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.

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.

The major purpose of this study was to investigate factors and challenges that hindered effective teaching of mathematics for understanding in senior secondary schools in the Omusati Education Region in Namibia. The study investigated how the participants dealt with identified challenges in the mathematics classrooms in selected senior secondary schools. Further, the study attempted to establish necessary support and / or training opportunities that mathematics teachers might need to ensure effective application of teaching mathematics for understanding in their regular classrooms. The sample was made up of eight senior secondary schools out of the population of 12 senior secondary schools in the Omusati Education Region. The schools were selected from the school circuits using maximum variation and random sampling techniques. Twenty out of 32 mathematics teachers from eight selected senior secondary schools in the Omusati Education Region responded to the interviews and two lessons per participant were observed. Interviews and observations were used to collect data from the 20 senior secondary school mathematics teachers with respect to teaching mathematics for understanding. Frequency tables, pie charts and bar graphs were used to analyze the data collected. The results indicated that teaching for understanding was little observed in mathematics classrooms. Part of the challenges identified were, overcrowded classrooms, lack of teaching and learning resources, lack of support from advisory teachers, and automatic promotions, among others. Mathematics teachers needed induction programmes, in-service training opportunities, and advisory services amongst others in order to be able to teach mathematics effectively. The study recommended that teaching for understanding should be researched in all subjects in Namibian classrooms and should be made clearly understood by all teachers in order to be able to use and apply it during their teaching. New teachers should be provided with induction programmes to give them support and tools at the beginning of their teaching careers. Further research on teaching for understanding should be conducted in other school subjects in Namibia in order to ensure teaching for understanding across the curriculum.

Key words: teaching, understanding.

Constructivist teaching is based on constructivist learning theory. This theoretical framework is based on the belief that learning occurs through what a student already knows; this prior knowledge is called a schema. Because all learning should pass through the filter of the pre-existing schemata, constructivists suggest that learning is best accomplished when a student gets actively engaged in the learning process rather than attempting to receive knowledge passively with the teacher avoiding most direct instruction and attempting to lead the student through questions and activities to discover, discuss, appreciate and verbalize the new knowledge (Richards et.al., 2001). Technology is increasingly gaining attention of those who are obsessed with improving teaching and learning. In this research attempts has been made to describe and analyze elementary teachers’ perceptions of using technology as a means for implementing classroom constructivist activities. Doing this, private schools were chosen were every classroom was equipped with a PC for the teacher as well as students. The PCs were networked so that all students could interact with the teacher and other students independently or as a group. Data was gathered through questionnaires from both teachers and students. Findings of the study show that teachers intend to look at the technology provided as an effective tools for developing constructivist practices and for gaining students’ interest. Students are given free rein to be in charge of learning experiences. This method initiates an active and positive learning environment that is technology based, including teamwork while maintaining independence where necessary, which is safe and avoids the anti-motivation effects of being judged. The results show that teachers reported an increase of test scores.

Key words: constructivist education, leadership, technology in education, technology integration

Context: For Graham Barnes, the starting point of his research was the observation that most psychotherapists are trained in a theory-centered style of practice, neglecting epistemological and hermeneutical aspects. The consequence is an absence of critical self-reflection about some basic assumptions of psychotherapy theories and clinical practices in the psychotherapy community. When using a particular theory, therapists forget that the theory is “using” them, as well, i.e., they are unaware of the effects the theory has on them and on their relationships with clients. As an alternative to this ignorance, Barnes developed the concept, research project and clinical application of what he called “second-order psychotherapy.” Problem: How can we encourage therapists to engage in systematic self-reflection on the influence of theory on the content and structure of their therapeutic conversations? Following Bateson’s epistemological guidelines, we give an example of how our conversation about understanding his ideas includes conversation about our understanding of the conversation about an understanding of his ideas. Method: Bateson created a new didactic form of dialogical presentation to facilitate the understanding of knowing, called a metalogue, in which the content and the structure of the conversation are intertwined in such a way that it becomes more transparent how the metalevel of relationships between the speakers influences the content and vice versa. Results: By presenting our dialogues as an exemplary metalogue, we propose that metalogues could be a valuable didactic way for promoting epistemological and constructivist teaching and learning, not only for psychotherapists, but for all professionals who need better understanding of their understanding. This second-order understanding opens the space for the inclusion of self-reflection on our relationship (and its evolution) and how our relationship has shaped our understanding. Implications: Our proposal is also meant as an encouragement for contemporary constructivist thinkers to continue to reflect on Bateson’s contribution to the foundation and evolution of constructivism.

