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 (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.

Context: The article discusses design strategies for infusing constructionism and creativity into widely recognised media such as e-books. Problem: E-books have recently included constructionist widgets but we do not yet have creative designs for readers who may want to both read and tinker with an e-book. Method: The generation and study of a community of interest collaboratively designing e-books, with a strong constructionist element. Results: Some first examples of social creativity in the collaborative design process are discussed in the article, showing the complexity of fusing reading with constructionism and the importance of the designers’ own ability to exchange widgets meant for the book and at the same time use them as boundary objects to communicate with each other. Implications: Social creativity in such design processes is considered as key for spreading and democratizing design for constructionism and creativity.

Scott B. (2011) Thinking mathematically. In: B. Scott, (ed.) Explorations in Second Order Cybernetics: Reflections on Cybernetics, Psychology and Education. Vienna, echoraum. https://cepa.info/1814

This paper discusses the nature of mathematical thinking from the viewpoint of cognitive psychology. This is followed by a discussion of the practical needs and problems associated with mathematics teaching in Primary Schools. Some necessarily cautious and speculative recommendations are made. Where appropriate, reference is made to the literature on mathematics teaching and associated methods and materials. The author also has opportunity to refer to his own experiences as a teacher of mathematics, in a Primary School. Finally, there is a discussion of the emerging media in education and their likely impact on a new generation of teachers and pupils.

Simon M. A. (1995) Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education 26(2): 114–145. https://cepa.info/3671

Constructivist theory has been prominent in recent research on mathematics learning and has provided a basis for recent mathematics education reform efforts. Although constructivism has the potential to inform changes in mathematics teaching, it offers no particular vision of how mathematics should be taught; models of teaching based on constructivism are needed. Data are presented from a whole-class, constructivist teaching experiment in which problems of teaching practice required the teacher/researcher to explore the pedagogical implications of his theoretical (constructivist) perspectives. The analysis of the data led to the development of a model of teacher decision making with respect to mathematical tasks. Central to this model is the creative tension between the teacher’s goals with regard to student learning and his responsibility to be sensitive and responsive to the mathematical thinking of the students.

Wilkerson-Jerde M. H. (2015) Locating the Learner in Collaborative Constructionist Design. Constructivist Foundations 10(3): 315–316. https://cepa.info/2138

Open peer commentary on the article “Designing Constructionist E-Books: New Mediations for Creative Mathematical Thinking?” by Chronis Kynigos. Upshot: Involving professionals in the design of c-books is a feasible and promising way for constructionism to influence large-scale educational practice. However, the role of learners as readers of c-books was unclear in Kynigos’s account. Here I review the critical role that learners play in the conceptualization of educational environments, and I make recommendations for centering learners in the process of collaborative constructionist design.