Abstract. This paper reports on the contextualization and logical reasoning efforts of five undergraduate prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The report of this exploratory study provides the foundation for conjectures about a theory of reasoning situation images. These mental constructs may be called upon by a learner in a reasoning situation and filtered through temporally, contextually, and personally rich experience. From this theory follow implications for teaching of logico-deductive mathematical reasoning.
Abstract. The goals of this chapter are to describe what it might mean for a college level mathematics curriculum to be culturally responsive and what learning from such curricula could accomplish. Toward this end, we address several topics. First we offer evidence of the national needs for mathematical competence for the citizenry and mathematical expertise in government, industry, and the academy. The focus includes both workforce and social justice issues. We then address the ways that current college mathematics curriculum leads to a mathematical education that falls short of meeting these needs, identifying some possible factors in that failure. Third, we describe how a culturally responsive curriculum might look. In particular, we outline two views of curriculum: as a content product associated with student outcomes (Taba, 1962; Tyler, 1949) and as a dialogic process associated with situated praxis (Grundy, 1987; Stenhouse, 1975). We examine how culturally responsive versions of each of these views of curriculum would look and how each could address the identified needs in college mathematics. The main concentration is on effective college mathematics instruction for non-mathematics majors. Fourth, we give a few examples of culturally responsive teaching and curricula in courses that currently exist and of the successes documented by these courses. We end by outlining some of the research questions that arise around the idea of culturally responsive curricula in college mathematics.