This paper proposed the application of the constructivist approach in virtual university where learners can learn based on their learning style, information and skills to succeed in life and also in their job. Constructivist learning and the strategies in constructivist learning can foster in-depth learning and practical application. Integration of communication and information technologies into curricula offers significant potentials for designing new learning environments, and advancing research and development in learning theories. Based on the main aspects of the constructivist approach, traditional universities and classroom cannot provide the conditions for learners to construct the knowledge for themselves, for this reason virtual university with the communication and information technologies (ICT) can implement constructivist strategies in the process of teaching and learning. In virtual university, constructivism promotes the learner’s skills to solve real-life problems and practical problems.

Key words: virtual university, constructivist learning, constructivist approach in virtual university.

This study built on a 2001–02 classroom observation study of Washington K-12 and technical schools that identified the extent of constructivist teaching activity. Results from classroom observations found that strong constructivist teaching was observable in 17 percent of the classroom lessons. The other 83 percent of the lessons observed may have contained some elements of constructivist teaching, but up to one-half had very little or no elements of constructivist teaching present. More constructivist teaching appeared to occur in alternative schools and integrated subject matter classes. There appeared to be no differences among elementary, middle/junior, and high schools in the degree to which constructivist practices were used. This study explored the relationship of this practice to student achievement, examining the percent of variance in student achievement accounted for by constructivist teaching beyond that contributed by low-income. Data came from the original observation study and from school-level standardized test scores of 4th, 7th, and 10th graders. Results found large correlations between study variables (a negative correlation between school-level family income and student achievement, large positive correlations between constructivist teaching and student achievement, and a negative correlation between constructivist teaching and school-level family income).

What evolutionary account explains our capacity to reason mathematically? Identifying the biological provenance of mathematical thinking would bear on education, because we could then design learning environments that simulate ecologically authentic conditions for leveraging this universal phylogenetic inclination. The ancient mechanism coopted for mathematical activity, I propose, is our fundamental organismic capacity to improve our sensorimotor engagement with the environment by detecting, generating, and maintaining goal-oriented perceptual structures regulating action, whether actual or imaginary. As such, the phenomenology of grasping a mathematical notion is literally that – gripping the environment in a new way that promotes interaction. To argue for the plausibility of my thesis, I first survey embodiment literature to implicate cognition as constituted in perceptuomotor engagement. Then, I summarize findings from a design-based research project investigating relations between learning to move in new ways and learning to reason mathematically about these conceptual choreographies. As such, the project proposes educational implications of enactivist evolutionary biology.

Key words: constructivism, design, education, enactivism, mathematics

Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the methodological utility of design-research as an approach to such theory development. Building on constructs from ecological psychology, cultural anthropology, studies of motor-skill acquisition, and somatic awareness practices, we develop the notion of an “instrumented field of promoted action”. Children operating in this field first develop environmentally coupled motor-action coordinations. Next, we introduce into the field new artifacts. The children adopt the artifacts as frames of action and reference, yet in so doing they shift into disciplinary semiotic systems. We exemplify our thesis with two selected excerpts from our videography of Grade 4–6 volunteers participating in task-based clinical interviews centered on the Mathematical Imagery Trainer for Proportion. In particular, we present and analyze cases of either smooth or abrupt transformation in learners’ operatory schemes. We situate our design framework vis-à-vis seminal contributions to mathematics education research.

Key words: mathematics, education, motor learning, conceptual learning, motor problem, conceptual metaphor

Enactivism theorizes thinking as situated doing. Mathematical thinking, specifically, is handling imaginary objects, and learning is coming to perceive objects and reflecting on this activity. Putting theory to practice, Abrahamson’s embodied-design collaborative interdisciplinary research program has been designing and evaluating interactive tablet applications centered on motor-control tasks whose perceptual solutions then form the basis for understanding mathematical ideas (e.g., proportion). Analysis of multimodal data of students’ hand- and eye- movement as well as their linguistic and gestural expressions has pointed to the key role of emergent perceptual structures that form the developmental interface between motor coordination and conceptual articulation. Through timely tutorial intervention or peer interaction, these perceptual structures rise to the students’ discursive consciousness as “things” they can describe, measure, analyze, model, and symbolize with culturally accepted words, diagrams, and signs – they become mathematical entities with enactive meanings. We explain the theoretical background of enactivist mathematics pedagogy, demonstrate its technological implementation, list its principles, and then present a case study of a mathematics teacher who applied her graduate-school experiences in enactivist inquiry to create spontaneous classroom activities promoting student insight into challenging concepts. Students’ enactment of coordinated movement forms gave rise to new perceptual structures modeled as mathematical content.

A rising epistemological paradigm in the cognitive sciences – embodied cognition – has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor phenomenology. Conceptual learning, per these theories, could emanate from, or be triggered by, experiences of enacting or witnessing particular movement forms, even before these movements are explicitly signified as illustrating target content. Putting these theories to practice, new types of learning environments are being explored that utilize interactive technologies to initially foster student enactment of conceptually oriented movement forms and only then formalize these gestures and actions in disciplinary formats and language. In turn, new research instruments, such as multimodal learning analytics, now enable researchers to aggregate, integrate, model, and represent students’ physical movements, eye-gaze paths, and verbal–gestural utterance so as to track and evaluate emerging conceptual capacity. We – a cohort of cognitive scientists and design-based researchers of embodied mathematics – survey a set of empirically validated frameworks and principles for enhancing mathematics teaching and learning as dialogic multimodal activity, and we synthetize a set of principles for educational practice.

In the drive to improve standards, the collection and dissemination of numerical data still directs much contemporary educational policy. However, recent publications and debates seemingly attempt to reorient discussion from performance to learning. In support, constructivism is often referenced as a contributor in this endeavour. However, constructivism is not a single unified theory either of knowledge or pedagogy. This article identifies one version of constructivist thinking, social constructivism, both in terms of its underlying epistemology (theory of knowledge) and related pedagogy. Contemporary educational theories are then outlined to demonstrate that many practical solutions and theoretical ideas now presented as ‘good learning and teaching’ have much in common with social constructivist thinking. Finally, the article concludes by identifying two issues that require further discussion and debate if pedagogy of a social constructivist nature is to be considered.

Education has institutionalized a process that reifies cultures, ecological communities, and ultimately evolution itself. This enclosure has lessened our sensitivity to the pedagogical (eteragogical) nature of our lived relations with other people and with other living beings. By acknowledging that learning and teaching go on between species, humans can regain an eteragogical sense of the interspecies curricula within which they exist. This article explores interspecies lived curricula through a selection of ideas from ecopragmatist Anthony Weston, and cybernetician Gregory Bateson, and through lived experiences with shorebirds of Lake Ontario. Some gulls and a tern teach the author to enrich and diversify, rather than constrict, the potentiality of life. In so doing, being ecological and being educative become unified concepts. Relevance: The publication is concerned with the relational implications between humans and other species of Bateson’s cybernetic theory of learning.

Consideration of a possible use of virtual reality technologies in school contexts requires gathering together the suggestions of many scientific domains aimed at understanding the features of these same tools that let them offer valid support to the teaching–learning processes in educational settings. Specifically, the present study is aimed at creating a theoretical framework for the didactic use of VR technologies in schools, highlighting the characteristics of these tools that are supported by a view of teaching that enhances sensorimotor activity in learning. The theoretical approach, through the study of the international scientific literature on this topic, offers interdisciplinary suggestions for realising teaching–learning practices that are supported by scientific principles and a concept of learning that is consistent with the processes that these tools may activate.