There are two purposes in this study. One is to compare how 7th and 8th graders reason on linear and quadratic geometric number patterns when they have not learned this kind of tasks in school. The other is to explore the hierarchical relations among the four components of reasoning on geometric number patterns: understanding, generalizing,…

This is a study of how urban elementary grades students develop and express functions. Data were analyzed according to the forms of representations students used, the progression in students' mathematical language and the operations they employed, and how they attended to one or more varying quantities. Findings indicate that students are capable…

Recent curricular reforms are following the lead of the Standards 2000 and, in diverse ways, integrating some algebraic work into primary school mathematics. Our research aims at producing a tool that will allow researchers to track the development of algebraic thinking in children as they progress through various primary programs. In this paper…

Simulations and games have been used in education for decades, but most of this development has been in the areas of business and economics. Well-designed simulations and games have been shown to improve decision-making and critical thinking skills as well as teaching discipline-specific concepts. Active learning also helps students develop…

This paper presents preliminary hypotheses about the relationship between faculty goals for the introductory calculus-based physics course and their beliefs about student learning of problem solving. All faculties have problem solving as a major goal for their courses. There appears to be however, an instructional paradox. When discussing how…

This volume contains the proceedings of the 7th international conference on Adults Learning Mathematics--A Research Forum held in July, 2000 in Massachusetts. It includes posters and short oral reports under these section headings: (1) Research into Practice; (2) Large- Scale Issues: Frameworks, Standards, and Assessment; (3) Theoretical…

Emphasizing higher order thinking skills is of primary concern within mathematics. Learning environments emphasizing the learners understanding of the subject matter are constantly under review, with one learner-centered emphasis upon instruction leading the way: WebQuests. The design and development of WebQuests for the mathematical classroom…

As Californians put on another sweater, light candles, and open their electricity bills with shaking hands, the rest of the nation wonders who or what caused the problem and whether they will be next. Mixing with accusations about deregulation, there are also insistent voices blaming misguided and heavy-handed government for dimming the lights in…

This study explored some aspects of reasoning needed to complete science performance assessments, i.e., students' hands-on investigations scored for the scientific justifiability of the findings. The reasoning demands of science performance assessments were studied focusing on three dimensions identified from a previous analysis of data from the…

In a previous study, we posited a link between Chinese sixth grade students' problem solving and problem posing based on a pattern-formation strategy (Cai & Hwang, 2002). A similar parallel structure between problem solving and problem posing did not obtain for the U.S. sixth graders in the study. The present study attempts to locate this type of…

Twenty-four Piagetian-based written items representing different forms (stages) of thought and different logical operations were solved by 553 participants from required introductory logic classes in a state university in a medium-sized midwestern city and from a suburban school district of that city. Responses to each item were scored by quality…

According to the Third International Mathematics and Science Study (TIMSS) which compared student performance in mathematics and science in 41 countries in 1995, fourth grade students in the United States perform only slightly above the international average in mathematics. The study showed that most U.S. students are mastering basic arithmetic;…

This paper reports on an assessment of the cognitive skills section of the "Test of Communication Knowledge." The test was designed by Dr. Rebecca B. Rubin to evaluate learning by undergraduate communication majors in the School of Communication Studies at Kent State University (Ohio). In particular, the test is based on a set of…

This paper addresses the improvement of instruction at the higher education level by the application of nine principles of learning by the instructor. These are: (1) the instructor should secure the interests of students in teaching and learning situations; (2) the instructor must guide students to perceive meaning in what is being learned; (3)…

The knowledge teachers in an elementary school had of constructivist principles in the context of standards-based teaching and assessment was investigated and then addressed through a graduate-level course developed by the researcher. The knowledge level of the teachers was studied through interviews, classroom observations, and responses of 46…