Evaluation of the relationship between metacognition and analogical reasoning in 80 children (mildly retarded, learning disabled, normal achieving, and gifted) suggests that retarded children's performance reflected a central processing deficiency across processes, learning-disabled children's performance reflected specific processing…

Six fifth-grade children participated in a four-day teaching experiment on complex additively structured problems to investigate difficulties in concurrently holding in mind situations in which items play multiple roles. Difficulties included distinguishing take-away difference from comparison difference and indirect evaluation of an additive…

Twenty-nine children with learning disabilities (LD) in grades 2 and 4 through 7 were compared with children without LD for their development of proportional structures of thought. Significantly fewer children with LD had constructed second-order logical structures necessary to act on problems using multiplicative and preproportional reasoning.…

Despite its apparent simplicity, random assignment is an abstract concept for many students. This article describes a classroom demonstration that uses a standard deck of playing cards. In small groups, students randomly assign playing cards (i.e., participants) to 2 treatment groups. Following randomization, students compare the relative…

Eight teachers were interviewed concerning how students verify conjectures. The study is a sequel to a previous study, "How Students Verify Conjectures" [Bergqvist, T. (2000). "How students verify conjectures." "Research reports in Mathematics Education" 3]. Teachers' expectations of students' reasoning and performance are examined, and also how…

One of the characteristics of the well-documented bifurcation in collegiate foreign language (FL) instruction is the difficult transition from lower- to upper-level instruction. Particularly pronounced are the expectations placed on readers at the upper level. No longer engaged in surface readings and sentence-level exercises that stay focused on…

This article describes an innovative curriculum module the first author created on the two-way exchange between statistics and applied ethics. The module, having no particular mathematical prerequisites beyond high school algebra, is part of an undergraduate interdisciplinary ethics course which begins with a 3-week introduction to basic applied…

In your interactions with secondary school students learning science, you have probably become aware of large differences in student ability to understand science concepts, conduct investigations, and/or solve specific problems. Some students are extremely capable, while others demonstrate peculiar and inappropriate reasoning strategies.…

Is it feasible and appropriate to develop a sustainability metrics which captures cosmological-spiritual dimensions of un/sustainability? Departing from the supposition that the crisis of unsustainability is a crisis of worldview and misguided cosmology which needs redirection on a cultural and global scale, this essay introduces the notion of a…

This submission contains the Proceedings of the 2008 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the Universite de Sherbrooke in Sherbrooke, Quebec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of…

This study reports on the historical conceptualization among Finnish 12-13 year-olds who were given a projective task to yield historical thinking. The case study examines expressions the subjects used and which were studied qualitatively, using "chunks of meaning" as units of analysis, in regard to both their meaning- content and their…

The research reported in this paper was designed to investigate the hypothesis that computer programming may support the teaching and learning of problem solving, but that to do so, problem solving must be explicitly taught. Three studies involved students in several grades: 4th, 6th, 8th, 11th, and 12th. Findings collectively show that five…

The 56 tests described in this bibliography include instruments developed by Jean Piaget and others, based upon his work. Some instruments apply his concepts to measuring children's abilities and knowledge in mathematics, science, music, and reading. Several tests are diagnostic tests to identify individuals who may need special attention. All…

Math historian Morris Kline suggests that math instruction should be made concrete and that teachers should not turn kids off by making intuitively understood concepts complex through the use of fancy language. He advocates using pictorial representations and examples of actual physical occurrences. The dyslexic student has special difficulties in…

A total of 121 third and fourth graders were randomly assigned to instructional treatments which each featured a short children's story. The treatments were oral-only, picture-only, and a combination of oral and pictures. Students saw and/or heard the presentation and were tested immediately and after a two-week retention interval for recall of…