Key words: Cybernetic epistemology, second-order psychotherapy, dialogotherapy, self-referential awareness, understanding, difference, schizophrenia, double bind, innocence

Context: Public universities in South Africa are currently facing the challenge of decolonising knowledge. This change requires a review of curriculums, as well as teaching and learning with the goal of embracing the epistemology of the learners, addressing issues such as social justice and transformation. Problem: Human communication is subject to several perceptual errors in both listening and seeing, which challenges the success of the communication in the education system. The ability of the teacher and the learners to effectively communicate with one another is a factor for the success of each reaching their goals. The teacher imparts her knowledge in the classroom, but according to von Foerster, “[i]t is the listener, not the speaker, who determines the meaning of an utterance,” for the listener contextualises this information based on her own past lived experience. Thus, the student’s epistemology and her expression of her understanding is integral in the classroom context and should be actively included into the education system. Method: I present a cybernetic approach to the teacher-learner system, challenging traditional ideas about the role of each actor within the system, with special attention given to Pask’s conversation theory. Results: Early empirical findings suggest that a conversational contextual approach results in higher student involvement and better memory retention among the learners. Conversational approaches that are epistemologically inclusive diffuse social problems where the student groups require their individual worldviews to be reflected within the curriculum. This reduces the friction of competing epistemologies within the education system, moving toward a co-created contextually-driven knowledge system. Implications: Many educators would like deeper engagement from their learners but have not found a way to successfully engage the student group. A cybernetic approach is one method that can be adopted to remedy this. This is particularly useful in contexts where there is cultural diversity and impending social change. Constructivist content: I address von Glasersfeld’s points on human cognition, linking it to Austin’s speech acts.

Key words: Contextual approach, conversation theory, decolonisation of knowledge, education, epistemology, teaching and learning.

Context: South African public universities are currently undergoing a transitional period as they traverse the sensitive road of curriculum redesign that achieves an inclusive approach to education for the goal of the decolonisation of knowledge. Problem: Many classrooms have students from several cultural backgrounds yet in these spaces there is often a single dominant discourse on offer. An ethical question is raised in terms of what content should be addressed in the classroom. Method: An approach to curricula design as a conversation is presented. The philosophical aspects underlying shifts in epistemology are presented following an eclectic approach to curricula design that embraces second-order science in achieving the ongoing goal of decolonisation. The method used to achieve this goal is conversational heterarchical curriculum design assuming non quidem tabula rasa. Students can act as reference points (Nunataks) for curricula design, thus reducing the abstraction in the syllabus. Results: A heterarchical conversational approach offers a platform whereby social justice may be addressed in the classroom by providing a means by which the students’ own epistemology is embraced within the curriculum as the students provide the trajectory for the course content based on their own epistemology. A dynamic curriculum is then available that has immediate use in the communities that the students reside in. Students demonstrate understanding of the content as it is tied to their own way of knowing. Implications: The benefits of this approach include moving away from defining science according to a realist view. Educators may accept the idea that knowledge is not impartial and that method is tied to epistemology. When the observer is included in science, an awareness arises that theories (at least in the social sciences) affect what is studied, which in turn affects society. Constructivist content: The approach builds on von Foerster’s ideas on reflexivity. Pask’s conversation theory is a vehicle for the attainment of reflexive conversational teaching and learning.

Key words: Adaptation, curriculum design, conversation theory, cybernetics, decolonisation, ethics, heterarchy, nunatak, reflexivity, second-order science, ubuntuism.

Radical constructivism grows out of the belief that knowledge is constructed and legitimated by individuals as they make sense of their experiences in particular contexts and drawing on their own histories. Extending this understanding of learning and ways of knowing to girls as they work in the terrain of science, we argue that honoring student experience as the starting place for science instruction fundamentally alters the nature of science, the purpose of teaching and learning science, and the focus of relationships in science class. The implications for this position are extensive: they suggest that the dynamic relationships between language and cultural background of students and teachers alter the ways in which science education historically has enacted discipline, curriculum and pedagogy. We argue that this is particularly important to understand, for science and science education have historically operated within the masculine domain and working with girls in science in ways that respect their (gendered and cultural) construction of knowledge and their experiences, fundamentally alters the enterprise of science – an idea contradictory to most visions of the purposes of education and current reform efforts in science education, even the most liberal.

In this paper, the author has discussed the epistemological and the pedagogical dilemma he faced in the past and that he is still facing within radical and social constructivist paradigms. He built up an understanding of radical constructivism from the works of Ernst von Glasersfeld and social constructivism from the works of Paul Ernest. He introduced the notion of constructivism including both radical constructivism and social constructivism in brief. Then he reconceptualized these forms of constructivism in terms of epistemological and pedagogical motivation leading to a dilemma. He emphasized how the dilemma within these paradigms might impact one’s actions and how resolving this dilemma leads to eclecticism. He summarized that one paradigm world does not function well in the context of teaching and learning of mathematics (and science). Finally, he concluded the dilemma issue with epistemological and pedagogical eclecticism.

Key words: Radical constructivism, social constructivism, epistemological-pedagogical dilemma, epistemological eclecticism, pedagogical eclecticism.

Expressions like “constructivism,” “construction of knowledge,” “learners construct meaning,” and similar ones are starting to become part of the language of science education. We are liable to hear them in professional meetings or inservice workshops and to read them in articles in the professional journals. As the term constructivism becomes more widespread, different people tend to use it with slightly different meanings, and some use it in a loose way to designate a complex of different pedagogical, psychological, or philosophical tendencies. (The ideas about constructivism explained in this chapter are in no way to be taken as an attempt to define the “orthodoxy” of constructivism. Consistent with a constructivist view, they are simply a model of what it means to know. The claim of this model is to be a viable view of knowledge. This chapter aims at presenting the model and exploring from there some relations with teaching and learning of science.) These tendencies seem to have in common the central assumption that all we come to know is our own construction.