An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

To reflect on the mathematics achievement of children engaging "Algebra and Analogies for Kids," the teacher researcher will explore the following inquiry: What happens when kids display analogical thinking in an algebra project? Specifically, the proposed study will examine the reasoning of five children in portfolios of best works and selected…

This report focuses on the performance of fourth-and eighth-grade students in Puerto Rico in various mathematics content areas on the 2005 National Assessment of Educational Progress (NAEP) in mathematics. The NAEP mathematics assessment was administered to public school students in Puerto Rico for the first time in 2003. Although NAEP had…

Students who have particular difficulty in mathematics are a growing concern for educators. Graphic organizers have been shown to improve reading comprehension and may be applied to upper level secondary mathematics content. In two systematic replications, one randomly assigned group was taught to solve systems of linear equations through direct…

This article illustrates how problem solving can be enhanced through careful planning and problem presentation. Often, students shut down or are turned off when presented with a problem to solve. The author describes how to motivate students to embrace a problem to be solved and provides helpful prompts to further the problem-solving process.…

Many students in U.S. schools have trouble understanding fractions and Algebra II, the one difficultly occurring at the end of elementary school, the other in high school. One reason is that schools generally focus on one aspect of mathematics--calculation--and often fail to address the second aspect--interpretation. Also responsible is the…

This study examined Algebra students' achievement and perceptions of their classroom environments in both online and traditional face-to-face learning contexts using two validated assessments, the Assessment of Algebraic Understanding (AAU) test and the What is Happening in this Class? (WIHIC) classroom perceptions instrument. Three virtual and…

This paper reports the mathematical generalizations of two groups of algebra students, one which focused primarily on quantitative relationships, and one which focused primarily on number patterns disconnected from quantities. Results indicate that instruction encouraging a focus on number patterns supported generalizations about patterns,…

This paper provides a microanalysis of one Algebra I teacher's instruction to explore the advantages that are afforded us by coordinating two perspectives to document and account for the teacher's mathematical understandings. We use constructs associated with Stein, Grover and Henningsen's domain of mathematical didactics and Realistic Mathematics…

Although one-to-one tutoring has often been regarded as the most effective method of teaching, surprisingly little is understood about tutoring expertise. This paper describes initial attempts to study one-to-one tutoring. The goal of the research was to construct a detailed cognitive model of the reasoning and knowledge of an expert human tutor.…

This paper reports a study that sought to explain student understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of data analysis, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examined the differences in the problem-solving activities of solvers who…

This study sought to provide an explanation of (n=13) university students' understanding of the concept of linear inequality as presented in a problem-solving setting. In the course of the analysis of the data, the transition from arithmetic to algebra emerged as a critical issue. Therefore, the study examines the differences in the…

The major goals of this study were to conceptualize a framework for analyzing student conceptions of mathematics, gather baseline information about the conceptions of mathematics held by mathematically talented students and by average high school students, and begin to generate hypotheses about how they are related to the nature of student…

This study examined the problem-solving behaviors, strategies, and achievement of college students enrolled in a one-semester college algebra and statistics course, with respect to the content areas of quantitative literacy, connections between algebraic and graphical representations, and mathematical modeling. Four instructional units of this…

Researchers and educators are calling for increased use of technology and attention to function concepts in school mathematics. Students often have considerable difficulty gleaning pointwise and global information from Cartesian (R squared) representations of functions, whether they are hand- or machine-produced. Described here is an interactive…