Against the backdrop of half a century of research in mathematics problem solving, Polya's last stage is especially conspicuous--by the scarcity of research on it! Much of the research focused on the first three stages (J.M. Francisco and C.A. Maher, "Conditions for promoting reasoning in problem solving: Insights from a longitudinal…

This article discusses the resources available for teachers to apply higher-level thinking and cognitive complexity to their instruction and assessments. While designing higher-level assessments might be a challenging task, doing so not only can improve student achievement in science, it also prepares students for a changing world. Students learn…

Prior research suggests that students' understanding of scientific concepts is pre-determined by their reasoning ability. Other efforts suggest that American students' scientific literacy is in decline. One difficulty Bybee (2009) acknowledges is that there are two divergent philosophical models of scientific literacy. The first describes the…

The concept of creativity has been the subject of much research since the 1950s. These theories mainly focus on the individual, personal characteristics of creativity. However, in the past few decades this person-centered spectrum of creativity has been broadened, and today we encounter several theories that emphasize the importance of…

In this paper, students used problem-solving skills to investigate what patterns exist in the Pascal triangle and incorporated technology using Geometer's Sketchpad (GSP) in the process. Students came up with patterns such as natural numbers, triangular numbers, and Fibonacci numbers. Although the patterns inherent in Pascal's triangle may seem…

The author is a product of school-based agricultural education. In a way, this distinguished lecture could also be called a tribute to his high school ag teacher, John Stimpert. Mr. Stimpert was a true professional and an excellent teacher. He changed and he changed the program with the changing school and community. The more the author became…

Learning mathematics is challenging. It requires discipline, logic, precision, perseverance, and accuracy. It can also be fun. When mathematics is set in a context that inspires students to want to solve interesting problems, students will have an intrinsic desire to learn the necessary skills to accomplish a specific goal. The game of Crypto! was…

This article examines the bicycle as not simply a means of transportation or as an exercise device, but rather as a vehicle for teambuilding and problem solving activities within a physical education curriculum. The activities described in this article focus on bike-centered initiatives that foster creative problem solving. They have universal…

Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

We describe the difficulties that advanced undergraduate and graduate students have with quantum measurement within the standard interpretation of quantum mechanics. We explore the possible origins of these difficulties by analyzing student responses to questions from both surveys and interviews. Results from this research are applied to develop…

The Virtual Genetics Lab II (VGLII) is an improved version of the highly successful genetics simulation software, the Virtual Genetics Lab (VGL). The software allows students to use the techniques of genetic analysis to design crosses and interpret data to solve realistic genetics problems involving a hypothetical diploid insect. This is a brief…

There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…

Early childhood teacher education courses must prepare students for the types of challenges they will face in communities and classrooms after graduation. By adopting a scenario-based approach, teacher educators and others designing online environments can help prepare students for these challenges. Solving complex problems inherent in a…

It can be difficult to connect with parents of students in upper elementary grades, because as they get older, students generally seek independence and do not want their parents involved as much as they have been in their younger years. Teachers must work at finding a way to reach out to parents. The author started parent science nights so she…

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…