Connecting Mathematics Education and Community: First Findings of a National Study

Robert Klein (Department of Mathematics) Craig Howley (Educational Studies Department) Aimee Howley (Associate Dean, College of Education)

Ohio University Athens OH

March 23, 2009

Paper presented at the annual meeting of the American Educational Research Association. “This material is based upon the work supported by the National Science Foundation under Grant No. 0119679. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.”

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Connecting Mathematics Education and Community: First Findings of a National Study Introduction Conceived by researchers at an NSF-funded national center, the study on which this paper is based aimed to gather and analyze data about current mathematics teaching and learning practices related to the struggle to make connections between school mathematics and rural communities. 1 This paper represents a first analysis and presentation of initial cross-case findings. Study directors and authors include faculty from the mathematics department, education administration, and education research. The outlook of the study is grounded more in the traditions of sociological and organizational analysis than in pedagogy and psychology—though the authors of this paper are admittedly concerned that students encounter meaningful (“significant”) mathematics instruction in schools everywhere. Indeed, proponents claim that community-based approaches to instruction are valuable for several, familiar reasons. Such approaches supposedly provide opportunities for learning in authentic ways (Sarkar & Frazier, 2008), and they purportedly clink new school learning to students’ lived experiences (Smith, 2002). Moreover, while such approaches intend to enhance connections between local schools and local communities (Woodhouse & Knapp, 2000), proponents make the substantive claim that with such connections help students make better sense of their lessons (Sobel, 2004). Nonetheless, little effort has been directed at studying how, in particular, mathematics education anywhere is making such connections. This study is one of the first efforts to do so (but see also, Green, 2008, and Howley, Perko, & Howley, 2009, both being presented at this conference).

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For the study’s “definition of rural,” see the methods section.

2 One warning to readers seems useful. The overall study is far more interested in the struggle to make these connections than in “best practice” in this sort of work. A form of schooling conducted in the name of particular places, in fact, hardly lends itself to the development of a set of practices that would be best everywhere. Indeed, two of the present authors have reported empirical results, including findings from studies in mathematics education, that cast doubt on the construct of best practice (e.g., Howley & Howley, 2007; Howley & Howley, 2004; Larson & Howley, 2006). As a result, the study does not concern itself at all with standards-based instruction in mathematics per se. Related Literature This discussion of related literature first examines relevant theory in order to describe the framework on which the study and this paper rest. Consideration then turns to the thin, but growing, extant empirical literature relevant to the study. Theoretical Literature The study proceeds from an appreciation for Kleibard’s (1995) historical and political notion of curriculum struggle, though we are not adopting his scheme to organize our findings. Instead, the study is framed with regard for the fact of curriculum struggle itself. This turn is a critical one: school change, on our view, is too couched as a matter of scientism—Kliebard’s “social efficiency”—not as a cultural and political dynamic. Indeed, in designing this work we expected that examples of the connection between mathematics and community (or place) might prove weak, fragile, and perhaps contested wherever attempted. In discovering candidate sites, for instance, we often heard that community connections were uncommon—or even unheard of—in mathematics instruction, and such reports surely augured well for the intended purpose of the study (if not so well for school practice).

3 The study is as deeply framed, of course, with a concern for rural education, specifically rural mathematics education. How does this construct (“rural mathematics education”) differ from an alternative construct—mathematics education in rural schools? Should we not be more concerned with difficult struggle to bring standards-based instruction to scale in rural schools? In brief, our focus construes rural education work (including mathematics education) as prospectively grounded in rural life-ways and commitments. This differs from the latter construct, under which, too often mathematics education in rural schools is regarded as (yet another) case of deficiency in need of stronger doses of standards-based reform. This claim is hardly unwarranted. In a review of relevant literature, one of the Center’s research teams has shown, in fact, that deficiency is the usual mode in which mathematics education in rural schools is most often considered (Howley, Howley, & Huber, 2005). Our approach to this issue has much in common with an “affordances” outlook (Gibson, 1977) or the more familiar “funds of knowledge” sensibility (Gonzáles, Moll, & Amanti, 2005). Again, this appreciation of the prospective relevance of everyday rural life (i.e., the intellectual content of community connectedness) is a framework and not part of our analytic method. In defining the central substantive interest as “connections between school mathematics and rural communities,” the study is also examining possible instances of “place-based education” in mathematics. Though reported instances of place-based education are comparatively common in social studies, literature, and science, they are much more rare— almost non-existent—in mathematics; even more rare than empirical research about mathematics education in rural schools (Silver, 2003). Place-based education is itself a work in progress (Gruenewald, 2003; Smith, 2002), but if to be distinguished from the variety of close cousins— environmental education, experiential education, project-based learning, and outdoor education,

