Open peer commentary on the article “Heterarchical Reflexive Conversational Teaching and Learning as a Vehicle for Ethical Engineering Curriculum Design” by Philip Baron. Upshot: The target article discusses constructivist teaching in the context of a university engineering course. As such it offers an opportunity to think about third-level constructivist teaching. In addition, it focuses on the ethical dimensions of the constructivist approach. The description of constructivist approaches offers the opportunity to reflect on implementing constructivist methods in teaching.

Glasersfeld E. von (1992) A constructivist approach to experiential foundations of mathematical concepts. In: Hills S. (ed.) History and philosophy of science in science education. Queen’s University, Kingston: 551–571. https://cepa.info/1433

During the last decade, radical constructivism has gained a certain currency in the fields of science and mathematics education. Although cognitive constructivists have occasionally referred to the intuitionist approach to the foundational problems in mathematics, no effort has so far been made to outline what a constructivist’s own approach might be. This paper attempts a start in that direction. Whitehead’s description of three processes involved in criticising mathematical thinking (1925) is used to show discrepancies between a traditional epistemological stance and the constructivist approach to knowing and communication. The bulk of the paper then suggests tentative itineraries for the progression from ele-mentary experiential situations to the abstraction of the concepts of unit, plurality, number, point, line, and plane, whose relation to sensory-motor experience is usually ignored or distorted in mathematics instruction. There follows a discussion of the question of certainty in logical deduction and arithmetic.

Glasersfeld E. von (1993) Learning and adaptation in the theory of constructivism. Communication and Cognition 26(3/4): 393–402. https://cepa.info/1446

Learning and adaptation are conceptually distinct and refer to different processes. Both concepts are incorporated in Piaget’s genetic epistemology and in the more radical constructivist model of cognition that has sprung from it. Misinterpretation of the different roles the two terms play in that theoretical model is one of the reasons why the constructivist approach has often been misunderstood by educators. In this paper I shall lay out the use of the two terms in the constructivist theory and give some indication of its application to learning and the practice of teaching.

Reprinted in: Smith L. (1996) Critical readings on Piaget. Routledge, London : 20-27.

Glasersfeld E. von (1999) How do we mean? A constructivist sketch of semantics (Special issue \Radical Constructivism in education\ edited by Marie Larochelle). Cybernetics & Human Knowing 6(1): 9–16. https://cepa.info/1508

The current frequent use of the words ‘information’, ‘communication’, ‘representation’, and ‘meaning’ introduces misleading metaphors into some of our most important social interactions. The paper presents an outline of the constructivist approach to the underlying phenomena as a more adequate and productive way of thinking – it shows linguistic ‘meaning’ to be the result of individuals’ reflection upon their experience.

When we speak of things which, as Wittgenstein said, cannot be spoken of, we inevitably say things that in some ways are wrong. In writing (as I did several times) that the constructivist approach to knowing provides an epistemological basis for ethics, because it justifies the need for others, I clearly stepped on dangerous ground. The statement was open to (and has occasioned) interpretations I did not intend. I am anxious to correct this.

Glasersfeld E. von (2006) A Constructivist Approach to Experiential Foundations of Mathematical Concepts Revisited. Constructivist Foundations 1(2): 61–72. https://cepa.info/7

Purpose: The paper contributes to the naturalization of epistemology. It suggests tentative itineraries for the progression from elementary experiential situations to the abstraction of the concepts of unit, plurality, number, point, line, and plane. It also provides a discussion of the question of certainty in logical deduction and arithmetic. Approach: Whitehead’s description of three processes involved in criticizing mathematical thinking (1956) is used to show discrepancies between a traditional epistemological stance and the constructivist approach to knowing and communication. Practical implications: Reducing basic abstract terms to experiential situations should make them easier to conceive for students.

Problem: How can constructivists speak of social interaction or communication with others, when, as they claim, their experiential world is their own construction? This question is frequently asked and is perfectly reasonable. The present paper is intended as an answer. Solution: After providing an outline of the constructivist approach to perception and the generation of recognizable objects in the experiential field, I argue that “others,” too, can be explained as an individual’s creation; a creation, however, that is just as constrained by the condition of viability as are the physical objects with which we furnish our world. Consequently, “society” too can be considered an individual construct rather than an ontological given. Benefits: The exposition may help to clarify the constructivist position with regard to social interaction and communication.

Hackenberg A. J. (2007) Units coordination and the construction of improper fractions: A revision of the splitting hypothesis. Journal of Mathematical Behavior 26: 27–47. https://cepa.info/764

This article communicates findings from a year-long constructivist teaching experiment about the relationship between four sixth grade students’ multiplicative structures and their construction of improper fractions. Students’ multiplicative structures are the units coordinations that they can take as given prior to activity – i.e., the units coordinations that they have interiorized. This research indicates that the construction of improper fractions requires having interiorized three levels of units. Students who have interiorized only two levels of units may operate with fractions greater than one, but they don’t produce improper fractions. These findings call for a revision in Steffe’s hypothesis (Steffe L. P. (2002). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior 20: 267–307) that upon the construction of the splitting operation, students’ fractional schemes can be regarded as essentially including improper fractions. While the splitting operation seems crucial in the construction of improper fractions, it is not necessarily accompanied by the interiorization of three levels of units. Relevance: This article takes a radical constructivist approach to mathematical learning and develops local theory about how students’ units coordinations are related to the fraction schemes they can construct.

Hackenberg A. J. (2010) Mathematical caring relations in action. Journal for Research in Mathematics Education 41(3): 236–273.

In an 8-month teaching experiment, the author aimed to establish mathematical caring relations (MCRs) with 4 6th-grade students. From a teacher’s perspective, establishing MCRs involves holding the work of orchestrating mathematical learning for students together with an orientation to respond to energetic fluctuations that may accompany student″teacher interactions. From a student’s perspective, participating in an MCR involves some openness to the teacher’s interventions in the student’s mathematical activity and some willingness to pursue questions of interest. Analysis revealed that student″teacher interactions can be viewed as a linked chain of perturbations; in MCRs, the linked chain tends toward perturbations that are bearable for both students and teachers. This publication is relevant for constructivist approaches because it examines how attention to affective responses (specifically, emotion and vital energy) can be included in a radical constructivist approach to knowing and learning.

Harris K. R. & Alexander P. A. (1998) Integrated, constructivist education: Challenge and reality. Educational Psychology Review 10(2): 115–127.

Although the desire for an education that emphasizes depth of understanding and meaningful learning has a long and distinguished history, constructivist reforms have not led to a comprehensive and coherent reform of educational practice in our schools. In fact, two previous “great reforms” based on constructivist principles have failed during this century. In this special issue ofEducational Psychology Review, authors focus on specific challenges faced in the current constructivist reform, including the need for viable intradisciplinary, interdisciplinary, and cross-disciplinary integration. Exemplars of the reality of progress made in integrated, constructivist approaches in the classroom follow. Diversity in our schools and classrooms and the challenge of high standards for all students contribute to the need for an integrated, constructivist approach that does not fail our students.