In this article, the author applies Makiguchi Tsunesaburo's (1871-1944) perspectives to language policy and planning (LPP). One theoretical question in LPP theory is why individuals opt to use particular languages and varieties of languages in certain contexts. The author contends that Makiguchi's theory of value can be used to systematically…

The article describes the solution of a geometric problem and how this problem was formed. During the investigation process, I discovered that the inscribed parabola in a triangle, known as the parabola of Artzt, a mathematical subject developed almost 120 years ago, was the decisive idea which directed me towards the solution. Moreover, in the…

Analysis of integer structure and right-end-digits can illustrate why 3 and 5 are features of primitive Pythagorean triples. The results also utilize the triangular and pentagonal numbers. (Contains 5 tables.)

This paper describes a pedagogical framework that teachers can use to support students who are engaged in solving open-ended problems, by explaining how two Japanese expert teachers successfully apply open-ended problems in their mathematics class. The Open-Ended Approach (OPA) framework consists of two main sections: Understanding Mathematical…

Linear functions are an important part of the middle school mathematics curriculum. Students in the middle grades gain fluency by working with linear functions in a variety of representations (NCTM 2001). Presented in this article is an activity that was used with five eighth-grade classes at three different schools. The activity contains 15 cards…

Background: Institutions of higher education, specifically schools of education, should play a pivotal role in supporting educators' development of data literacy for teaching. While novice teachers are often prepared to use test-based assessment data, they learn these experiences in isolated courses that do not connect to instruction or school…

Digital games have become popular for engaging students in a range of learning goals, both in the classroom and the after-school space. In this article, I discuss a specific genre of video game, the massively multiplayer online role-playing game (MMO), which has been identified as a dynamic environment for encountering 21st-century workplace…

Purpose: The purpose of this paper is to explore how learning technology could be applied to the development of educational tools for global climate change. The task to be performed in an informed dialogue is to assess the causes and drivers for global climate change and to produce an improved basis of scientific understanding for the…

Since 1973, the National Assessment of Educational Progress (NAEP) has gathered information about student achievement in mathematics. Results of these periodic assessments, produced in print and web-based formats, provide valuable information to a wide variety of audiences. They inform citizens about the nature of students' comprehension of the…

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Afterschool teachers who tutor students or provide homework help have a unique opportunity to help students overcome the social or emotional barriers that so often block learning. They can embrace a creative and investigative approach to math learning. Margaret Kulkin's interest in being a math attitude "myth-buster" led her to apply to…

Recent years have seen a growing interest in intelligent game-based learning environments featuring virtual agents. A key challenge posed by incorporating virtual agents in game-based learning environments is dynamically determining the dialogue moves they should make in order to best support students' problem solving. This paper presents a…

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

Artificial satellites are easily observed most nights when the weather is fine. The website called "Heavens Above" at www.heavens-above.com will help locate these satellites flying over one's location. It also includes how bright they will appear. The direction of travel of each satellite in the night sky also indicates the type of satellite. For…

After completing their introductory studies on thermodynamics at the university level, typically in a second-year university course, most students show a number of misconceptions. In this work, we identify some of those erroneous ideas and try to explain their origins. We also give a suggestion to attack the problem through a systematic and…