric…

Technology use and a focus on 21st century skills, coupled with recent adoption of Common Core State Standards for Mathematics, marks a new challenge for mathematics teachers. Communication, discourse, and tools for enhancing discourse (NCTM, 1991, 2000) play an integral role in successful implementation of technology and mathematics standards.…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…

Over the last few decades school accountability for student performance has become an issue at the forefront of education. The federal No Child Left Behind Act of 2001 (NCLB) and various regulations by individual states have set standards for student performance at both the district and individual public and charter school levels, and certain…

This study aims to help address a need for information about efficacious mathematics curriculum and instruction at the high school level. Data from national and international studies, including the National Assessment of Educational Progress (NAEP), show very low mathematics proficiency rates for high school students. Many educators recognize a…

How do people learn novel mathematical information that contradicts prior knowledge? The focus of this thesis is the role of structure in the acquisition of knowledge about hyperbolic geometry, a non-Euclidean geometry. In a series of three experiments, I contrast a more holistic structure--training based on closed figures--with a mathematically…

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…

Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…