Discussed are the recognition and the relevance, in terms of teacher/student awareness and subsequent effective teacher treatment techniques, of cognitive disequilibrium as experienced by the student, when such disequilibrium is provoked by mathematical contradictions and/or counterexamples, within the classroom paradigm of constructivism. (JJK)

Points out that successful mathematical performance depends not only on declarative and procedural content knowledge, but also upon mathematical thinking skills such as problem-schema knowledge, decision-making skills, and metacognitive knowledge. Argues that the growing need for remediation should influence schools' traditional overemphasis on…

Examines mathematics problem solving in a computer software environment using graphical representations of the results of simulations with adolescent students. Discusses the strengths and limitations of inferring goals and plans, the use of verbal protocols, and ways for computer-based learning environments to scaffold acquisition of domain…

Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…

Utilizes the study of quadratic equations to illustrate the use of combinations of software to enhance critical thinking in preservice mathematics teachers. Concludes that the use of multiple software enriches students' learning experiences and improves their critical-thinking skills. (ASK)

Describes several short geometry tasks that go beyond the simple recognition of figures and properties. Presents scoring rubrics and questions that might be useful to middle school teachers developing short open-ended questions that encourage and assess students' thinking. (ASK)

This article tells the story of Darrell, a lively, intelligent boy who has some learning disabilities. Although his parents are educators and are highly committed to advocating for Darrell, for most of his elementary school years, they were unable to succeed in providing Darrell a mathematics education equal to his regular education peers.…

Despite some characterization as being uninvolved in the education of their children, African American parents have always valued education and recognized it as the key to economic and political freedom. Despite laws in the United States prohibiting the education of slaves, African Americans were the first southerners to campaign for universal,…

Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students' thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of "pedagogical…

The article describes a unit for seventh-grade students, using children's literature to teach visual, auditory, and algebraic patterns. (Contains 7 figures.)

Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

The purpose of the present study is twofold: (a) to compare the validation of percentage of nonoverlapping data approach and percentage of data points exceeding the median of baseline phase (PEM) approach, and (b) to demonstrate application of the PEM approach in conducting a quantitative synthesis of single-subject research investigating the…

This report describes how journaling and email were used to benefit both the teacher and her students on a college campus in Georgia. The report outlines how decisions were made about the content of the journals, submission deadline considerations, and concerns about the e-journal process. Benefits to the teacher/professor are enumerated and…

This report is part of a long-term research on the construction of mathematical meanings through the interaction with various technologies. The research involved a set of teaching experiments based on body motion with sensors and calculators at different school levels, from kindergarten to secondary school. Here I refer to the one developed in a…

Integrating mathematics with family and consumer sciences (FCS) has enabled youth to pass the Minnesota 8th Grade Math Basic Skills test. The test focuses on the eight content areas: (1) problem solving with whole numbers and fractions; (2) problem solving with percentage/ratio; (3) number sense; (4) estimation; 5) measurement; (6) tables and…