This article examines the use of the computer algebra system SAGE for undergraduate student research projects. After reading this article, the reader should understand the benefits of using SAGE as a source of research projects and how to commence working with SAGE. The author proposes a tiered working group model to allow maximum benefit to the…

Math self-concept (MSC) is considered an important predictor of the pursuit of science, technology, engineering and math (STEM) fields. Women's underrepresentation in the STEM fields is often attributed to their consistently lower ratings on MSC relative to men. Research in this area typically considers STEM in the aggregate and does not account…

Drawing on Eccles' expectancy-value model of achievement-related choices, we examined the personal aptitudes and motivational beliefs at 12th grade that move individuals toward or away from science, technology, engineering, and mathematics (STEM) occupations at age 29. In the first set of analyses, occupational and lifestyle values, math ability…

We used both student interviews and diagnostic testing to reveal students' misconceptions about number representations in computing systems. This article reveals that students who have passed an undergraduate level computer organization course still possess surprising misconceptions about positional notations, two's complement representation, and…

Considers three questions regarding computer science courses: (1) Can performance be predicted?; (2) Does a solid mathematical background provide the student with an advantage?; and (3) Is gender a factor in performance or aptitude? Reports a strong math background was related to achievement in a beginning course while gender was not related. (MVL)

According to the National Council of Teachers of Mathematics (2000), children need to learn how to create and use mathematical diagrams to represent and reason about phenomena in the world. The author proposes a model of diagram literacy that includes six types of knowledge required for diagrammatic competence--implicit, construction, similarity,…

Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)

This paper discusses the overall design of the PIXIE Intelligent Tutoring System, and more specifically a series of recent enhancements. The original system has been implemented to involve three separate phases: the offline, or model generation phase; the online, or tutoring, phase; and the analysis phase. The offline phase, which is completed…

New developments in the use of automatically scorable constructed response item types for large-scale assessment are reviewed for five domains: (1) mathematical reasoning; (2) algebra problem solving; (3) computer science; (4) architecture; and (5) natural language. Ways in which these technologies are likely to shape testing are considered. (SLD)

Presented is a scheduling algorithm that uses all the busses at each step for any rectangular array. Included are two lemmas, proofs, a theorem, the solution, and variations on this problem. (KR)

Reported is whether and how mathematics has changed during the 75 years of the Mathematical Association of America's (MAA) existence. The progress of mathematics is organized into 9 concepts, 2 explosions, and 11 developments. (KR)

This collection of research papers considers extensions of the Rasch model. In Chapter 1, K. C. Cheung explains how measurement and testing in the classroom can be made more meaningful, particularly through the use of Rasch family item response models. In Chapter 2, K. W. Koon and K. C. Cheung apply the Rasch model in constructing a part-whole…

Six studies discussed in this paper compared error-specific or model-based remediation (MBR) with reteaching in algebra. MBR points out, and highlights as incorrect, errors specific to the student's solution before reteaching the correct procedures. Reteaching shows the student the correct procedure without addressing specific errors. Three of…

This paper provides an overview of the four major aspects of the PIXIE Intelligent Tutoring System: the field work undertaken to determine how teachers diagnose and remediate in introductory algebra; the set of experiments run to determine the relative effectiveness of Model-Based-Remediation (MBR) and Reteaching; systems work carried out to…

The implementation of the program used in this study, TPIXIE, was predicated on the assumption that acquiring the skill to diagnose student errors was important for teacher trainees. The TPIXIE system (part of the PIXIE family of intelligent tutoring systems) was designed to present users with a series of task-student-answer pairs (where the…