Project Title

Methods and Content for Teaching Middle School Mathematics: A Historical Approach

Project Members

Calvin Jongsma, Ph.D., Dordt College (Sioux Center, IA)

Dave Klanderman, Ph.D., Trinity Christian College (Palos Heights, IL)

Proposal in Brief

We propose to explore the curricular and pedagogical possibilities in taking a historical approach to teaching mathematics courses for preservice middle school mathematics teachers.

Project Description and Rationale

Textbooks aimed at prospective middle school teachers are mainly of two types. First, some books focus on methods and strategies at the expense of the mathematical content taught on these grade levels. Second, some books cover the requisite mathematical content but do so with little concern for pedagogy or connections with other material. And few, if any, of the books pay more than cursory attention to historical development, particularly with respect to topics normally included in the middle school mathematics curriculum. History of mathematics remains a missing standard, though it has great potential for introducing perspective, depth, and connections into the middle school mathematics curriculum.

Both of us have sought to integrate historical context into methods and content courses we teach to pre-service middle school teachers. Our experience has been that students come to appreciate exploring the origins and development of such topics as computation, measurement, geometry, elementary number theory, and algebra. Historical context has the potential to provide an overview and rationale for mathematical concepts and give non-routine work with varied procedures (e.g., working with the Babylonian sexagesimal numeration system helps students reflect on our base-ten positional system; learning about Egyptian unit fractions helps students better appreciate the meaning and facility of our fraction arithmetic). At times historical developments also give pedagogical insights or provide ideas for sequencing topics (e.g., the historical development of theories of ratio and proportion indicate fruitful ways to approach this topic in the classroom; the lateness of negative number arithmetic says something about its conceptual difficulty for students). When students consider the cultural and philosophical contexts of different civilizations, they often gain a greater appreciation for the mathematics of these cultures and see new connections between mathematics and other parts of life and the curriculum. This provides a natural context in which to take up worldview and faith-perspective issues related to mathematics. Students also gain a deepened understanding of the technical mathematics they will be teaching on the middle school level.

During the workshop this May, we want to explore the possibility of writing a historically focused textbook to use either as a primary or supplementary text in middle school methods or methods/content courses for mathematics. There are a number of ways in which we might incorporate a historical approach into such a text: as the central organizing theme for all mathematical topics; as providing an in-depth historical treatment of certain main topics while giving briefer contexts for the remaining topics, with optional student projects (listing website and paper resources) to complete a more in-depth treatment for these topics; by describing how classroom teachers can use the history of mathematics in their courses; or some combination of the above approaches. We will certainly welcome feedback from the other attendees at the workshop, whether or not they teach courses that might use such a textbook. For that reason, and to establish initial contact with Christian professors who do teach such courses at sister institutions, we propose beginning our work in the context of the proposed CCCU workshop at Westmont.

Project Outcome

Through discussions together and with others we will refine our approach and develop a detailed historical unit for at least one mathematical topic. We will also develop a prospectus for the proposed textbook and begin to flesh out the details as time allows.