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…

Learning about linear relationship with one unknown, middle school students may often demonstrate a certain degree of proficiency manipulating algebraic symbols. When encouraged, they can verbalize and explain the steps they perform, thereby demonstrating awareness of the procedures with symbols according to fixed rules. It is well known that…

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…

Study results indicate that teachers should be less concerned with teaching relationships between problem elements and more concerned with helping students to identify logical assumptions made in problem statement. (Author)

Problems short on computation and long on logical thinking are suggested for development of logical thinking. A set of such problems is presented. (MP)

Examines the relationship between development of logical processes required in deductive reasoning and their use by preschoolers, also considering possible explanations for children's deductive reasoning. The relationship of problem content to real-world knowledge and the sequence of presentation of problem types were found to affect the display…

Describes experience of teaching truth tables and problems that exercise students' critical reasoning. (KHR)

This manual provides a comprehensive approach to problem solving; it is written in narrative style with numerous examples. The guide is organized in eight sections that cover the following topics: (1) problem-solving overview (with suggested readings and recommendations for schools); (2) a five-step model for solving problems; (3) strategies for…

The effect of special instruction in certain reading skills involved in solving verbal problems was compared with the effect of supervised practice in solving verbal problems on the improvement of verbal problem-solving ability of 179 fourth graders. The sample from six classes in three public elementary schools in Cuyahoga Falls, Ohio, was…

These materials were developed for use in workshops with teachers. The document suggests a four-stage framework which students can apply to problems: (1) get to know the problem; (2) choose what to do; (3) do it; and (4) look back. Suggestions are included for each of the four stages of the probem solving process. Other specific techniques for…

This paper describes the rationale behind and the development and utilization of a bibliographic instruction course which incorporates formal abstract reasoning skills. The limitations of the search strategy technique of bibliographic instruction are discussed as well as the fact that many college students have not developed sophisticated…

This book combines suggestions for the teaching of problem solving with activities and carefully discussed non-routine problems which students should find interesting as they gain valuable experience in problem solving. The over 300 activities and problems have been gleaned from a variety of sources and have been classroom tested by practicing…