Adults and children often encounter situations where they have to make judgments about "how much" or "how long" or "how many." The significance of estimation as an ordinary, everyday, and natural aspect of measurement needs to be conveyed to students through their mathematical experiences. Many students, however, tend…

Performing inquiry should enhance the intellectual development of students on numerous levels. We evaluate whether inquiry-based activities elicit inquiry behaviors by comparing these activities with traditional review sessions. We find that both inquiry-learning and teaching behaviors increase during inquiry-based activities, but that teachers…

The students of a Mathematical Modeling and Problem Solving class investigate and explore the mathematics involved in fitting a box spring mattress up a stairwell by solving various optimization problems and by using The Geometer's Sketchpad. The results show that a very small fraction of the class was actually able to solve the problem without…

For several years a number of instructors at the University of Cincinnati have experimented with the concept of problem-based learning (PBL) in their composition courses. The concept, rooted as it is in Socratic method and the hands-on problem-solving advocated by John Dewey, is not new, and though some of its applications may call for adjustments…

GIS Live is a live, interactive, web problem-solving (WPS) program that partners Geographic Information Systems (GIS) professionals with educators to implement geospatial technologies as curriculum-learning tools. It is a collaborative effort of many government agencies, educational institutions, and professional organizations. Problem-based…

The purpose of this study is to find out if meaningful educational activities and the use of a manipulative in those activities might have an impact on student achievement. Using manipulative as cognitive tools should improve the teaching and learning process, and encourage student reflections on retaining the information. It has been claimed that…

This article explores the use of discourse analysis and conversation analysis as an evaluation tool in problem-based learning. The basic principles of the methods are discussed and their application in analysing talk in problem-based learning considered. Findings suggest that these methods could enable an understanding of how effective…

Beyond Crossroads is a call to action. Within this call, AMATYC has updated its 1995 Crossroads standards, developed a new set of guiding principles, and created a blueprint for implementing these revised principles and standards. The principles guiding Beyond Crossroads are a significant overhaul of their predecessors and are bold statements that…

Purpose: The literature advocates educational decision-making processes that are either intuitive or systematic. While the two approaches seem to be incompatible, each has its merits. Intuitive thinking is considered to be holistic and creative, whereas the systematic approach has the advantages of a theoretical foundation and accuracy in data…

Project-based learning taps into students' interests by allowing them to create projects that result in meaningful learning experiences. The method requires teachers to identify projects that challenge students to work individually or in groups to create plans, solve problems they encounter, test their ideas, and present their projects to peers.…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…

This article describes an activity that incorporates 9 of the 10 National Council of Teachers of Mathematics (NCTM) Standards. Students explore a stacking garden containing multiple layers. The garden allows students to focus on finding the amount of border material needed and the amount of space available for planting. The problem balances the…

Background: Research about sport pedagogy has recently emerged as a significant interest in student reflective practice within the PE teaching/learning system. This learning process is considered as a type of knowledge of co-construction in action. This epistemological assumption postulates that the "knowledge-in-action" is the result of an active…

A comparative study was conducted to compare two approaches to engineering design curriculum between different schools (inter-school) and between two curricular approaches, "Project Lead the Way" (PLTW) and "Engineering Projects in Community Service" (EPIC High) (inter-curricular). The researchers collected curriculum…