This review study synthesises the literature on how computational thinking (CT) and mathematical thinking (MT) are integrated into mathematics education research with a focus on tasks. A review of 28 relevant articles on the Web of Science Core Collection database indicated that (1) CT helps students develop and apply mathematical concepts and…

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

This paper describes a program of research aimed at better understanding mathematics conceptual learning. Rather than studying the products of learning (conceptual steps), it focuses on the process (mechanism) of students' learning -- learning that occurs through their mathematical activity in the context of a sequence of mathematical tasks.…

The author responds to the recent work of Kaminski, Sloutsky, and Heckler (2008) and advances two major concerns about their research and its applicability to learning mathematics: a confounding variable that arises from the mathematical differences between the generic examples and concrete examples poses a threat to the construct validity of the…

The goal of this article is to examine students' mathematical development that occurs as a teacher works within each of 2 zones of learning: students' zones of proximal development (ZPD) and students' zones of potential construction (ZPC). ZPD, proposed by Vygotsky, is grounded in a social constructivist perspective on learning, whereas ZPC,…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

Describes an observation study of a second-grade classroom where a problem-centered approach to mathematics is used. Discusses analogies between scientific communities and social life in the class. Authors discuss analogies that helped them cope in the classroom with the complexity of children's beliefs, their dialogues about mathematics, and the…

This review of recent Piagetian research in mathematics education is divided into three parts. In the first part the author states the assumptions upon which the remainder of the paper rests. These assumptions are based on Piaget's theory of cognitive development and he presents six relevant points. The second part is a review of recent research…

Current knowledge about cognitive development in mathematics is reviewed, specific effective strategies for presenting materials in class are described, and effective strategies for mathematics program content and organization are outlined. Substantial information on recent research and on instructional materials is included. (MSE)

Discusses how children's knowledge can be measured/described, knowledge patterns across diverse concepts, interaction of knowledge/learning, and ways children construct more advanced problem-solving rules to replace less adequate ones. Evidence, drawn from studies on children's acquisition of knowledge about balance beams, suggests that knowledge…

Three addresses by internationally renowned mathematics researchers and a fourth paper on the role of research are presented. Each of the addresses focuses on the learning process, but from different points of view. Heinrich Bauersfeld provides an analysis of the miscommunication inherent in many teacher-student interactions. Four deficient areas…

The purposes of this study were to: (1) determine the influence of a series of experiences involving the equivalence relation "same length as" and the asymmetric transitive relations "longer than" and "shorter than" on the ability of first and second grade children to classify and seriate objects on the basis of length; (2) investigate the…

This paper offers for discussion and critique a conceptual framework that applies a situative perspective on learning to the study of learning to teach mathematics. From this perspective, such learning occurs in many different situations--mathematics and teacher preparation courses, pre-service field experiences, and schools of employment. By…