There has been a lot of material written about logarithmic spirals of golden proportion but this author states that he has never come across an article that states the exact equation of the spiral which ultimately spirals tangentially to the sides of the rectangles. In this article, the author intends to develop such an equation. (Contains 5…

One classroom using two units from a "Standards"-based curriculum was the focus of a study designed to examine the effects of real-world contexts, delays in the introduction of formal mathematics terminology, and multiple function representations on student understanding. Students developed their own terminology for y-intercept, which was tightly…

This article describes concepts exhibited by seventh-grade prealgebra students as they approached algebraic-thinking tasks. (Contains 7 Figures.)

Numerical fractions are commonly used to express ratios and proportions (i.e., real numbers), but little is known about how they are mentally represented and processed by skilled adults. Four experiments employed comparison tasks to investigate the distance effect and the effect of the spatial numerical association of response codes (SNARC) for…

In early years' (primary grade) classrooms in Australia repeated patterns are commonly explored as an early introductory activity to mathematics. Most young students have an extensive knowledge of and exhibit success in copying, continuing, creating and transferring patterns into other media. By contrast, research indicates one of the most…

In this study we examined how two students viewed the general nature of their proportional reasoning errors as they attempted to generalize numeric situations. Using a teaching experiment methodology we studied the reasoning of two students over 18 instructional sessions. One student, Dallas, appeared to recognize that the proportional reasoning…

A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential…

Many children enjoy collecting items such as seashells, state quarters, and trading cards. Asking students to think about the ways in which similar items differ, how objects can be grouped by a common characteristic, and how groups can be subsets of a larger category leads to an understanding of fundamental mathematics and science concepts: sets,…

The report shares what everyone has learned from the 2010-2011 Maryland Model for School Readiness (MMSR) data about the school readiness of Maryland's children: statewide, by subgroups, and for each of Maryland's 24 local jurisdictions. Some of the highlights are: (1) The percentage of Maryland kindergarteners fully ready to start school…

The purposes of this study were to investigate preservice mathematics teachers' orientations, content knowledge, and pedagogical content knowledge of probability; the relationships among these three aspects; and the usefulness of tasks with respect to examining these aspects of knowledge. The design of the study was a multi-case study of five…

In an attempt to better support the mathematics and science learning experiences of preservice teacher candidates, a new course of study was created as part of a teacher certification program at a mid-Atlantic liberal art university. Entitled Investigations in Science and Mathematics, the two semester course adopted an integrated inquiry and…

This report presents results of the 2009 National Assessment of Educational Progress (NAEP) in mathematics at grades 4 and 8. The results from the 2009 assessment presented in this report are compared to those from previous years, showing how students' performance in mathematics has progressed over time. Results for students in the nation, the 50…

A schema-based instruction allows students to approach a mathematics problem by focusing on the underlying semantic or problem structure, thus facilitating conceptual understanding and adequate skills. The purpose of this study was to examine the effectiveness of schema-based intervention on the mathematical word problem solving skills of middle…

This study is an evaluation on whether middle-level mathematics teachers' participation in a week-long in-service course on middle-level mathematics concepts increases their understanding of this content. A secondary purpose of this study is an exploration of teacher perceptions before and after the institute via self-report surveys. Participants…

The purpose of this study was to determine the efficiency of 4MAT method of instruction in which learning style and cerebral hemispheres are taken into account in teaching the binary operation and its properties in mathematics. The sample of this study comprised 58 ninth grade students in two separate classes in a high school. One of the classes…