Drawing from philosophical, historical, and psychological research, this book redefines conceptual change as it applies to learning and instruction. Divided into three sections, this book addresses 1.) Foundations of conceptual change research, 2.) Examines the influence that personal beliefs have on conceptual change, and 3.)Focuses on mathematics learning and teaching.
*Reflects current state-of-the-art conceptual change work
*Each section includes a specialized introduction and ends with thought-provoking commentaries
*Written by experts in the field

"I can work best now while peeling potatoes. . . . It is for me what lens-grinding was for Spinoza."--L. Wittgenstein
More than 250 years separate the publication of Baruch Spinoza's "Ethics" and Ludwig Wittgenstein's "Tractatus Logico-Philosophicus." Both are considered monumental philosophical treatises, produced during markedly different times in human history, and notoriously challenging to interpret. In "Peeling Potatoes or Grinding Lenses, " Aristides Baltas contends that these works bear a striking similarity based on the idea of "radical immanence." Each purports to understand the world, thought, and language from the inside and in a way leading to the dissolution of all philosophy. In that guise, both offer a powerful argument against fundamentalism of all sorts and kinds.

To Spinoza, God is just Nature. God is not above or separate from the world, humanity, or mere objects for, as Nature, He inheres in everything. To Wittgenstein, logic is not above or separate from language, thought, and the world. The hardness of the logical "must" inheres in states of affairs, facts, thoughts, and linguistic acts. Outside there are no truths or sense--only nonsense.

Through close readings of the texts based on lessons drawn from radical paradigm change in science, Baltas finds in both works a single-minded purpose, implacable reasoning, and an austerity of style that are rare in the history of philosophy. He analyzes the structure and content of each treatise, the authors' intentions, the limitations and possibilities afforded by scientific discovery in their respective eras, their radical opposition to prevailing philosophical views, and draws out the particulars, as well as the implications, of the arresting match between the two.

Traditionally it has been thought that scientific controversies can always be resolved on the basis of empirical data. Recently, however, social constructionists have claimed that the outcome of scientific debates is strongly influenced by non-evidential factors such as the rhetorical prowess and professional clout of the participants. This volume of previously unpublished essays by well-known philosophers of science presents historical studies and philosophical analyses that undermine the plausibility of an extreme social constructionist perspective while also indicating the need for a richer and more realistic account of scientific rationality.