The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

Students who are labelled as low attaining in mathematics are often seen as a homogeneous group and as such can be assigned learning attributes by others that observe their identity work in the classroom. Rachel Helme argues that by giving attention to an otherwise marginalised voice, it may be possible to challenge the discourse of deficiency,…

This study aims to explore a phenomenon of a one-off manifestation of mathematical creativity on the part of a student, against the background of her normative and not especially creative behavior--a flash of creativity. We seek to elaborate on this phenomenon in terms of the 4P (person, press, process and product) model of creativity. Namely,…

Describes an exploratory investigation of how children reacted to problems with missing, surplus or contradictory data. It was found that the majority of children gave unsatisfactory answers to such problems. (PK)

Appreciating the power and beauty of mathematical thought should be an integral component of a student's mathematical education. The meaning of aesthetics in the realm of mathematical reasoning, the relationship of aesthetics to problem solving, the results of two studies, and recommendations for developing aesthetics are included. (MNS)

How the author moved from concern about research to development of prescriptive models of heuristic problem solving and the exploration of metacognition and belief systems is discussed. Student beliefs about problem solving, and their corollaries, are included. (MNS)

Examined the effects of disruptive behavior in mathematics classes. Reported a case study of 31 Greek students considered to be very difficult. Concluded that an alternative approach toward students' concerns--based on human communication, discussion, and negotiation--improved classroom behavior in general. (MDH)

Discusses problem posing as a feature of creative activity or exceptional mathematical ability, inquiry-oriented instruction, mathematical activity, improving students' problem solving, a window into students' mathematical understanding, and improving students' disposition toward mathematics. (Contains 70 references.) (MKR)

Shares a psychological look at student images of mathematical learning and problem solving through students' writings about mathematical experiences. The analysis is done from a Jungian psychoanalytic orientation with the goal of assisting students develop a deeper perspective from which to view their mathematics experience. (MDH)

Considers how the domains of mathematics education and history of mathematics may interact in the process of mathematics teaching. Focuses on the teachers' role and explores the relationship between research in mathematics education and the history of mathematics. Contains 24 references. (DDR)

Speculates on whether our knowledge of a mathematical topic is really the same as the knowledge of the topic held by our mathematical ancestors centuries ago. Provides specific examples of using the cultural context of mathematics as an instructional strategy. (DDR)

Discusses "connectionism," an alternative learning model wherein meaning resides in the function of the whole state of a network, rather than being localizable in certain symbols or areas. Topics discussed include integration with other learning models; the culture of the mathematics classroom; and characteristics of alternative…

Presents activities that integrate story telling, history, and problem solving as a stimulus for discussion and creativity in the elementary mathematics classroom, and a way to relieve children's anxiety in an escalating curriculum. (MDH)

Presents contributions by six mathematics teachers responding to the question: "How has the history of mathematics mattered to me in my mathematics teaching?" Answers touch the topics of how and why, how benefits are accrued, use of original texts, integration into core curriculum courses, and pitfalls of history. (MDH)