Susan Staats

Stretching, sliding and strategy: indexicality in algebraic explanations

In this study, we describe the linguistic expression of strategy in explanations of algebraic procedures. Stating the steps of an algebraic procedure does not require a student to indicate the relationship between different mathematical actions, but describing algebraic strategy does. The coordinated nature of strategic proficiency suggests that linguistic forms known as indexical language, “pointing words” that link speech to context, may be fundamental resources for expressing this type of competence. A class of first-year university mathematics students developed a habit of reporting procedures that we consider a speech genre. The classroom genre emphasised procedural explanations, but when students expressed strategic competence, they often relied on indexical language. Indexical verbs of motion like slide and drop proved to be a particularly efficient means of expressing algebraic strategies. This informal speech style extended the communicative capacity of the classroom speech genre, and allowed classmates to participate better in strategic mathematical reasoning.

Mathematical Modeling and Culturally Relevant Pedagogy

Mathematical modeling and culturally relevant pedagogy (CRP) are both pedagogical approaches that rely on students’ knowledge of everyday situations, yet mathematics education research has not fully attended to the ways in which they can be united in the classroom. We use an interpretation of culture as students’ lived experiences, a perspective drawn from the Funds of Knowledge approach, which can uncover knowledge that is relevant for rich mathematical tasks and that can support socially conscious reflection. This chapter proposes a new pedagogical model, suggesting that the cycle of mathematical modeling provides key moments to access students’ culturally based knowledge and that this approach can address weaknesses in typical implementations of culturally relevant pedagogy. Mathematical modeling asks students to complete a problem-solving cycle involving sense-making, developing problem-solving tools, interpretation and validation of results, and further cycles of model improvement. The early stage of sense-making and the reflective stages at the end of the first modeling cycle are key points at which teachers can plan discussions to foreground students’ cultural knowledge and critical consciousness. We provide examples of this approach through a task on modeling neighborhood fence designs, and we provide reflections on implementing this approach with preservice secondary teachers in an early stage of their pedagogical education.

The poetics of argumentation: the relevance of conversational repetition for two theories of emergent mathematical reasoning

ABSTRACT Poetic structures emerge in spoken language when speakers repeat grammatical phrases that were spoken before. They create the potential to amend or comment on previous speech, and to convey meaning through the structure of discourse. This paper considers the ways in which poetic structure analysis contributes to two perspectives on emergent mathematical reasoning: Toulmin’s model of argumentation and Martin, Towers, & Pirie’s theory of collaborative coactions in multi-speaker discourse. Poetic structures appear in varied argument types and at varied educational levels. They appear to facilitate speakers’ expression of warrants, backings, qualifications, and coactions.

Internationalizing College Algebra

Few undergraduate classes match the potential of college algebra to internationalize the university experience. The complexity and variability of the world’s most pressing issues—of health outcomes, income, access to education, access to clean water—mean that a great deal of influential information is conveyed mathematically, usually as tables of values and graphs.