Gerald Goldin, Distinguished Professor of Mathematics Education, received his Ph.D. in physics from Princeton and studied mathematics education at Penn, He co-chaired the PME Working Group on Representations, organized New Jersey’s Statewide Systemic Initiative, and directed two research centers at Rutgers. He publishes on education, mathematics, and physics, and is a Humboldt Prize awardee. His current investigations include mathematical affect and engagement.

Goldin G. A. (1989) Constructivist epistemology and discovery learning in mathematics. In: Vergnaud G., Rogalski J. & Artigue M. (eds.) Proceedings of the 13th International Conference on the Psychology of Mathematics Education (PME 13), Volume 2. International Group for the Psychology of Mathematics Education, Paris: 15–22.

Goldin G. A. (1990) Epistemology, constructivism, and discovery learning of mathematics. In: Davis R. B., Maher C. A. & Noddings N. (eds.) Constructivist views on the teaching and learning of mathematics. National Council of Teachers of Mathematics, Reston VA: 31–47. Fulltext at https://cepa.info/2976

Excerpt: What is the best way to characterize the body of knowledge that we call mathematics? How do children and adults learn mathematics most effectively? How can we best study their learning processes, and assess the outcomes of learning? Can meaningful learning be consistently distinguished from nonmeaningful or rote learning? What constitutes effective mathematics teaching, and how can elementary and secondary school teachers be enabled to provide it?

Goldin G. A. (1996) Theory of mathematics education: The contributions of constructivism. In: Steffe L. P., Nesher P., Cobb P., Goldin G. A. & Greer B. (eds.) Theories of mathematical learning. Lawrence Erlbaum, Hillsdale: 303–306.

Open peer commentary on the article “Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld’s Conceptual Analysis” by Victor V. Cifarelli & Volkan Sevim. Upshot: The key philosophical premise of von Glasersfeld’s radical constructivism is not necessary to the insightful conceptual analysis presented by Cifarelli and Sevim, which could benefit from abandoning it.