Jeremy Sawyer recounts that, after Lev S. Vygotsky's death, Jean Piaget conceded the Russian psychologist correctly understood the social origins, functions, and developmental trajectory of children's egocentric speech (now called private speech) but dismissed this work as irrelevant to children's egocentrism or nondifferentiation of perspectives.…

This paper uses posthumanism as the theoretical framing to understand the curriculum transformations towards creating sustainable learning environments at some higher education institutions (HEIs) and the early childhood care and education (ECCE) centres in South Africa. The choice of these two bands in education is necessitated by the fact that…

Generalization is critical to mathematical thought and to learning mathematics. However, students at all levels struggle to generalize. In this paper, I present a theoretical analysis connecting Piaget's assimilation and accommodation constructs to Harel and Tall's (1991) framework for generalization in advanced mathematics. I offer a theoretical…

The purpose of this research is to construct a preliminary genetic decomposition delineating the mental constructions underlying probabilistic independence. This delineation is considered within the framework of APOS theory. While the use of the term independence in probability is often conflated with causation, the definition relies instead upon…

This paper addresses a problem that greatly complicates the implementation of dialogic educational approaches in schools: the dilemma between driving children's talk towards normatively accepted conceptions and, at the same time, avoiding the introduction of these normative conceptions into the dialogue by the teacher. I argue that this dilemma is…

Felix Klein's Erlangen program classifies geometries based on the kinds of geometric transformations that preserve key properties of their figures, rather than focusing on the geometric figures themselves. This shift in perspective, from figurative to operative, fits Piaget's characterization of mathematical development. This paper considers how…

The emerging field of mathematics educational neuroscience provides researchers with new approaches to understanding mathematical development, as well mathematics itself. This paper focuses on the role of the hand in constructing mathematics through activity. We rely on Piaget's distinction of three kinds of activity: sensorimotor activity,…

"Critical", "Criticism", and "Critic" all come from the age-old Greek word "Kritikos", meaning able to authorise, discern, or decide. In contemporary English, a "Critic" is someone whose job is to make appraise judgements, for example, about films, books, music, or food. It means giving a fair and…

This article examines the literature associated with social constructivism. It discusses whether social constructivism succeeds in reconciling individual cognition with social teaching and learning practices. After reviewing the meaning of individual cognition and social constructivism, two views--Piaget and Vygotsky's--accounting for learning…

In the last century, Jean Piaget proposed one of the most famous theories regarding cognitive development in children. Piaget proposed four cognitive developmental stages for children, including sensorimotor, preoperational, concrete operational, and the formal operational stage. Although Piaget's theories have had a great impact on developmental…

Lo's variation theory is a learning and teaching theory based on Marton's phenomenographic approach and is one of the most important backbones of learning studies. The proponents of variation theory demarcate their approach from constructivist learning approaches, stressing constructivism as philosophical framework, but not as learning theory. At…

A growing body of research incorporates children's perspectives into the research process. If we are to take children's perspectives seriously in education research, research methodologies must be capable of addressing issues that matter to children. This article engages in a theoretical discussion that considers how a posthuman research…

In this article, I examine changes in the field of cognitive development and in my own thinking over the past 40 years. The review focuses on three periods. In the first, Piaget's theory was dominant, and my research and that of many others was aimed at understanding the many fascinating changes in children's thinking that Piaget documented, and…

This article addresses the problem of "education for all," and offers a research proposal that replaces procedural learning by a learning practice whereby all are engaged. Although educational research since 1990 of dialogical learning (DL) and collaborative learning (CL) have shown that it is possible to promote the learning practices…

Piaget's theories of the structure of knowledge, constructivist learning, and stages of development in thinking have been a cornerstone of cognitive psychology and teacher education for half a century (Piaget, 1983). More recently, his ideas about stages of cognitive development have received criticism from many quarters (Weiten, 1992), including…