Certain aspects of theoretical frameworks in mathematics education can remain unexplained in the literature, hence unnoticed by the readers. It is thus interesting to participate in a dialogue where they can be discussed and compared in terms of the aims, objects studied, results and their relation to teaching. This study is focused on how APOS…

Spatial thinking has roles to facilitate learners to remember, understand, reason, and communicate objects and the connections among objects that are represented in space. This research aims to analyze the spatial thinking process of students in constructing new knowledge seen from the field-independent cognitive style learners based on…

One of the guiding questions in this discussion is how is it that certain ideologies become so ingrained and resistant to challenge and scrutiny? The central assumptions sustaining the argument conceive curriculum--the backbone of educational practice--to be an expression of ideological activity; the understanding of ideology as lived experience;…

The cognitive conflict hypothesis asserts that information that directly contradicts a prior conception is 1 of the prerequisites for conceptual change and other forms of nonmonotonic learning. There have been numerous attempts to support this hypothesis by adding a conflict intervention to learning scenarios with weak outcomes. Outcomes have been…

The development of scientific concepts and methods that supported analyses of individual cognition and learning occurred during the 1950s, 1960s, 1970s, and 1980s, with outstanding contributions by Newell and Simon (1972), van Dijk and Kintsch (1983), and others, providing an impressive and rapid scientific advance. At the same time, another…

This article considers the pedagogical research informed by the writings of L. S. Vygotsky concerned with the teaching and learning of languages beyond the first (L2). Following a brief overview of developments in the application of Vygotskian theory to explicating processes of L2 development in instructional settings, we consider more recent…

An iterative unpacking strategy consists of sequencing empirically-based theoretical developments so that at each step of theorizing one theory serves as an overarching conceptual framework, in which another theory, either existing or emerging, is embedded in order to elaborate on the chosen element(s) of the overarching theory. The strategy is…

Educational research and practice have proven that there are many benefits for applying learning theories' recommendations through teaching and learning of different subjects in all school levels. Based on interrelationships among learning theories of contextualism, connectivism, constructivism, and cognitivism, the researcher proposed an…

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

The teaching brain is a new concept that mirrors the complex, dynamic, and context-dependent nature of the learning brain. In this article, I use the structure of the human nervous system and its sensing, processing, and responding components as a framework for a re-conceptualized teaching system. This teaching system is capable of responses on an…

Successful learning sometimes requires that the learner abandons or rejects one or more prior concepts, beliefs, or intuitive theories. Such "nonmonotonic changes" are widely believed to have a low probability of occurring spontaneously and to be difficult to promote with instruction. A theory of nonmonotonic cognitive change should explain both…

The Lawson Classroom Test of Scientific Reasoning (LCTSR) was used to gauge the relative effectiveness of three different methods of pedagogy, "Reading, Presenting, and Questioning" (RPQ), "Experimenting and Discussion" (ED), and "Traditional Methods" (TM), on increasing students' level of scientific thinking. The…

Many types of learning require the mapping of information across situations. The proposed organizational framework extends the cognitive study of mappings across problems to include mappings across representations, solutions, and sociocultural contexts. I apply one-to-one, one-to-many, and partial mappings to analyze representative cases that…

The impulse to investigate the natural world is deeply rooted in our earliest childhood experiences. This notion has long guided researchers to uncover the cognitive mechanisms underlying the development of scientific reasoning in children. Until recently, however, research in cognitive development and education followed largely independent…

This paper offers steps towards overcoming current fragmentation within sociocultural approaches by expansively reconstructing a broad dialectical view on human development and learning (drawing on Vygotsky's project) underwritten by ideology of social justice. The common foundation for sociocultural approaches is developed by dialectically…