Affect and mathematical competence are each multifaceted constructs. Accordingly, the studies in this Special Issue address multiple pathways between the two in young children. This commentary highlights the variability of these pathways and asks how affective variables are specifically related to core mathematical activities such as problem…

In this paper, I comment on the set of papers in this special issue on mathematical problem posing. I offer some observations about the papers in relation to several key issues, and I suggest some productive directions for continued research inquiry on mathematical problem posing.

Problems in mathematics education as a social activity are the major focus of this document. Paragraphs that describe major problems in mathematics education point out at least eleven major issues as seen from the author's perspective. (MP)

This paper is an attempt at clarifying the concept of "problem," in order to improve the teaching of problem solving. Four categories are employed in the analysis: formulation, context, solutions, and methods of approach. Examples are included. (MNS)

An alternative explanation is presented for the pattern of relative difficulty of arithmetical word problems to that suggested in a 1983 article. It is argued, that for many problems, much of the symbolic manipulation is accomplished externally, not internally. (MNS)

School mathematics curriculum worldwide has failed to bridge the gap between school mathematics and out-of-school problem-solving activities. Presented is the need for a mathematics curriculum unifying the civil, academic, bureaucratic, and school social domains to prepare students as functional citizens. (MDH)

Discusses the limitations in the explain-practice and active learning methods of teaching mathematics. Proposes that problem-centered learning is a teaching method that encourages student reflection, and presents examples demonstrating that encouraging reflection results in greater mathematics achievement. (MDH)

Responds to F. Uhlig's article on linear algebra that appeared in an earlier edition of this journal. (KHR)

This comment attempts to identify different "semiotic perspectives" proposed by the authors of this special issue according to the problems they discuss. These problems can be distinguished as problems concerning the representation of mathematical knowledge, the definition and objectivity of meaning, epistemological questions of learning and…

Proposes a four-category classification of semantic structures of one-step word problems involving multiplication and division: forming the n-th multiple of measures, combinatorial multiplication, composition of operators, and multiplication by formula. This classification is compatible with semantic structures of addition and subtraction word…

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…

Explores the challenge of providing all future citizens with an appropriate quantitative literacy by means of teaching mathematics through useful applications with local and global perspectives. (Author/KHR)

Develops properties of tasks that are pedagogically efficient and allow students to discover mathematical concepts for themselves. Illustrates the structure and philosophy of powerful tasks for the concept of angle. Presents seven examples of powerful tasks, including two involving two-dimensional graphic systems. (Contains 39 references.)…

An attempt is made to establish a link between ordinary arithmetical situations and relevant mathematical concepts by the analyzing of complexity of concepts. (MP)

This paper presents a theoretical framework for investigating the role of algorithms in mathematical thinking using a combined ontological-psychological outlook. The intent is to demonstrate that the processes of learning and of problem solving incorporate an elaborate interplay between operational and structural conceptualizations of the same…