Initial algebra is a critical stage in the teaching of algebra and occurs when students are transitioning from arithmetic to algebra. Irish mathematics education at post-primary level has undergone a period of major reform beginning in 2010, which encompassed a radical change in the methods for teaching algebra. Despite this reform evidence…

In educational practice, a test assembly problem is formulated as a system of inequalities induced by test specifications. Each solution to the system is a test, represented by a 0-1 vector, where each element corresponds to an item included (1) or not included (0) into the test. Therefore, the size of a 0-1 vector equals the number of items "n"…

Presents a general mathematical framework for information retrieval, in which query evaluation is seen as a mapping from the free term algebra built by query descriptors and weights to the semantic algebra of evaluation value. Competing mathematical models that try to describe how retrieval systems behave are reviewed. (Author/MBR)

Algebra word problems were analyzed in terms of the information integration tasks that are required to solve the problems. These tasks were classified into three levels: value assignment, value derivation, and equation construction. Novices (35 first year algebra students) and experts (13 analytic geometry students) were compared on the proportion…

The reversal phenomenon was studied with nearly 1,000 Australian students in grades 9-12. The insertion of a multiplication sign in an equation tended to lower the incidence of reversals, but switching from initial letters to other letters made little difference. (MNS)

The relationship between the historical evolution of algebraic ideas and their conceptual development is examined. A study with secondary school students indicates a possible parallelism between algebraic evolution and conceptual development and indicates how historical analysis can guide teaching. (MNS)

This study examined the links students are able to make between formal expressions and situations to which they might refer. Students' understanding of a basic set of transformational rules in elementary algebra sign changes in addition and subtraction expressions with parentheses was assessed, exploring: (1) informal intuitive understanding of…

It has been suggested that males perform better than females in mathematics after ninth grade because more males than females enroll in advanced mathematics courses in high school. However, factors other than enrollment may be involved. Therefore, this study investigated whether the performance of males (B=500) and females (N=500) was different in…

This paper proposes an hypothsis describing how some college students incorrectly view semantically laden letters and provides both clinical and written data that supports that hypothesis. Several word problems were given to nine college math students. These students were then interviewed as they attempted to solve these problems. In addition to…

Learned helplessness is a variable which has commonly been considered in research on sex-related differences in mathematics achievement. In this study, learned helplessness has been defined in terms of a debilitating or facilitating response resulting from failure on mathematical word problems. The construct has been called Performance Following…

Develops an approach for advance estimation of user charges based on information actually retrieved by searching numeric databases, and defines a method for query cardinality estimation. Based on the relational data model, which uses relational algebra, this method uses formal file descriptions to describe the database files. (LRW)

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Because the failure rate for Math 110 (a college algebra course for non-science/technology-oriented majors at the University of Maryland) was so high, it was decided to offer selected registrants the opportunity to take a free refresher workshop series to improve their mathematics skills before they took the course. In summer 1985, 809 students…

Students enrolled in two sections of college algebra (Math 110) at the University of Maryland in spring 1984 were informed about assistance available from the Math Lab. They were also informed that a sticker would be attached to any one of the four semester exams when grades indicated that the student should pursue one or more of the Lab services.…

The goal of this study was to find a way to quantify three criteria of representational quality, described by Greeno, so that it would be possible to examine statistically the relationship between representational quality and other variables related to problem solution. The sample consisted of 18 college students, 84 percent of whom had…