The new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. "The Art of Problem Posing, Third Edition" encourages readers to shift their thinking…

This conference proceedings contains three plenary session reports, 12 working group and 79 research reports, 35 short oral reports, 60 poster session reports, and two discussion group reports. Major papers (excluding "short orals" and "posters") include: (1) "Semantical Obstacles in Mathematics Understanding" (Carlos Arteaga and Manuel Santos);…

This paper discusses the author's personal experiences in developing and implementing a problem-based college mathematics course for liberal arts majors. This project was initiated in response to the realization that most students are dependent on "patterning" learning algorithms and have no expectation that self-initiated thinking is a…

An integrated mathematics/science elementary methods course was developed as part of Connecticut's statewide systemic initiative. Considers: (1) What does integration mean? (2) What content should be taught? and (3) How should it be taught? Implementation team included an exemplary elementary teacher. Appendix presents a sample integrated lesson.…

The purpose of this article is to present various techniques that will engage young children, ages 3-8, in learning science and mathematics. Children actively engage in acquiring basic science and mathematics concepts as they explore their environment. The methods presented are intended to meet the developmental levels of young learners as they…

Free, open, online homework help sites appear to be extremely popular and exist for many school subjects. Students can anonymously post problems at their convenience and receive responses from forum members. This mode of tutoring may be especially critical for school subjects such as calculus that are intrinsically challenging and have high…

"QuickSmart" is a basic academic skills intervention designed for persistently low-achieving students in the middle years of schooling that aims to improve the automaticity of basic skills to improve higher-order processes, such as problem solving and comprehension, as measured on standardized tests. The "QuickSmart" instructional program consists…

This book is designed to help teachers use journals to integrate authentic assessment with the instruction of mathematics. It provides a structure to encourage students to write regularly in mathematics. The book is designed to help teachers develop their own assessment questions and activities for additional mathematical explorations. For each…

This qualitative research investigated the effect of a homework model designed to develop students' problem solving behaviors by advancing their ownership of understanding and responsibility. Students were expected to be active learners by isolating and communicating points of homework confusion. The teachers in this study provided feedback…

This paper describes a program for increasing problem solving and critical thinking skills in mathematics. The targeted population consisted of one kindergarten, one first- and one second-grade classroom in an elementary school located in an older established community 12 miles west of Chicago. The problem was documented through student…

This resource book contains 20 magic tricks based on the properties of whole numbers that are intended to spark the interest and imagination of students. Following each activity, students are asked to write about their discoveries and to create their own magic tricks. A matrix of skills for all the activities and lists of the materials required…

This resource book contains 15 magic tricks based on the properties of whole numbers that are intended to spark the interest and imagination of students. Following each activity, students are asked to write about their discoveries and to create their own magic tricks. A matrix of skills for all the activities and lists of the materials required…

Open-ended tasks were used to examine gender differences in complex mathematical problem solving. The results of this study suggest that, overall, males perform better than females, but the gender differences vary from task to task. A qualitative analysis of student responses to those tasks with gender differences showed that male and female…

The use of a visual representation in learning about proportional relations was studied, examining students' understandings of the invariance of a multiplicative relation on both sides of a proportion equation and the invariance of the structural relations that exist in different semantic types of proportion problems. Subjects were 49 high-ability…

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…