This paper presents the results of a systematic review of the empirical literature, reported in research journals, on Mathematics Learner Identity (MLI). In the mathematics education research field, arguments have been made that the conceptualization of Mathematics Identity (MI) is inconsistent and this makes the literature as a whole incoherent.…

We offer criteria that an observer can use to determine whether an argument that uses an example to argue for a general claim appeals to that example generically. We review existing literature on generic example and note the strengths of each contribution, as well as inconsistencies among uses of the term. We offer several examples from the…

The goal of this article is to introduce the topic of "learning to reason from samples," which is the focus of this special issue of "Educational Studies in Mathematics" on "statistical reasoning." Samples are data sets, taken from some wider universe (e.g., a population or a process) using a particular procedure…

Based on the findings of an error analysis revealing that Indonesian ninth- and tenth-graders had difficulties in solving context-based tasks, we investigated the opportunity-to-learn offered by Indonesian textbooks for solving context-based mathematics tasks and the relation of this opportunity-to-learn to students' difficulties in solving these…

In the last three decades there have been a variety of studies of what is often referred to as "everyday" or "street" mathematics. These studies have documented a rich variety of arithmetic practices involved in activities such as tailoring, carpet laying, dieting, or grocery shopping. More importantly, these studies have helped to rectify…

Simplicity arguments are to be found in most geometrical works, from those of Proclus in his "Commentaries on the First Book of Euclid's Elements," up to those of contemporary manuals. Our goal is to read these arguments in their historical contexts to analyze agreements, disagreements and the multiplicity of points of view. For a better…

Presents results of a series of analyses of educational situations involving cultural issues. Of particular significance are the ideas that all cultural groups generate mathematical ideas, and that "Western" mathematics may be only one mathematics among many. The values associated with Western mathematics and other issues are also discussed.…

The literature on proportional reasoning is reviewed. After methodology is discussed, strategies used to solve proportion problems, variables that influence performance, and training studies are each considered. (MNS)

Identifies key questions concerning children's intuitions and conceptions of probabilistic notions. Research on the theoretical framework for probability studies, misconceptions and strategies, and pupil attainment is reviewed, and the methodology is evaluated. Finally, implications for classroom practice are discussed. (MNS)

Two books ("The Mathematical Experience" and "Mathematics Tomorrow") raise many issues about mathematics and education, including how mathematics education must be disciplined by focusing on the real world. Examined are ways the books take adequate account of the constraints present in problems they consider. (JN)

A review of work related to the topological primacy thesis and a critique of some aspects of it are presented. On the basis of the psychological research, it is concluded that topological concepts ought to be taught. (MP)

The concept of equivalence is shown to be an elusive one that provides difficulty for preschoolers through college students. The idea persists that the equal sign is a "do something," or operator symbol, rather than a symbol for an equivalence relation. (MP)

It is argued that the view of mathematics as an activity emphasizing intuitive thinking is compatible with an axiomatic-deductive approach. (MP)

Analyzes the context and status of mathematics education reform in Malawi through four developments in the reform of secondary education. Describes attempts to increase access to secondary education for the majority of Malawians. Suggests that limitations in the reform process are a function of inadequate understanding of the social-contextual…

Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)