4 for instance—clearly a conception of place is critical. A number of writers in rural education conceive place as the interaction of community and land; land that influences community and vice-versa; in other words, land ethic (Haas & Nachtigal, 1998; cf. Leopold, 1949/1987). As rural education researchers, we prize rural places and the various rural ways of living and being in the world, which ways of living and being we construe as inherent features of place, and hence, prospectively, of a land ethic properly speaking. For this reason, we tend to believe the rural sites lend themselves best to the continued elaboration of place-based education: in most cities the land has become real estate and is barely even visible under the buildings that occupy it. In most suburbs, mobility is so furious as to render the population as non-participants in a land ethic; there, something other than the land forms the character of the inhabitants. Curriculum and instruction in rural schools might (i.e., prospectively) also prize the land and ways of living and being in the world that reflect engagement with the land. Indeed, this circumstance seems to be what some place-based proponents imagine . We ourselves are not exactly proponents of place-based education, but we might be characterized accurately as supporters. This approach is to some extent consistent with the conventional constructivist pedagogy since connecting instruction to a child’s community (rural, suburban, or urban) can be argued to respect students’ knowledge and culture as a starting point for the creation of new or modified knowledge structures. Thus the study’s outlook is roughly consistent with constructivist models of learning and prevailing epistemologies that link social context and culture to educational praxis. That is, in this work, the engagement of the study team with these positions and ideas is more descriptive than prescriptive, and more curious than evangelical.

5 Empirical Literature One of the first relevant empirical studies examined the work of teachers and community members in five districts to design place-based activities and infuse them into their schools’ curricula (Wither, 2001). The study examined the development of the activities, but the researcher also reported that implementation confronted challenges. For example, teachers not involved with the planning valued place-based education less highly than the need to address the more self-evidently pressing school problems (test scores, AYP, conventionally construed “best practice, and so forth 2 ). Principals also offered only limited support, according to Wither. The source of such resistance is argued by DeYoung (2003) in an ethnographic study that examined the tension between academic and community purposes of schooling. DeYoung found that educators rarely understood the rural community’s outlook on schooling. DeYoung argues elsewhere that this divide is systemic in rural communities, partly because rural—as opposed to suburban and urban neighborhoods—retain a traditional community identity (e.g., DeYoung, 1995). In a recent mathematics education dissertation, Green (2008) shows how difficult sustaining place-based education is, absent continued funding and third-party assistance. Others have also noted the outright suspicion that rural people harbor for schooling in many rural places (Budge, 2007; Corbett, 2007; Theobald, 1997). Moreover, despite their purported value and their claimed particular relevance to schools in rural locales, rural educators often do not make use of these approaches (Howley, 2003), in part perhaps for reasons hinted at by Wither. Overall, the extant literature reveals both the relevance and the fragility of place-based initiatives. The few case studies describing instruction that links school learning to community

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That is, doing things right trumps doing the right thing, especially in situations where accountability requirements go unmet (see Olsen & Sexton, 2009, on “threat rigidity”).

6 and place demonstrate how much effort is needed to establish and sustain these initiatives (Budge, 2007; DeYoung, 2003; Green, 2008; Wither, 2001). Similar insights also come from reading the case studies in Gruenewald and Smith’s (2008) edited volume and from unpublished evaluations of place-based programs, such as those sponsored by CO-SEED (Powers & Duffin, 2003). Further, in science, social studies, and writing, community-based projects are much more common than in languages and mathematics (see Green, 2008, for a mathematics case). Methods The principal source for this study derives from 85 interviews with rural educators, parents, and students, averaging about an hour each, which yielded an estimated 1,500 pages of transcript data. Interviews were augmented by 27 classroom observations and 29 fieldnotes, plus an assortment of documentary artifacts and publicly accessible data about the seven sites. The study intended to elicit interviewees’ stories about their work—its nature, its purposes as they conceived them, its reception, and its challenges. Our semi-structured interview protocols (see Appendix A for an example, the teacher-interview protocol) were framed to guide such conversations. Eight researchers used the study protocols (interview, observation, and fieldnote) at the seven sites; one site was visited by a pair of researchers (the second and third coauthors). This section continues with, first, brief descriptions of the seven study sites. Next it presents a description of initial data analysis methods; as noted previously, this work-in-progess plans will continue to pursue additional in-depth analysis as this working draft evolves. Future iterations will provide a more complete methodology.

