If British Columbia education policy wanted to promote growth in numeracy and mathematics, the curriculum would provide opportunities to use mathematical concepts in social situations and give students time to move from concrete to abstract thought. Instead, the curriculum emphasizes extensive mechanical understanding and algorithmic manipulation…

Recent contributions from theory, research, and practice in second-language instruction are discussed in relation to mathematics education. Three methods of teaching and learning second languages are described--"Delayed Oral Production," the "Silent Way," and the "Counseling Learning/Community Language Learning." (KR)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

Among conclusions of the review of the literature are that learning-disabled (LD) females have lower IQ's and more severe academic achievement deficits in some aspects of reading and math, but are somewhat better in visual-motor abilities, spelling, and written language mechanics than LD males. (Author/DB)

Argues that the emphasis in law courses on memorizing facts fails to teach the desired concepts of reasoning and problem-solving. Recommends the use of open-book tests. Suggests that because law is an imprecise subject, and there are no right or wrong answers, it should be taught in an open format. (LS)

Children's magical explanations and beliefs were investigated in two studies. Found that many four-year olds view magic as a plausible mechanism, yet reserve magical explanations for certain real world events that violate their causal expectations. Parents and culture at large may at first actively support magical beliefs whereas peers and schools…

Examined the developmental sequence through which adolescents progress in solving a physics problem (balance beam ratio and proportion) and a social problem (predicting the behavior of a story character). Although most of the 9- through 19-year-olds performed at predictable and similar developmental stages on each task, a minority were more…

Examined the conceptions of freedom of speech and religion held by 48 adolescents and young adults, using a structured interview containing assessments of civil liberties in general, in straightforward applications, and in conflict with other social and moral concerns. Findings indicate that sophisticated conceptions of civil liberties emerge by…

The importance of instructing gifted students in correlational reasoning is emphasized, with attention to what the skill involves and why it is difficult to learn; effective teaching strategies; and successful programs in whole-class, cooperative-learning, and computer formats. Implications in programming for gifted students are discussed. (SW)

Challenges the readers comprehension of mathematical induction by presenting four examples of arguments that misrepresent the concept. Discusses the reasons why the arguments lead to false conclusions. (MDH)

This article presents the "concrete semiconcrete abstract" (CSA) teaching sequence for teaching basic math skills to students with and without learning disabilities. Guidelines include providing a minimum of nine instructional lessons (three at each level), each with four lesson steps. Validation of the CSA sequence and lesson format with 15…

This study focused on the validation of Generalizable Reasoning Skills assessment instruments with students with disabilities in secondary vocational programs. Results indicated that student self-ratings, teacher ratings, and a performance test were internally consistent and precise measures of reasoning skills for some uses but that most…

The reasoning abilities to be expected of the concrete operational and formal operational student, the percentage of secondary science students that are capable of each type of reasoning pattern, and effective strategies to teach science to concrete reasoners are described. Implications for curriculum development are discussed. (KR)

Beginning geometry students misunderstand the requirements of formal proof because of confusion between deductive reasoning and argumentation. Presented is a cognitive analysis of deductive organization versus argumentative organization of reasoning and the applications of this analysis to learning. Implications of a study analyzing students'…

Examples of high school case studies are used to illustrate prototypical mathematical images and the use of imagery in metaphoric and metonymic ways in mathematics. Discusses pattern imagery and other types of imagery as central components in a model of mathematical reasoning. (34 references) (MDH)