Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts-in-action and theorems-in-action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric…

The National Council of Teachers of Mathematics calls for an increased emphasis on proof and reasoning in school mathematics curricula. Given such an emphasis, mathematics teachers must be prepared to structure curricular experiences so that students develop an appreciation for both the value of proof and for those strategies that will assist them…

Students in grades four-six were asked to complete multiplication examples and write a story problem (reported earlier, SE 533 279). Their stories were categorized in terms of their logic and realism. Many errors were noted, leading to the conclusion that knowledge of multiplication does not necessarily lead to logical multiplication. (MNS)

Three definitions of "back-to-the-basics" are given and discussed. The idea that science provides opportunities to practice the most "skill-thinking" is also discussed. (MK)

Provides examples of if-then and combinatorial reasoning situations that have proved successful with college students and can be used with secondary school students. Proposes that practice with these problem solving processes can eliminate the need to memorize formulas that students may not understand. (ML)

Selects five critical elements for success in problem solving in mathematics and in computer programing: general strategy; planning; logical thinking; variables; and debugging. Describes the role of the five elements based on a literature review. Forty-one references are listed. (YP)

Discusses the claims that experiences in computer programming enhance performance on conditional reasoning tasks. Describes three experimental studies designed to address that hypothesis using three different populations of students. Results of all three studies indicate nonsignificant treatment effects. (TW)