This classroom note shows how Fibonacci numbers with negative subscripts emerge from a problem-solving context enhanced by the use of an electronic spreadsheet. It reflects the author's work with prospective K-12 teachers in a number of mathematics content courses. (Contains 4 figures.)

The long awaited blessings of having a child bring simultaneous bouts of confusion and uncertainty regarding the vast parenting responsibilities that come with raising that child. When the child has a disability, sometimes the tasks can seem especially daunting. In this article, the authors aim to guide parents of children who display challenging…

Self-assessments can play a powerful role in developing a child's motivation and achievement. Self-assessments require students to think carefully about what they have learned and how they learn and to develop critical-thinking and problem-solving skills. Students who engage in the productive practice of self-assessment, inevitably strengthen…

Project-Based Learning (PBL) is an innovative approach to learning that teaches a multitude of strategies critical for success in the twenty-first century. Students drive their own learning through inquiry, as well as work collaboratively to research and create projects that reflect their knowledge. From gleaning new, viable technology skills, to…

As a teacher of technical writing, the author applauds the emphasis on the strategies of research and on documented, problem-solving writing across the curriculum and on bringing writing-for-the-workplace into the first-year writing classroom. However, as a teacher of literature, he rejects the notion that responding to literature has no practical…

Over the last few years, cognitive load theory has progressed and advanced rapidly. The articles in this special issue, which document those advances, are based on contributions to the 3rd International Cognitive Load Theory Conference (2009), Heerlen, The Netherlands. The articles of this special issue on cognitive load theory discuss new…

The issue of the area of irregular shapes is absent from the modern mathematical textbooks in elementary education in Greece. However, there exists a collection of books written for educational purposes by famous Greek scholars dating from the eighteenth century, which propose certain techniques concerning the estimation of the area of such…

According to Jacoby (1996), service-learning, officially defined in 1967, is "a form of experiential education in which students engage in activities that address human and community needs together with structured opportunities intentionally designed to promote student learning and development." Service-learning combines academic study,…

A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper,…

Many workshops and meetings with the US high school mathematics teachers revealed a lack of familiarity with the use of transformations in solving equations and problems related to the roots of polynomials. This note describes two transformational approaches to the derivation of the quadratic formula as well as transformational approaches to…

As the impact of humans on the Earth and on its ecological systems that sustain people become more visible--in terms of climate change, resource depletion, and species extinctions--so, too, it is becoming clearer that living sustainably is essential, not optional. To live sustainably requires a mind shift for many people. Education for…

Many statistics texts pose inferential statistical problems in a disjointed way. By using a simple five-step procedure as a template for statistical inference problems, the student can solve problems in an organized fashion. The problem and its solution will thus be a stand-by-itself organic whole and a single unit of thought and effort. The…

Middle school students often struggle when writing testable problems, planning valid and reliable procedures, and drawing meaningful evidence-based conclusions. To address this issue, the author created a student-centered lab handout to facilitate the inquiry process for students. This handout has reduced students' frustration and helped them…

Improving outcomes for children and adolescents with mental health needs demands a broad meta-systemic orientation to overcome persistent problems in current service systems. Improving outcomes necessitates inclusion of current and emerging evidence about effective practices for the diverse population of youth and their families. Key components of…

Simulation environments make it possible for science and engineering students to learn to interact with complex systems. Putting these capabilities to effective use for learning, and assessing learning, requires more than a simulation environment alone. It requires a conceptual framework for the knowledge, skills, and ways of thinking that are…