Place-Based Mathematics Education: A Conflated Pedagogy?.

The debate between local interests and national perspectives plays out on many stages, including that of mathematics education. The Common Core State Standards Initiative (CCSSI, 2010) laid the foundation for standardized academic goals across the country. The primary target of the Common Core resembles that of earlier systems of standards: rigorous mathematical understanding that is abstract enough to be extended to a wide range of careers and situations (CCSSI, 2010; National Council of Teachers of Mathematics, 2000), and that presumably serves national interests (Gutstein, 2010; Howley, in press). In contrast, some rural educators argue that mathematical reasoning should emerge out of fluency with the mathematics of, and for, the local context (Bush, 2005). Mathematics teachers who care for place-based efforts, especially those in rural areas, are often caught in a tug of war between these extremes (Kannapel, 2000). Place-based mathematics education (PBME) considers the unique history, geography, culture, and community of a place to be valuable resources for enhancing, and being enhanced by, students' learning of mathematics.1 Among other reasons, teachers practice PBME to increase relevancy for their students and to help sustain the local place (Howley et al., 2011). In a cross-case analysis of exemplar PBME sites in seven states, Howley et al. (2011) found that attempts at PBME were plagued by constraints on time, limited resources, and dissonance resulting from unconventional pedagogy. Further jeopardizing the sustainability of PBME were doubts harbored by students, parents, administrators, and community members as to its effectiveness in increasing students' mathematical knowledge. A primary concern is whether PBME compromises the mathematical rigor demanded by state and national standards. Alternatively, from the perspective of teachers' seeking to sustain their local places, there is concern as to whether PBME that is taught in a mathematically rigorous way can maintain authenticity to place.This article reports on a study conducted to investigate the sustainability of PBME. Since the empirical research literature on PBME is scant (Bush, 2005; Howley, Howley, & Huber, 2005), and because of the substantial challenges in practicing PBME, it is logical to contribute to the literature through use of extreme examples. Howley and her colleagues (2011) chose an extreme sample based on site reputation; this study used an extreme sample in terms of academic training. Fifteen mathematics educators who had graduated from a three-year doctoral program in rural mathematics education were interviewed. The challenges and successes they experienced in attempting to implement PBME were then analyzed for themes.Related LiteratureThere is a dearth of empirical research on PBME (Bush, 2005; Howley et al., 2005). Thus, I begin by reviewing empirical studies on related pedagogies2 and on place-based education in general.Learning Methods and Perspectives Related to PBMEAccording to the Trends in International Mathematics and Science Study 1999 [TIMSS 1999] (Mullis et al., 2000) videotape analysis of mathematics classrooms across the United States, typical instruction consists of a teacher introducing material to students, followed by repeated examples (Stigler & Hiebert, 2004). There are exceptions. For example, in learning methods that are inquiry-or problem-based, students collaboratively investigate open-ended problems with reduced teacher guidance (Hmelo-Silver, Duncan, & Chinn, 2007; Savery, 2006). Hmelo-Silver et al. (2007) reviewed several studies on the effects of using these investigative methods in mathematics classes. On the whole, these studies suggested that inquiry-and problem-based methods in mathematics are roughly as effective as traditional methods for teaching procedural knowledge and provide significant advantages for solving multi-step problems. Hmelo-Silver and her colleagues also pointed out the empirical gains of investigative methods in softer skills such as self-guided learning, reasoning, and collaboration. …