Mathematical induction is a powerful method of proof, taught in most undergraduate programs involving mathematics and in secondary schools in some countries. It is also commonly known to be complex and difficult to comprehend. During the last five decades, mathematics education research has produced numerous studies on the learning and teaching of…

This paper presents the results of a systematic scoping literature review of higher education mathematics and statistics support (MSS) evaluation focusing on its impact on students. MSS is defined as any additional organised mathematical and/or statistical aid offered to higher education students outside of their regular programme of teaching by…

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…

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.…

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…

This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…

Analyzes two aspects of teachers' planned presentations of subject matter (knowledge about subject matter and knowledge about students); illustrates using functions and undefined mathematical operations; and discusses the interconnectedness of subject-matter knowledge, knowledge about students, and knowledge about ways of presenting subject…

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)

Suggests that strategy choice is a misleading characterization of efficient mental calculation and that teaching mental calculation methods as a whole is not conducive to flexibility. Proposes an alternative in which calculation is thought of as an interaction between noticing and knowledge. Presents an associated teaching approach to promote…

The common goal of the empirical studies discussed in this analysis was to assist children in developing a meaningful understanding of the rational number construct, founded on durable fraction concepts. Some research has focused on partitioning; some on ratio and proportion. Contains 59 references. (Author/MKR)

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)

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)