This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

The purpose of this study was to examine whether a video-induced positive and negative mood has a differential effect on subsequent problem-solving activities in a web-based environment. The study also examined whether task conditions (task demands) moderated the mood effect. As in traditional experimental mood-effect studies, the affective video…

In this article, framed as a conversation, the authors discuss the learning resulting from a variety of geometry tasks they have conducted with their students. None of them are convinced that all the geometry tasks within the numeracy strategy prescribed in English schools are necessarily good for children or aimed at the right age range. Using…

This article presents a story of Robert Andrew's mental engagement with mathematics. It has been jointly written by Robert, who is a Y8 student, and his father, Paul Andrews, who is a mathematics educator. It starts with Robert who presents the context for the story and is followed by Paul's commentary which draws on what Robert has written.…

This study investigated the use of diagrammatic representation as an aid for recalling a past event for 30 4-5-year-olds in their preschool year prior to commencing primary school. The children were randomly placed into one of two groups: "talkers" (verbal memory) or "drawers" (diagrammatic memory). They were interviewed individually, both one day…

This article deals with the increasing academic pressure facing five-year-old children who are in kindergarten schools in the U.S. Part of the reason kindergarten is becoming more and more academic is a growing understanding of the importance of early learning and the capabilities of young children. Proponents of ramping up standards in early…

Before the advent of symbolism, i.e. before the end of the 16th Century, algebraic calculations were made using natural language. Through a kind of metaphorical process, a few terms from everyday life (e.g. thing, root) acquired a technical mathematical status and constituted the specialized language of algebra. The introduction of letters and…

Three related studies replicated and extended previous work (J.A. Danielson et al. (2003), "Educational Technology Research and Development," 51(3), 63-81) involving the Diagnostic Pathfinder (dP) (previously Problem List Generator [PLG]), a cognitive tool for learning diagnostic problem solving. In studies 1 and 2, groups of 126 and 113…

"Cognitive Tutor[R] Algebra I," a full year course, delivers instruction in single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The…

The purpose of this scholarship of teaching research is to assess the effectiveness of a cross-cultural problem-solving assignment in two senior-level family and consumer sciences courses at the University of Wyoming. We focus on the development of selected cognitive and affective critical-thinking skills in undergraduates and their international…

We report on two case studies in which we investigated mathematics for teaching. We were interested in the mathematical knowledge teachers need to know, and know how to use, in order to teach mathematics well. The two case studies focused on the teaching of probability in Grade 8 and the teaching of functions in Grade 10. We discuss the…

I identify and discuss ways in which different types of connections are described in the South African mathematics National Curriculum Statement and its related documents, particularly at the Further Education and Training (FET) level. I argue that connections are central to the way the discipline of mathematics, its learning outcomes, and…

Reasoning and learning are closely related, both being the methods of solving problems, learning usually results from the process of reasoning. All inventions, discoveries, art, literature and advances in culture and civilization are based on thinking, reasoning and problem solving capacity of human being. A sound reasoning leads to better…

The most intriguing reforms in K-12 education today are entrepreneurial ventures like the New Teacher Project, the KIPP Academies, and New Leaders for New Schools, which command notice for their efforts to reimagine schooling. In "The Future of Educational Entrepreneurship: Possibilities for School Reform," the author collaborates with a…

This study aims at investigating the validity and reliability studies of the "Computer Anxiety Scale" (Ceyhan & Gurcan Namlu, 2000) on educational administrators. The data gathered from 143 educational administrators of state schools located in Eskisehir show that the scale consists of 2 factors. The first of these factors, affective…