As we typically teach in an introductory mechanics course, choosing a "good" coordinate frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of…

This study examined the problem posing strategies of pre-service primary school teachers in different problem posing situations (PPSs) and analysed the issues they encounter while posing problems. A problem posing task consisting of six PPSs (two free, two structured, and two semi-structured situations) was delivered to 40 participants.…

In this article on introductory calculus, intriguing questions are generated that can ignite an appreciation for the subject of mathematics. These questions open doors to advanced mathematical thinking and harness many elements of research-oriented mathematics. Such questions also offer greater incentives for students to think and reflect.…

There are many factors that influence designers in the architectural design process. Cognitive style, which varies according to the cognitive structure of persons, and spatial experience, which is created with spatial data acquired during life are two of these factors. Designers usually refer to their spatial experiences in order to find solutions…

Developing the problem solving competency is one of the main goals of school education, as it is a very important competency in someone's everyday life and career as well. Mathematics is highly appropriate for developing this competence. This research studies future Primary and Preschool Pedagogy specialization students' mathematical problem…

The project method became a famous teaching method when William Heard Kilpatrick published his article "Project Method" in 1918. The key idea in Kilpatrick's project method is to try to explain how pupils learn things when they work in projects toward different common objects. The same idea of pupils learning by work or action in an…

The following kinematics problem was given to several students as a project in conjunction with a first-semester calculus-based physics course. The students were asked to keep a journal of all their work and were encouraged to keep even their scrap paper. The goal of the project was to expose the students to the process of doing theoretical…

One of the most popular student modeling approaches is Constraint-Based Modeling (CBM). It is an efficient approach that can be easily applied inside an Intelligent Tutoring System (ITS). Even with these characteristics, building new ITSs requires carefully designing the domain model to be taught because different sources of errors could affect…

The ability to search, process, extract, evaluate and integrate information for learning purposes has clearly become the basic skills of the twenty first century. Although this process is often taken as a cognitive process, research has shown a strong connection between emotion and cognition. Recent research has suggested that positive emotions…

Today, much problem solving is performed by teams, rather than individuals. The complexity of these problems has exceeded the cognitive capacity of any individual and requires a team of members to solve them. The success of solving these complex problems not only relies on individual team members who possess different but complementary expertise,…

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

A well-known mathematical puzzle regarding a worm crawling along an elastic rope is considered. The resulting generalizations provide examples for use in a teaching context including applications of series summation, the use of the integrating factor for the solution of differential equations, and the evaluation of definite integrals. A number of…

Several educators have advocated teaching thermodynamics using a"global" approach in place of the conventional "local" approach. This article uses four examples of experiments to illustrate the two formulations and the definitions of heat and work associated with them. Advantages and disadvantages of both approaches are…

It is frequently assumed that by virtue of their hearing losses, deaf students are visual learners. Deaf individuals have some visual-spatial advantages relative to hearing individuals, but most have been linked to use of sign language rather than auditory deprivation. How such cognitive differences might affect academic performance has been…

The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…