Open peer commentary on the article “Heterarchical Reflexive Conversational Teaching and Learning as a Vehicle for Ethical Engineering Curriculum Design” by Philip Baron. Upshot: I question the scope of curriculum design as proposed by the target article in relation to radical constructivist learning theory and terminology. In addition, I provide contextualization and clarification regarding the relationships between learning, teaching and design.

This chapter sets out to provide conceptual clarity around these two epistemological stances by comparing constructivism with constructionism in relation to three particular categories – (1) their origins and epistemological premises, (2) their ontologies, and (3) their purposes. It then proceeds to articulate some implications concerning the use of each epistemology to contribute to research in the field of education and to the notion of globalisation more generally. It notes in particular the positive contribution of constructionism in bringing about educational reforms and in taking a critical view towards the taken-for-granted notion of globalisation discourses. It shows how constructionism can make a positive contribution to research agendas that seek to bring about educational reform to improve the quality of teaching and learning and contribute to the betterment of societies precisely because it questions the very notions of globalisation, competitive market forces and the universalising of markets and production. Constructionist pedagogies may then be discerned and implemented as the result of the correct alignment of the theoretical perspective, research methodology and data collecting strategies with the constructionist epistemology. In making the important distinction between constructivism and constructionism, this chapter makes a significant contribution to the refinement of theories of knowledge, and to their usage in qualitative research in education to bring about improved learning and teaching to contribute positively to the betterment of societies in a globalised world.

Key words: constructivism, constructionism, epistemology, education reforms, globalisation.

Open peer commentary on the article “Enactive Metaphorizing in the Mathematical Experience” by Daniela Díaz-Rojas, Jorge Soto-Andrade & Ronnie Videla-Reyes. Abstract: Teaching and learning mathematics through enactive metaphorizing necessarily rests on interactions of teachers and learners. In this commentary, I illustrate that supporting learners’ enactive metaphorizing may begin with teachers creating space for learner activity and having experience with enactive metaphorizing, but will require much more from teachers and teacher educators.

This article offers a re-description of the concept of learning context. Drawing on Niklas Luhmann and Gregory Bateson, it suggests an alternative to situated, social learning and activity theory. The conclusion is that the learning context designates an individual’s reconstruction of the environment through contingent handling of differences and that the individual emerges as a learner through the actual construction. The selection of differences is influenced by the learner’s actual knowledge, the nature of the environment and the current horizon of meaning in which the current adaptive perspective becomes a significant factor. The re-description contributes to didactics through renewed understanding of the participants’ backgrounds in teaching and learning. Relevance: The paper focuses on learning context as individuals’ mental construction, on the distinction between teaching as context for learning and learning contexts, and on re-description of participants’ backgrounds as temporary horizons of meaning.

The paper will explore the conceptual underpinnings of constructivism as a learning theory in connection with PBL as an approach to teaching. Terms such as “student-centred learning” and teaching methods such as “group-work” are commonly represented as constructivist and presented in juxtaposition with a transmission view of teaching and learning. This paper will investigate the origins of these notions in constructivism, drawing on different learning theorists, and the possibilities for constructivism as a referent to analyse teaching and learning in the PBL context. Firstly, the discussion will centre on constructivism as a theory and how it has influenced teaching approaches commonly adopted in PBL settings. Secondly, constructivism as a practice will be discussed. Finally, the implications of constructivism in the PBL setting will be discussed.

Open peer commentary on the article “A Cybernetic Approach to Contextual Teaching and Learning��� by Philip Baron. Upshot: I present a new concept, the “In-sight Quotient,” which encourages learners to go deeper into the subconscious structure of learning. This enables them to manage the quality of their own individual learning experience. The lecturer becomes no longer a teacher but a “neuro-programmer.”

In their response to my (1996) article, Steffe and Thompson argued that I have taken an early position of Vygotsky’s and that his later work is subsumed in and developed by von Glasersfeld. I argue that the two theories, Vygotsky’s and radical constructivism, are, on the contrary, quite distinct and that this distinction, when seen as a dichotomy, is productive. I suggest that radical constructivists draw on a weak image of the role of social life. I argue that a thick notion of social leads to a complexity of sociocultural theories concerning the teaching and learning of mathematics, a perspective that is firmly located in the debates surrounding cultural theory of the last 2 decades.

Open peer commentary on the article “A Cybernetic Approach to Contextual Teaching and Learning��� by Philip Baron. Upshot: The target article does an excellent job of describing the theoretical basis of a cybernetic approach to teaching at the university level. In addition, it also describes changes that must occur in the teacher’s perspective and attitude. Yet I am left wondering how any of this can actually happen.

My purpose in this paper is to illustrate the way in which an enactivist methodological approach guided me as I conducted a two-case longitudinal study where the learning of algebra was explored in different contexts throughout time. Three groups of students in two different schools in the city of Puebla, Mexico, were followed from the last year of primary school (Year 6) to the second year of their secondary education (Year 8). Learning was characterised as the ongoing structural change that allows individuals or groups to act effectively in a changing environment [Maturana (GAIA, a way of knowing: political implications of the new biology. Lindisfarne, New York, pp 65–82, 1987)]. An enactivist methodology, which revolves around the idea of research being a form of learning [Reid (Proceedings of the 20th conference of the international group for the psychology of mathematics education. PME, Valencia, pp 203–209, 1996)], implied that, as I carried out the study, what I was doing was learning about how people learn algebra. My initial questions arose from my experiences with the teaching and learning of mathematics, which gave me a sense of the complexity involved in the learning processes. Later, as I became immersed in the process of investigation of the teaching and learning of algebra, my conceptions continually evolved. The meaning of the phrase ‘algebraic learning’, which I used as a way of maintaining a wide perspective that allowed me to explore the events in the classroom in a complex way, arose as I engaged with enactivist ideas about learning, with the research literature on the learning of algebra, in conversations with people and in interactions with the participants of my project. I went through a process of continual development and change which I describe in this paper.

Key words: enactivism, algebraic learning

Excerpt: In a typical study of students’ conceptions and conceptual change, researchers analyze what a student does or says in a classroom or in an interview and recognizes ideas that match or do not match their own understanding of the topic. Attributing the perspective they recognize in the student, those studies support the idea that a conception is the way by means of which an individual intrinsically conceives (of) a given phenomenon. They then hypothesize the existence of some mental structures that can be theoretically and objectively re-constructed based on what is observed in a student’s performance. Thus, researchers studying conceptions commonly assume that the observer and the observed are separate entities. However, even in the most theoretical and hardest of all sciences, physics, the independence of the measured object and the measuring subject is not taken for granted: Light, for example, will present itself as waves or as particles depending on how we examine it. The artificial sense of separation from the object(s) of study found in many accounts on students’ conceptions makes irrelevant the relationship that exists between the observer and the observed: an interdependence and co-emergence of the observer and the observed. This tight relation exists because each participant not only reacts upon what others say but also acts upon the reactions that his/her own actions give rise to. With this situation come epistemological, practical, and ethical implications for those researching in mathematics and science education. Positing or questioning the existence of an objective reality mediates how we accept or reject another human being and the worldviews s/he develops. It provides a rationale that guides our actions. This is especially important when it comes to teaching and learning at a time where the ability to deal with the plurality and diversity of human culture have emerged as significant referents for our social behavior.