SCHOLARSHIP

Mathematics educators frequently ask the following kinds of questions:

• Why should children learn mathematics? How will it benefit themselves and society?

• What mathematics should children learn?

• How do children acquire mathematical knowledge?

• How are children similar and different from one another?

• What results can wise instruction hope to achieve in light of the above constraints?

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Up until approximately 1900, mathematicians and philosophers furnished the leading answers to these questions. At the turn of the century, however, a new scientific discipline known as psychology was securing its place in American intellectual culture. Psychology changed the terms of the conversation.

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Perhaps the most influential early psychologist on mathematics education was Edward Thorndike. His experimental work with animals revealed psychological laws that many believed would revolutionize school pedagogy. Thorndike, along with John Dewey and others, was attacking the classical tradition and recommending progressive school practices tailored to students' needs and interests. Tensions arose, however, between the scientific psychologists of Thorndike's persuasion and university mathematicians who felt that their subject was losing its status as a curricular priority. The mathematicians also regretted the vocational or shopkeeper bent of progressive reform. The National Council of Teachers of Mathematics (NCTM) was founded by mathematicians to counter progressive curriculum trends.

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Thorndike's influence on the mathematics curriculum is controversial today, as are his psychological theories. In this study I examine the historical context of Edward Thorndike's "connectionist" psychology, his involvement in mathematics curriculum design and educational research, and his social agenda for promoting democracy and human welfare through public education and sociological research on schools.

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I intend to argue a number of original points.

1. Although Thorndike is usually associated today with "behavioral" psychology, his views on psychology and curriculum shared important features with the pragmatic views of John Dewey. Thorndike's "psychological" rather than "logical" approach persisted in the work of Gestalt psychologists and Piaget's constructivism.

2. Thorndike's mathematics curriculum has been thought to emphasize drill and memorization at the expense of insight and understanding. Upon examining Thorndike's curriculum textbooks, I find his attention balanced between fluency and understanding of principles. His teaching sequences consist of inductive problems meant to cultivate good habits of thinking; he criticized deductive teacher lectures meant to be absorbed and applied. Thorndike's was a relatively student-centered and problem-based curricular program.

3. Thorndike's successful scientific program had the fortunate effect of increasing the disciplinary quality of mathematics education research. However, it had the unfortunate effect of overselling the virtues of social science at the expense of the humanities, including history and social or political philosophy.

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Chair: William Wraga

Committee: Andrew Izsák, Dorothy White, and John Rudolph