While some disasters involving engineered structures are due to events in nature (e.g., tornadoes, hurricanes, earthquakes), others may be caused by inadequate materials, design flaws, and poor maintenance. These catastrophes result in the loss of human lives and cost billions of dollars. In the set of lessons described here, students design a…

Many educators believe that mathematical investigation involves both problem posing and problem solving, but some teachers have taught their students to investigate during problem solving. The confusion about the relationship between investigation and problem solving may affect how teachers teach their students and how researchers conduct their…

In a recent paper (Denny 2002 Eur. J. Phys. 23 449-58), entitled "The pendulum clock: a venerable dynamical system", Denny showed that in a first approximation the steady-state motion of a weight-driven pendulum clock is shown to be a stable limit cycle. He placed the problem in a historical context and obtained an approximate solution using the…

This module was initially developed for a course in applications of mathematics in biology. The objective of this lesson is to investigate how the allele and genotypic frequencies associated with a particular gene might evolve over successive generations. The lesson will discuss how the Hardy-Weinberg model provides a basis for comparison when…

The 3 most often-used performance measures in the cognitive and decision sciences are choice, response or decision time, and confidence. We develop a random walk/diffusion theory--2-stage dynamic signal detection (2DSD) theory--that accounts for all 3 measures using a common underlying process. The model uses a drift diffusion process to account…

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

Mathematics may be inconceivable without its diagrams and symbols--its representations. Mathematical representations help individuals organize their thinking; they bring a visual component to abstract ideas and serve as templates for computation with understanding. But the inevitability of representations is no guarantee that they are used…

Upper primary school children often routinely apply proportional methods to missing-value problems, even when it is inappropriate. We tested whether this tendency could be weakened if children were not required to produce computational answers to such problems. A total of 75 sixth graders were asked to classify 9 word problems of three types (3…

Problems on the dynamics of changing mass systems often call for the more general form of Newton's second law Fnet = dp/dt. These problems usually involve situations where the mass of the system decreases, such as in rocket propulsion. In contrast, this experiment examines a system where the mass "increases" at a constant rate and the net force…

This interpretative phenomenological analysis study explored seven adult survivors' experiences of coping with childhood sexual abuse and identified their coping strategies on the road to recovery. Data for the analysis was collected using semistructured interviews. The analytical process yielded two key theme clusters: avoidant coping strategies…

Problem-based learning (PBL) is an instructional approach that is organized around the investigation and resolution of problems. Problems are neither uniform nor similar. Jonassen (1997, 2000) in his design theory of problem solving has categorized problems into two broad types--well-structured and ill-structured. He has also described a host of…

Two experiments tested whether differences in problem-solving strategies influence the ability of people to monitor their problem-solving effectiveness as measured by confidence judgments. On multiple choice problems, people tend to use either a constructive matching strategy, whereby they attempt to solve a problem before looking at the response…

This material has been used twice as an out-of-class project in a mathematical modeling class, the first elective course for mathematics majors. The only prerequisites for this course were differential and integral calculus, but all students had been exposed to differential equations, and the project was assigned during discussions about solving…

Insects are fascinating creatures--especially when you and your students get up close and personal with them! To that end, the authors facilitated an inquiry-based investigation with an emphasis on identification of the different types of insects found in the school yard, their characteristics, their habitat, and what they eat, while engaging the…

Relations were examined between epistemic profiles, metacognition, problem solving, and achievement in the context of learning in an educational psychology course. Two hundred thirty-one university students completed self-report inventories reflecting their epistemic profiles and use of metacognitive strategies, and were epistemically profiled as…