The purpose of this study was to validate inferences about scores of one task designed to measure subject matter knowledge and three tasks designed to measure aspects of pedagogical content knowledge. Evidence for the validity of inferences was based on two expectations. First, if tasks were sensitive to expertise, we would find group differences.…

Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

Physicians and other health professionals are an important part of the national scientific and technical workforce, and it is important to understand the factors that attract (or fail to attract) young adults into these fields. Using data from the 20-year record of the Longitudinal Study of American Youth (LSAY) and working within a social…

Florida Atlantic University implemented a number of changes in the College Algebra course in an attempt to improve student success. We summarize these changes, and how they have affected the course. We also discuss possibilities for future improvements. (Contains 3 figures and 1 footnote.)

The article reports aspects of the evolution of a teaching approach over repeated trials for beginning symbolic algebra. The teaching approach emphasized the structural similarity between arithmetic and algebraic expressions and aimed at supporting students in making a transition from arithmetic to beginning algebra. The study was conducted with…

This study was an empirically substantive examination of mathematics achievement differences between urban and rural Taiwanese students at a cognitive attribute level. Participants were eighth-grade students who participated in the "Trends in International Mathematics and Science Study" of 1999. The rule-space method was applied to…

Typically, mathematics and science are seen as linked together, where both subjects involve numbers, critical thinking, and problem solving. Our study aims to develop a better understanding of the connections between student's achievement scores in mathematics and science, student gender, and self-efficacy. We used the Trends in International…

In order to improve student success within developmental programs, we conducted a study of 1st year students taking required, developmental mathematics courses at a large, urban public university. Findings suggest that merely the number of years of mathematics that students take in high school is not a precise indicator of student readiness and…

The purpose of this study was to analyze how self-efficacy interacts with technology integration in Algebra 1 classrooms. A case study approach was used to discover how technology was integrated into Algebra 1 classrooms in a comprehensive high school. The findings were analyzed based on the teachers' locus of control to understand how the…

The conventional algebra-intensive math curriculum commonly dictates students' options for entering and completing college, including their ability to transfer from two-year to four-year institutions. The assumption that higher-level algebra is necessary for college success has led some equity advocates to promote algebra for all students. Nearly…

Purely combinatorial proofs are given for the sum of squares formula, 1[superscript 2] + 2[superscript 2] + ... + n[superscript 2] = n(n + 1) (2n + 1) / 6, and the sum of sums of squares formula, 1[superscript 2] + (1[superscript 2] + 2[superscript 2]) + ... + (1[superscript 2] + 2[superscript 2] + ... + n[superscript 2]) = n(n + 1)[superscript 2]…

Part of the power of algebra is that it provides students with tools that they can use to model a variety of problems and applications. Such modeling requires them to understand patterns and choose from a variety of representations--numeric, graphical, symbolic--to construct a model that accurately reflects the relationships found in the original…

The purpose of this article is to provide an image of what proof could look like in beginning algebra, a course that nearly every secondary school student encounters. The authors present an actual classroom vignette in which a rich opportunity for student reasoning arose. After analyzing the proof schemes at play, the authors provide a…

This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

This research aims to produce mathematics problems based on PISA level with valid and practical content of change and relationships and has potential effect for Junior High School students. A development research method developed by Akker, Gravemeijer, McKenney and Nieveen is used this research. This development research consists of three stages;…