John Richards is President of Consulting Services for Education, Inc. (CS4Ed, http://www.cs4ed.com) and Adjunct Faculty, Harvard Graduate School of Education. He is the senior author of the Software and Information Industry Association’s PreK-12 annual market survey and with Chris Dede (Eds.) has just published Digital Teaching Platforms, Teachers College Press. From the mid-1970s until the late 1980s John worked with Ernst von Glasersfeld, Les Steffe, Paul Cobb, and Pat Thompson – an incredibly productive and challenging time as they worked through the conceptual foundations of number, and Ernst’s fundamental insights regarding radical constructivism.

Glasersfeld E. von & Richards J. (1983) The creation of units as a prerequisite for number: A philosophical review. In: Steffe L. P., Glasersfeld E. von, Richards J. & Cobb P. (eds.) Children’s counting types: Philosophy, theory, and application. Praeger, New York: 1–20.

Glasersfeld E. von, Steffe L. P. & Richards J. (1983) An analysis of counting and what is counted. In: Steffe L. P., Glasersfeld E. von, Richards J. & Cobb P. (eds.) Children’s counting types: Philosophy, theory, and application. Praeger, New York: 21–44.

Open peer commentary on the article “Learning How to Innovate as a Socio-epistemological Process of Co-creation: Towards a Constructivist Teaching Strategy for Innovation” by Markus F. Peschl, Gloria Bottaro, Martina Hartner-Tiefenthaler & Katharina Rötzer. Upshot: Peschl et al. argue that innovation, or the creation of sustainable change in the market, is a natural topic to be understood from a radical constructivist perspective and is similar in structure to von Glasersfeld’s theory of learning. I argue that this is an accurate and interesting extension of the theory, but that their understanding of innovation needs to be extended to consider the viability of the innovation in the market. It is only in the context of the market that the innovation is perceived as novel, or that it can be understood as sustainable.

Richards J. (2016) Negotiating the Classroom. Constructivist Foundations 12(1): 78–78. https://cepa.info/3815

Open peer commentary on the article “Negotiating Between Learner and Mathematics: A Conceptual Framework to Analyze Teacher Sensitivity Toward Constructivism in a Mathematics Classroom” by Philip Borg, Dave Hewitt & Ian Jones. Upshot: Borg et al. argue that there is a Mathematics-Negotiation-Learner (M-N-L) structure that can be used as a conceptual framework in order to evaluate the application of radical constructivism in teaching. This structure assumes a coherent consensual domain that is the mathematics being negotiated. However, there are at least four different consensual domains that make up mathematics. The mathematics that is the consensual domain in an RC classroom has distinct features that are designed to support the student’s construction of mathematics.

Richards J. & Glasersfeld E. von (1979) The control of perception and the construction of reality. Dialectica 33(1): 37–58. https://cepa.info/1345

German translation: (1984) Die Kontrolle von Wahrnehmung und die Konstruktion von Realität. Delfin III: 9–25

Richards J. & Glasersfeld E. von (1980) Jean Piaget, the psychologist of epistemology: A Discussion of Rotman\ s “Jean Piaget: Psychologist of the Real”. Journal for Research in Mathematics Education 11(1): 29–36. https://cepa.info/1349

Excerpt: Piaget is not a realist, for each individual constructs his own reality. In contrast with the title of Rotman’s book, Piaget is not a psychologist of the real but of the concept of the real. What he has studied for almost 70 years is not reality but the construction of reality. When he reports his findings, when he explicates his theory, however, he is compelled to use more or less ordinary language-and ordinary language is, of course, rife with the ontological implications of naive realism. Nevertheless, we believe that he has made his position quite clear. To Rotman’s assertion that he is a “psychologist of the real” he responds, “Je m“en fous de la realite."

Richards J. & v. Glasersfeld E. (2000) Die Kontrolle von Wahrnehmung und die Konstruktion von Realität. In: Schmidt S. J. (ed.) Der Diskurs des radikalen Konstruktivismus. Suhrkamp, Frankfurt: 192–229.

Richards J., Steffe L. P. & Glasersfeld E. von (1981) Reflections on interdisciplinary research teams. In: Wagner S. & Geeslin W. E. (eds.) Modeling mathematical cognitive development. Clearinghouse for Science, Mathematics and Environmental Education, Columbus OH: 135–143. https://cepa.info/1354

Richards J., Steffe L. P. & Glasersfeld E. von (1983) Perspectives and summary. In: Steffe L. P., Glasersfeld E. von, Richards J. & Cobb P. (eds.) Children’s counting types: Philosophy, theory, and application. Praeger, New York: 112–123.