7 The Study Sites We visited only schools in rural areas or small towns. For each nominated school (see the next subsection for nomination and selection procedures) we consulted the Common Core of Data of the National Center for Education Statistics, which has coded the locale of every school and district in the nation starting in 1989. Qualitative researchers know, however, that not every school thus categorized (via the school zip code and the preponderance of the locales of the schools in a district) presents itself as similarly “rural.” We used Google earth to examine the actual setting of schools to ensure the face validity of the NCES categorization of each site. By each of these criteria, the schools studied were rural. The NCES locale codes are a commonly accepted taxonomy, but they define only lines on the earth (school and district attendance zones). Rural really. But what is rural really? In our work, then, we have tended to attempt the explanation that what rural really is is a set of meanings related to ordinary rural ways of living, being, working, and knowing. These qualities are not only not well-defined, but they vary dramatically from place to place. Overall, however, rural people dwell in relationship to the land, to family and kin, and to the “old homeplace.” In a sense, sustaining and cultivating the variability of related rural meanings is the point of place-based education. This may strike some readers as a peculiar claim: Isn’t every place a place? Our answer is “no.” Bear with us. Rural communities’ unique connections and productive interactions with the land (and vice-versa) are the defining features of the construct place; these conditions are everyday realities in rural areas. But in suburban enclaves and in cities, the land is concertedly real estate (building sites). On this insight, one can argue (as two of us previously have) that defense of rural place is the point of place-based education. Without this purpose, what some call “place-based education” is indistinguishable from environmental education, project-based

8 learning, outdoor education, inquiry learning or some other progressive praxis (e.g., Howley, Perko, & Howley, 2009). These worthy cousins to place-based are available to practitioners everywhere; placebased education, we argue, is different. It’s a necessarily rural practice. For this reason, then, the choice of rural schools is a not only a logical one for this study, but an essential one. Before turning to actual methodology, in the following seven paragraphs, we describe the seven study sites. The South Valley Local School District is located in rural Appalachian Ohio. The district has two school buildings located on the same campus: South Valley Elementary School and South Valley High School. It serves approximately 900 students in grades K-12. Approximately 60% of students qualify for subsidized meals. Median household income in 2000 was about $30,000. Middle school students have consistently performed about the state average and met state proficiency requirements for many years. The math teacher whose practices constitute this case is employed at the middle school. The Magnolia City School District is located in one of the rural counties of southern Alabama. The city of Magnolia itself has a population of approximately 2,000 people. As of 1999, 40.7% of families with related children of 18 years or younger live in poverty status, and 55.65% of students in Covington County receive free or reduced lunch. The Magnolia City Schools enroll 162 students in the high school and 84 students in the middle school. Magnolia High School received a bronze medal rating from U.S. News and World Report’s list of America’s Best High Schools. The average ACT score for 2006 was 19.7. Meriwether Lewis Junior Senior High School is located between the two Salmon Falls Valley towns along the valley’s primary highway; 2002 populations were around 1000 and 400

9 respectively. In 2007-2008 the school enrolled about 250 students in grades 7-12. In 2007-2008, approximately 31% (vs. 38% statewide) of students were eligible for subsidized meals. Meriwether Lewis graduated 92.1% of its students “on-time” as compared to the state’s 72.4%. Meriwether Lewis and the Salmon Falls Valley Elementary School share a campus and are the only schools in the school district. Teachers come to know students in the district and their families well over the six years they spend at Meriwether Lewis. Students do well on state tests. Eastcove Community School is located on an “unbridged” island 12 miles off the coast of Maine. Though not affluent, Eastcove, however, is a not a classically impoverished rural community; family incomes were just 5 percent lower than the state average (Bureau of the Census, 2008). Rather more remarkably the poverty rate for the 25 percent of residents under the age of 18 was just 2.8 percent. Perhaps these figures reflect the relative equality of the income distribution among the island’s year round residents: 29 percent of the families subsist on incomes of less than $35,000; 58 percent have incomes from $35,000 up to $75,000; and just 13% of families have incomes of $75,000 or greater. This is an arguably egalitarian distribution of essential resources. The upper grades outperform the state on mathematics proficiency by a substantial margin. Perhaps interestingly, the upper grades implement a more extensive placebased effort than the lower grades, according to the principal. The Green Mountain School is unique among our sites. Some small town New England districts operate only a single K-6 school. In such circumstances, these very small town districts “tuition” their children to higher grades—they pay other entities to school their children. Green Mountain, a K-8 school, accepts such tuition students from neighboring towns. Unlike the other schools in this study, Green Mountain School (founded in the 1960s) is a non-profit private school—but one that also receives public funding. In the 2007-2008 academic year the school

