In 2002/03, the Charlotte-Mecklenburg Schools in North Carolina initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking algebra in 8th grade increased from half to 85%, then reverted to baseline levels, in the span of just five years. We use this policy-induced variation to…

This research attempted to determine variables predictive of success in mathematics achievement among pre-service teachers at UMKC. It was conducted during the Winter 2006 semester at a medium-sized urban university. The participants (all students enrolled in geometry courses) were invited to volunteer; 49 agreed to participate. Three structured…

In 2010, St. Leonards Primary School in Tasmania, along with other selected schools throughout Australia, trialled the draft Australian Curriculum: Mathematics. Mathematics had been a whole school focus at St. Leonards Primary School for several years, and the school found that the opportunity to be part of the trial strongly connected with their…

Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

A system for construction of simple poster-board models is described. The models dynamically demonstrate the symmetry operations of proper rotation, improper rotation, reflection, and inversion for the chemically important point groups D[subscript 3h], D[subscript 4h], D[subscript 5h], D[subscript 6h], T[subscript d], and O[subscript h]. The…

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…

Students appear to be able to see number relationships and patterns but have difficulty recognizing the visual properties of shapes, especially if the shapes are in different positions. Their difficulty in the visual and spatial realm is often linked to a lack of drawing experience and possibly undeveloped fine-motor skills. The author, as a…

Graphing bivariate data in a scatter plot and drawing an approximate line of best fit for the data have become commonly recommended activities for middle school and high school students. The graphing calculator has provided a mechanism for students both to approximate a best-fit line and to calculate the best-fit line using a built-in option. Two…

Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…

One of the most difficult topics to teach in geometry is the concept of proof. This article describes ProofBlocks as an innovative approach to helping students develop proficiency in proof. ProofBlocks is an intuitive approach to teaching proof that makes proof accessible to students without sacrificing the rigor of traditional approaches. When…

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

Activities that enable students to move between two and three dimensions will help them understand solid geometry. This knowledge is critical for teachers, and they need to learn this skill so that they can give their students the opportunity to experience hands-on geometry and benefit from the challenge of creating nets, building models, and…

This short article gives a geometrical interpretation of the relationship between the harmonic mean, the arithmetic mean and the self-weighted mean. (Contains 1 figure.)

This study explored how mathematics content and methods courses for preservice elementary and middle school teachers could be improved through the integration of a set of instructional materials based on the National Assessment of Educational Progress (NAEP). A set of eight instructional modules was developed and tested. The study involved 7…

The World Bank 2007 TIMSS Video Study provided a distinctive insight into the practices of the Indonesian classroom and identified key strengths and weaknesses of current teaching. This investigation considered this evidence in the development of a structured lesson design that specifically addressed the instructional practices of the teaching and…