The concept of a function is fundamental to virtually every aspect of mathematics and every branch of quantitative science. Presently this type of thinking is carolled at the secondary level, and yet it has many benefits for deepening the understanding of early arithmetic. This is particularly so in the way that operations can be considered as…

In part 1 of this work we showed how modern mathematical research could, with a suitably chosen problem, be included in the first year curriculum of undergraduate mathematicians. With the use of Computer Algebra Systems, even the average undergraduate mathematician can aspire to discover interesting yet still unexplained behaviour in many areas of…

This study investigated whether two different versions of an online professional development course produced different impacts on the intended outcomes of the course. Variations of an online course for middle school algebra teachers were created for two experimental conditions. One was an actively facilitated course with asynchronous peer…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

Research in the field of attribution theory and academic achievement suggests a relationship between a student's attributional style and achievement. Theorists and researchers contend that attributions influence individual reactions to success and failure. They also report that individuals use attributions to explain and justify their performance.…

Because of the educational importance of mathematics and science, IEA's (International Association for the Evaluation of Educational Achievement) Trends in International Mathematics and Science Study, widely known as TIMSS, is dedicated to providing countries with information to improve teaching and learning in these curriculum areas. Conducted…

Between 2003 and 2007, and without significant outside funding, the School District of Philadelphia created 25 new small high schools. This study, begun by Research for Action in 2006, follows the start-up and early implementation of these small high schools in Philadelphia. The study found that parents and students are interested in small high…

This correlation study examines the relationship between participation in online embedded professional development communities and student achievement gains in a College Algebra course taught by high school teachers to high school students for college credit. The participating teachers met weekly through a web-based meeting format using…

In grade 8 (the only grade in which subgroup trends were analyzed by achievement level), California students made gains across the board in reading at the basic, proficient, and advanced levels for racial/ethnic subgroups, low income students, and boys and girls. In math, there were some declines at the basic achievement level. In terms of…

In grade 8 (the only grade in which subgroup trends were analyzed by achievement level), Arkansas showed across-the-board gains--improvements in reading and math at the basic, proficient and advanced levels for all racial/ethnic subgroups, low income students, and boys and girls. The gains were quite large in most instances, especially at the…

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…