Wavering, M. J. (2011). Piaget's logic of meanings: Still relevant today. School Science and Mathematics, 111(5), 249-252. doi:10.1111/j.1949-8594.2011.00083.x

In his last book, Toward a Logic of Meanings (Piaget & Garcia, 1991), Jean Piaget describes how thought can be categorized into a form of propositional logic, a logic of meanings. The intent of this article is to offer this analysis by Piaget as a means to understand the language and teaching of science. Using binary propositions, conjunctions, and disjunctions, a table of binary operations is used to analyze the structure of statements about conclusions drawn from observations of science phenomena. Two examples from science content illustrate how the logic of binary propositions is used to symbolize typical reasoning of secondary-school science students. The content areas are the period of a pendulum and the Archimedes' Principle, which were chosen based on observations in secondary science classrooms. The analyses of the student responses in these two observations demonstrate the commonalities of arguments used by students of science as they try to make sense of observations. The analysis of students' reasoning, demonstrates that Piaget's logic of meanings is a useful and relevant tool for science educators' understanding of the syntactical aspects of pedagogical content knowledge.

The key insight:
“Many of the phenomena studied in science classrooms fall into the category of equivalence relationships. Knowing this and recognizing the use of the logic entailed help[s] teachers to recognize not only correct structures of reasoning but maybe more importantly [to] recognize faulty reasoning or the application of scientific misconceptions. Teachers are then able to provide more effective instruction and activities to help students improve their understanding based on deeper knowledge of how students derive meaning from what they are learning” (p. 251).