Authenticity is a term commonly used in reference to pedagogical and curricular qualities of mathematics teaching and learning, but its use lacks a coherent framework. The work of researchers in engineering education provides such a framework. Authentic qualities of mathematics teaching and learning are fit within a model described by Strobel,…

John McNamara shares his wisdom and humbly credits Camillo Grazzini, Jenny Höglund, and David Kahn for his growth in Montessori. Recognizing more than what he has learned from his mentors, he shares the lessons he has learned from his students themselves. Math, science, history, and language are so integrated in the curriculum that students…

Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability…

This Application Brief highlights Seattle University's Red Winged Leadership (RWL) exercise, an innovative curriculum for graduate business leadership education. RWL requires students to apply course materials to a visible and challenging class project, and to critically examine and recognize leadership in the broader community. Both allow for…

Social studies educators have encouraged the use of primary sources and inquiry in the classroom for decades; however, inquiry-based instruction in which students engage meaningfully with primary sources remains the exception rather than the norm. The publication of the College, Career and Civic Life (C3) Framework for Social Studies State…

Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

The article presents and illustrates the learning journey (LJ)--a new management development approach to inter-organisational learning based on observation, reflection and problem-solving. The LJ involves managers from different organisations and applies key concepts of action learning and systemic organisational development. Made up of…

Traditionally, "z" is assumed to be a complex number and the roots are usually determined by using de Moivre's theorem adapted for fractional indices. The roots are represented in the Argand plane by points that lie equally pitched around a circle of unit radius. The "n"-th roots of unity always include the real number 1, and…

Making sense of mathematical concepts and solving mathematical problems may demand different forms of reasoning. These could be either domain-based, such as algebraic, geometric or statistical reasoning, while others are more general such as inductive/deductive reasoning. This article aims at giving visibility to a particular form of reasoning…

By describing the motion of a charged particle in the well-known nonuniform field of a current-carrying long straight wire, a variety of teaching/learning opportunities are described: 1) Brief review of a standard problem; 2) Vector analysis; 3) Dimensionless variables; 4) Coupled differential equations; 5) Numerical solutions.

To familiarize first-year students with the important ingredients of a physics experiment, we offer them a project close to their daily life: measuring the effect of air resistance on a bicycle. Experiments are done with a bicycle freewheeling on a downhill slope. The data are compared with equations of motions corresponding to different models…

The very nature of algebra concerns the generalization of patterns (Lee 1996). Patterning activities that are geometric in nature can serve as powerful contexts that engage students in algebraic thinking and visually support them in constructing a variety of generalizations and justifications (e.g., Healy and Hoyles 1999; Lannin 2005). In this…

Because of the gross difficulties in measuring the societal impact of academic research, qualitative approaches have been developed in the last decade mostly based on forms of interaction between university and other societal stakeholders. In this paper, we suggest a framework for qualitative analysis based on the distinction between three…

Proliferation of prescriptive models in an "engineering" field is not a sign of its maturity. Quite the opposite. Materials engineering, for example, meets the criterion of parsimony. Sadly, the very large number of models in "instructional design," putatively an engineering field, raises questions about its status. Can the…

Physical educators generally understand the importance of the affective domain for student growth and development. However, many teachers struggle with assessing affective behaviors in a way that can be documented and reported. The five-step process outlined in this article can assist teachers in developing an effective way to assess the affective…