Mathematics Education as a Design Science

We propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and philosophy of science and mathematics and ongoing findings of M&M research are drawn to illustrate our notion of mathematics education research as a design sicence. Our ideas are intended as a framework and do not constitute a, “grand” theory (see Lester. 2005, this issue). That is, we provide a framework (a system of thinking together with accompanying concepts, language, methodologies, tools, and so on) that provides structure to help mathematics education researchers develop both models and theories, which encourage diversity and emphasize Darwinian processes such as: (a) selection (rigorous testing), (b) communication (so that productive ways of thinking spread throughout relevant communities), and (c) accumulation (so that productive ways of thinking are not lost and get integrated into future developments).     

Integrating Science and Mathematics Education: Historical Analysis

A number of national science and mathematics education professional associations, and recently technology education associations, are united in their support for the integration of science and mathematics teaching and learning. The purpose of this historical analysis is two‐fold: (a) to survey the nature and number of documents related to integrated science and mathematics education published from 1901 through 2001 and (b) to compare the nature and number of integrated science and mathematics documents published from 1990 through 2001 to the previous 89 years (1901–1989). Based upon this historical analysis, three conclusions have emerged. First, national and state standards in science and mathematics education have resulted in greater attention to integrated science and mathematics education, particularly in the area of teacher education, as evidenced by the proliferation of documents on this topic published from 1901–2001. Second, the historical comparison between the time periods of 1901–1989 versus 1990–2001 reveals a grade‐level shift in integrated instructional documents. Middle school science continues to be highlighted in integrated instructional documents, but surprisingly, a greater emphasis upon secondary mathematics and science education is apparent in the integration literature published from 1990–2001. Third, although several theoretical integration models have been posited in the literature published from 1990–2001, more empirical research grounded in these theoretical models is clearly needed in the 21st century.