This guide contains classroom-tested problems designed to introduce and reinforce mathematical concepts in a quick, "fun" way. Activities emphasize the logic and reasoning skills needed to build a strong foundation in mathematics. The problems are thinking activities and require only elementary level mathematics skills. Activities are…

The fragmentation of strategies that distinguishes the more successful elementary grade students from those least successful has been documented previously. This study investigated whether this phenomenon of divergence and fragmentation of strategies would occur among undergraduate students enrolled in a remedial algebra course. Twenty-six…

This book explores individual cognitive processes and the psychology of scientific discovery. Nine studies are presented that investigate childrens' and adults' attempts to make scientific discoveries from a theoretical perspective. Contents include: (1) "Investigating Scientific Thinking: Why and How"; (2) "Scientific Discovery as Problem…

This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…

Drawing on the author's classroom experiences and the curriculum in a program she established called "Literacy through Photography," the book presents a guide to teaching children to express themselves with photographic images. The book includes over 60 black and white photographs as well as anecdotes about the author's work. Five sections follow…

As a part of a long term district-wide study, we report on achievement test results involving students in a third-grade classroom taught by a teacher in a professional development program led by the authors and directed towards the integration of algebraic reasoning with elementary school mathematics. The teacher's practice, reported upon…

This paper describes a models and modeling framework that has been applied to various areas in teaching, learning and problem solving. It examines the implications of that framework on metacognition and higher order thinking during everyday problem-solving situations that required teams of students to produce complex solutions in approximately 1-2…

This toolkit contains a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. A core belief underlying the Toolkit is that good mathematics teaching begins with understanding how mathematics is learned, so these materials…

An inquiry approach to learning is a process whereby students explore, investigate, search for information, discover and seek solutions without much guidance from the teacher in an open classroom environment. Inquiry teaching is not the only method that can be used in the classroom. Unlike other instructional methods, inquiry does involve students…

This paper poses and answers 20 questions about mathematical reasoning. Questions include: (1) Is mathematical reasoning mathematical? (2) Is mathematical reasoning useful? (3) Is mathematical reasoning an appropriate goal of school mathematics? (4) Can teachers teach mathematical reasoning? (5) Can mathematical reasoning be taught? (6) Do skills…

This study describes a program designed to increase the communication skills of at-risk students. The targeted population consists of kindergarten through third grade students in two elementary schools in a community in central Illinois. The status of family income ranges from low to high levels. Evidence for the existence of inadequate…

This report describes a program for developing and improving critical thinking skills in adolescents in order to prepare them for life-long learning. The targeted population consisted of high school math and social studies students from two middle-class communities located in northern Illinois. The students' lack of critical thinking skills was…

This document describes the North Carolina Open-Ended Assessment for grades 4 and 8 and presents results for the 1999-2000 administration. The assessment emphasizes higher level thinking skills and requires students to apply or demonstrate skills and knowledge beyond the recall level on challenging subject matter. The open-ended assessment has…

This study was conducted to measure the development of critical thinking in college students through the creation of instruments to measure critical thinking skills. A Critical Thinking Assessment (CTA) was developed based on other such instruments and the literature. This instrument was tested in a pilot study involving 750 incoming university…

A study examined the change in the critical thinking skills of associate degree nursing students as they progressed through their educational process at the Reedsburg campus of Madison Area Technical College (MATC) in Wisconsin. The study sample consisted of two cohorts of 24 students each (students entering MATC's associate degree nursing program…