| This dissertation reconceptualizes mathematics education's subject matter. Historically, mathematics has been help up as a bastion of certainty. Its characterization as objective, logical, and as existing outside of human involvement has made it resistant to pedagogical shifts similar to other subject areas. Recent reform efforts that have sought to relate psychosocial elements to mathematics education have had to work against particularly entrenched understandings of mathematics. Consequently, reformers often respond to absolutism by offering versions of mathematics that are subjective, relative, and fallible. The “math wars” have been raging for several years and show no signs of letting up, pitting traditionalists—those calling for more rigor and a “back to basics” approach to mathematics education—against reformers—those advocating a child-centered, applied approach to mathematics education.; Absolutism and constructivism are presented as ways of thinking that tend to undergird the traditionalist and reform sides of the math wars, respectively. This project develops an evolutionary philosophy of mathematics education in order to provide a way to avoid the dualistic trap of being forced to understand mathematics in strictly absolutist or constructivist terms. The evolutionary perspective focuses on the creation of mathematical knowledge that occurs when humans interact with their environments.; The evolutionary perspective emerges through scrutiny of relevant work in several fields. General philosophy, philosophy of mathematics and science, cognitive psychology, cultural anthropology, and history all employed in the effort to develop an understanding of mathematics that accounts for its remarkable stability and universality as well as its ability to grow and change. Emphasizing the empirical and functional dimensions of mathematics—from its origins stability without claiming that mathematical knowledge is true in Platonic or strictly formal senses.; The final portion considers mathematics class in light of this alternative philosophy. The evolutionary perspective provides a focus on students' ability to develop, employ, and evaluate mathematical thinking to solve genuine problems. The truth or usefulness of a given piece of mathematical knowledge is, according to this perspective, judged according to how well it works given the context of the initial problem. |
