Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

Anne Roche and Doug Clarke discuss the importance of developing students' persistence in relation to problem solving during the use of challenging tasks. They provide a useful list of strategies that teachers can use to encourage persistence amongst their students.

Using errors as a method of learning has been made explicit through a two-staged peer review and discussion. During organic chemistry discussion sessions, quizzes are followed by a structured peer review designed to help students identify and discuss student errors. After the face-to-face discussion, a second stage of review involves analyzing and…

School psychology in Singapore gained greater prominence with the development of the National Mental Health Blueprint in 2007 that included a focus on children and adolescents. A partnership between the Ministry of Health and the Ministry of Education was formed to develop a community mental health pilot program called 'Response, Early…

To address third- and fourth-year chemistry students' difficulties with the challenge of interpreting [superscript 1]H NMR spectra, a problem solving-cooperative learning technique was incorporated in a Spectra of Organic Compounds course. Using this approach helped students deepen their understanding of the basics of [superscript 1]H NMR…

The author argues that there is still too much teaching to the test, and the consequence is growing "constellations" of problem-based learning (PBL), some of which are useful, and some of which are not. Today, what passes for PBL practice often seems more like guidelines than any kind of reasoned pedagogy. While at one level the range of…

The author explores concrete ways to help students learn more and have fun doing it while they support each other's learning. The article specifically shows the relationships between cooperative learning and deep learning. Readers will become familiar with the tenets of cooperative learning and its power to enhance learning--even more so when…

Model-eliciting activities (MEAs) are not new to those in engineering or mathematics, but they were new to Melissa Parks. Model-eliciting activities are simulated real-world problems that integrate engineering, mathematical, and scientific thinking as students find solutions for specific scenarios. During this process, students generate solutions…

International educational consultation is challenging work that requires not only attention to best practices in consultation but also additional focus on cultural norms and regularities. In the three articles of this special issue, the consultation competencies of consultants play a critical role, as exemplified by entry issues, problem-solving…

The author's teaching goal is always to make certain that his students, children and adults alike, have some reason for joining him on his mathematical journeys. The lesson he describes in this article provides him with the unusual opportunity to call attention to strategies that have had a long history and remarkable results. With careful…

As part of the author's doctoral program at the University of Hawai'i at Manoa, she conducted a study to determine whether and how former sixth-grade students at Waikiki School were using the thinking processes and strategies they were taught in elementary school when they were in middle school. In order to find this out, she interviewed eight…

Fermat's principle is considered as a unifying concept. It is usually presented erroneously as a "least time principle". In this paper we present some software that shows cases of maxima and minima and the application of Fermat's principle to the problem of focusing in lenses. (Contains 12 figures.)

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

An approximate formula for the period of pendulum motion beyond the small amplitude regime is obtained based on physical arguments. Two different schemes of different accuracy are developed: in the first less accurate scheme, emphasis is given on the non-quadratic form of the potential in connection to isochronism, and a specific form of a generic…

Understanding the functional neuroanatomy of planning and problem solving may substantially benefit from better insight into the chronology of the cognitive processes involved. Based on the assumption that regularities in cognitive processing are reflected in overtly observable eye-movement patterns, here we recorded eye movements while…