Three distinct points A = (a, 0, 0) B = (0, b, 0) and (c, 0, 0) with abc not equal to 0 are taken, respectively on the "x", "y" and the "z"-axes of a rectangular coordinate system in R[superscript 3]. Using the converse of the theorem of Pythagoras, it is shown that the triangle [delta]ABC can never be a right-angled triangle. The result seems to…

The Developmental Audit[R] offers an alternative to traditional assessments that diagnose disorder and focus on pathology. These assessments often end with negative labels for the child and discouraged spirits for all involved in that young person's life. The Developmental Audit[R], on the other hand, encourages youth in conflict to help identify…

The author teaches a content course in problem solving for middle school teachers. During the course, teacher candidates have the opportunity to confront their insecurities as they actively engage in solving math problems using a variety of strategies. As the semester progresses, they add new strategies to their problem-solving arsenal and…

In this short note, by using one of Li and Liu's theorems [K.-H. Li, "The solution of CIQ. 39," "Commun. Stud. Inequal." 11(1) (2004), p. 162 (in Chinese)], "s-R-r" method, Cauchy's inequality and the theory of convex function, we solve some geometric inequalities conjectures relating to an interior point in triangle. (Contains 1 figure.)

Increasing complexity is one of the most pertinent issues when discussing the role and future of design, designers and their education. The evolving nature of digital media technology has resulted in a profession in a state of flux with increasingly complex communication and design problems. The ability to collaborate and interact with other…

This paper firstly introduces the concept of constructivist learning which advocates that students actively construct knowledge themselves with teachers' assistance. Based on the six important elements of constructivist learning and teaching planning approach, detailed examples of designing the six constructivist elements of situation, groupings,…

Education experts argue that using rich mathematical tasks in student-centered classrooms is especially conducive to student learning (NCTM 2000). That said, they also acknowledge that using complex tasks and developing student-centered classrooms can be intimidating and challenging for teachers (Chazan and Ball 1999). One difficulty associated…

We discuss a mathematics capstone course designed to help students grow in mathematical independence. We describe how the course is structured to support this goal and the major assignments: a course wiki, a group expository project, and an individual problem to solve and extend. Students learn to ask and answer their own questions, helping them…

"Strategy sharing" is a certain type of discussion that centers on students' ideas and occurs when children present different approaches to problems and provide information about how they solved the problem (Wood, Williams, and McNeal 2004). A teacher may orchestrate a strategy-sharing discussion to achieve one or more of the…

As we journey further into the 21st century, apprehensions emerge among business leaders in American markets. These concerns do not go unwarranted or unnoticed. Contemporary data portrays a despondent picture regarding new graduate preparedness for the global workforce. The findings reveal that employers feel the new entrants are deficient in the…

This paper describes changing the way a business statistics course is taught through the use of just-in-time teaching methods. Implementing this method allowed for more time in the class to be spent focused on problem solving, resulting in students being able to handle more difficult problems. Students' perceptions of the just-in-time assignments…

This article describes two methods for use in program development and refinement. Problem mapping and forcefield analysis are explained with a real-world example about parenting education. Both methods are visual and consider multiple causes and effects of a problem. The methods are effective for clearly thinking through a problem, identifying…

In this paper we offer a theoretical discussion on the mathematical content knowledge development of secondary school mathematics teachers. We discuss relevant studies from literature and use different views and conceptions of school mathematics to propose a model to develop or transform the mathematical content knowledge of secondary school…

This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…