Teachers' knowledge of students' mathematical thinking is a growing area of research in mathematics education. The literature has reported plentiful evidence of the interplays between teachers' mathematical knowledge and their knowledge of students' mathematical thinking. The present study builds on this body of work to explain how such interplays…

Elementary students' early development of embedding and disembedding is complex and paves the way for later STEM learning. The purpose of this study was to clarify the factors that support students' embedding (i.e., overlapping shapes to form a new shape) and disembedding (i.e., identifying discrete shapes within another shape) through the use of…

Researchers have emphasized the importance of characterizing students' abilities to coordinate changes in covarying quantities. In this paper, we characterize three undergraduate students' coordination of covarying quantities' amounts of change during a teaching experiment. We adopt Piagetian notions of figurative and operative thought to describe…

This study aims to help concrete thinkers learn science through the use of Piagets' cognitive processes (CPs) during scientific inquiry. A total of 203 fourth-grade students participated as volunteers in a pre-post control group study. The students were from urban, remote rural, and suburban regions of Indonesia. Data analysis demonstrated 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…

Conservation and executive function (EF) are important early childhood skills; however, knowledge about their relationship is scarce. Hence, in this study, this relationship is investigated, and a comparison is conducted between the Piagetian conservation and EF tasks to obtain the total hemoglobin (mMmm) for the left and right brain activity in…

An equal-armed balance at equilibrium--the bar is horizontal--tips into disequilibrium upon displacing a weight. Equilibrium is restored by reversing that move--putting the weight back where it was, or doing the same on the other side. Piaget adopted the idea of equilibration to describe how the intellect, in relating to the world, develops.…

Critical thinking when engaged in science problem solving around even simple tasks such as the Piagetian volume conservation task is a complex endeavor. Tasks such as the conservation task often require the interaction of multiple cognitive systems. Parity judgment, retrieval, and lateral thinking are three examples of such systems interacting…

This study draws on four case studies of young children in order to explore the relationship between children's action schema [Athey, C. (1990). "Extending though in young children: A parent-teacher partnership." London: Paul Chapman] and their developing speech, language and communication. What emerged was a connection through…

History teaching and learning make intellectual demands on both teachers and students, requiring them to travel back in time and engage with complex issues and distant lifestyles. History education research advocates the use of approaches that portray History as an intellectually engaging subject but the application of cognitive research to…

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…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

Teacher knowledge of students' mathematical thinking has been a growing research area in mathematics education. Although researchers have made substantial progress in understanding students' mathematical thinking and created research programs and curricula tailored to the research findings, teacher education programs have, by and large, not been…

Part 1 in this four-part series of articles discussed Piaget's theories of learning and development (Crossland, 2016). Part 2 explores how post-Piagetian researchers have addressed criticisms of Piaget's theories by linking recent evidence including that from neuroscience. The outcomes show that good teachers make a difference by implementing…

Parts 1 and 2 in this four-part series of articles (Crossland, 2016, 2017a) discussed the recent research from neuroscience linked to concepts from cognitive development that brought Piaget's theories into the 21st century and showed the most effective provision towards more optimal learning strategies. Part 2 reviewed Demetriou's latest thinking…