10 enrolled a total of 127 students. About 35% of TGMS students receive scholarships (school reported data), decennial US Census data for this rural town show that median household income was about 5% under the national average (for 1999) of $42,000, and the modal salary range was $50-75,000, whereas just 8.2% of families with children under the age of 18 existed on incomes below the official poverty line (as of 1999). Great Plans Union District in Nebraska is now a consortium of four independent school districts led by a single superintendent, through a unique arrangement among the local boards. The “dual superintendency” is sufficiently common in the Great Plains that it has generated a small research base; the Great Plains Union arrangement, however, is perhaps unique in North America. The quadruple superintendency is of 13 years standing in one district, and 5, 2, and one year in the other districts. Nine schools are involved, and each district operates its own high school, with high school (7-12) enrollment varying from 45 to 197. The study conducted interviews at all high school locations. The subsidized meal rate for all elementary schools combined was about 31% in 2007-2008; family incomes in the four communities vary from about $35,000 to $46,000 and poverty rates for families with children under 18 from 0% to 12%.. ACT math and composite scores in the two longest associated districts (7-10 year averages per schools’ websites) were all about 22, approximately the national average. Clearly, this site is the most complex “case” in the study. Rochambeau High School [insert copy from your notes, etc.] Data and Analysis The Center that sponsored the study maintained active relationships with scholars in rural education and mathematics education. In concert with these scholars, the research team developed a list of initial contacts in mathematics education, science education, experiential

11 education, outdoor education, and rural education. The list of nominators reached 81, of whom the study team was eventually able to contact 58. These individuals nominated 61 rural sites, from which the team selected seven to provide variety by geographic location, education level, and extensiveness of engagement with this approach to rural education. Table 1 provides information about sites and the scope of data collected at each.

Table 1: Interviews and Observations by Site Site

Interviews

South Valley OH Magnolia AL Rochambeau KY Great Plains Union District NE Green Mountain School VT Eastcove ME Meriwether-Lewis WA

14 8 11 22 3 16 11

Classroom Observations 5 3 2 6 4 2 5

Field Notes 2 3 1 6 3 7 7

At each site, members of the research team interviewed teachers, students, parents, administrators, and in a few instances non-parent community members. Additionally, each investigator observed mathematics lessons of various sorts, taught by self-contained classroom teachers at the elementary schools, math teachers in the middle and secondary schools, vocational agriculture teachers, science teachers, and in a few instances community members. The investigator at each site also collected relevant documents such as instructional materials, newspaper articles, and examples of students’ work. General data analysis thus far has entailed two levels of coding. First, using the qualitative software package, Atlas-TI, a member of the research team developed inductive (i.e., open) codes that were closely tied to the data. Then the researcher combined those codes to create conceptually distinct categories, codes that some researchers refer to as “axial” (Strauss &

12 Corbin, 1998). In this fashion, the full research team produced individual case studies, which are currently being edited for a project report. This paper, however, is a first attempt at cross-case analysis. As such it draws partly on close reading of the relevant case studies by the three authors, but partly also on an initial reading of transcripts by the first author in order, very tentatively, to surface themes related to struggle to make community connections. As this work evolves from conference paper to journal-article manuscript, the three authors intend to analyze the transcripts formally, as suggested, for instance by Stake (2006). Our current “findings,” then, are more in the nature of surmises and should not be read as fully warranted findings; please read this draft as a work in progress. Findings Preliminary analysis of the data, along the forementioned lines, tentatively suggests several common themes: (1) the influence of place-specific conditions, (2) initiative and support, and (3) the praxis of the real. Presentation of each of these themes embeds the study’s concern with “struggle.” While approaches differed across sites, the most common approach involved constructing a “praxis of the real” in which mathematical abstractions are interpreted and used in “applied” or alleged “real-world” contexts. Other shared approaches involved importing community (people, contexts) to the classroom or exporting students to the community for some purpose of study. Nonetheless, the notion of a “real-world context” is problematic since the “reality” constructed in and by the problem is closer to a virtual reality than a lived one. In a formal instructional context, of course, this dilemma may be inherent. This struggle—an intellectual one—highlights, perhaps, the strange distinction between school as artificial and community as real.

13 The work of connecting mathematics to place involves, quite literally, “locating meaning,” involving a conscious struggle to appropriate “understanding of , and exert some control over, their environment” (Burton, 1984, p. 36). This struggle is about “extending a range of possible choices” (p. 36) for those engaged in the development of mathematical thinking. This struggle involves (re)negotiating scarcities of time and other resources, local support, and the availability of suitable and appropriate contexts for study. A related struggle involves a perceived difficulty in recognizing mathematical connections to place and subsequently creating meaningful, appropriate, and engaging curriculum around those connections. We now turn to a discussion of the three themes. Each, even at this juncture, is supported through excerpts from interview transcripts. The Influence of Local Conditions Findings from the study confirm the complex and important ways that locality can impact mathematics education. Data demonstrated several ways that place finds expression and ultimately impacts or constructs priorities in the mathematics curriculum. Economic priorities and strengths. Rural places are sometimes romanticized as “removed.” Though this characterization prioritizes urban centers (the missing “from”), rural communities are often found in areas whose natural environments dictate the kind of economic, vocational, and avocational activities that they will support. One of the sites, Eastcove, is an unbridged island located 12 miles from the Northeast coast of the United States and supports small-scale lobstering, boat-building, and seasonal recreation economies. Another site, Salmon Falls (Meriwether Lewis Junior-Senior High School), exists in a narrow valley in the Cascade Range and supports seasonal tourism, mostly in the form of outdoor recreation. Both Rochambeau and Great Plains schools occupy land that supports agricultural-farming economies

14 and, in the case of Rochambeau, pontoon boat construction and seasonal tourism related to a nearby lake. In each of these cases, using community connections to highlight the importance of mathematics means negotiating the (often small number of) economic priorities of the local communities. The natural resources in the area, and local economies that result from them also dictate the kinds of funding resources, both private and public, available to schools for programs, projects, and non-routine expenses such as field trips and equipment costs. For those locations like Eastcove and Salmon Falls with strong seasonal tourism, the money brought from population centers by affluent visitors partially funds educational foundations that support teacher-sponsored efforts. Locations like Great Plains or Rochambeau, on the other hand, depend on their yearround residents for sources of local funding. Rochambeau received generous school board funding, but to purchase expensive tools procured a Toyota grant (that manufacturer is a local resource in Kentucky). Salmon Falls Educational Foundation (SFEF) raises money from businesses and individuals, both locally and regionally, and then distributes the proceeds as grants to local educators. Created by an area parent, SFEF’s success is likely the combination of local enthusiasm and access to seasonal tourist dollars. Isolation and population density. Interviewees in several sites described isolation, both professional and cultural, as a theme of locality. Mathematics teachers in small, rural-remote sites usually have few or no colleagues with whom to consider professional issues; in these schools, quite often, a single math teacher serves all students. They also saw geographic remoteness as limiting their professional development opportunities.

15 In related ways, the density or sparseness of the school community constituents impacts the degree of participation by the community. Meriwether Lewis family homes dot more than twenty miles of the main highway in Salmon Falls Valley. Transportation issues limit the availability of parents and community members for school events, and impact student participation in after-school events. Community networks. Local natural features also influence the ways that community networks form and are maintained. The smaller, more densely populated communities among our sites seemed to exhibit a richer sense of community pride, culture, and awareness than sites where population was more dispersed. In Eastcove in particular, the 350 inhabitants of the island were fond of describing things as either “good enough” for the island, or “too good”: things that were too good were interpreted, in the words of one interviewee, as “destructive of the unique culture of the island.” In Salmon Falls, as well, Ms. Jay was able to know those in her community well enough and broadly enough to recruit community members to visit her class for Careers in Math days. As in other rural studies we have conducted (e.g., Howley & Howley, 2006; Howley & Harmon, 2001; DeYoung, Howley, & Theobald, 1995), interviewees asserted that closing the school was tantamount to closing the community. Indeed, community support was mentioned in a number of sites as important to the sustainability of the schools’ efforts. Such support, in thriving efforts, take a form additional to enthusiasm, participation, and funding. Embedded in the relationship of small rural schools and communities is familiarity, in some sites, and to varying degrees, with local culture, enterprises, and lifeways. For some teachers, in some sites, this knowledge of place—which one might identify as contextual currency—seemed to enable active pedagogical engagement with the community and its resources.

16 Initiative and Support The projects studied depended significantly on initiative, including the rallying of support. Initiative and support arose quite differently from site to site, demonstrating effectively the dangers in using them as prescriptions or models for future implementations of place-based projects. The constructs themselves, one might argue, depend on local conditions. Teacher initiative. With the exception of the Great Plains site, teachers invented the efforts to connect place to mathematics instruction. In the cases of Meriwether Lewis and Rochambeau, the programs seemed to us unsustainable without the stewardship of the teachers. As the only middle-grades mathematics teacher at Meriwether Lewis, Ms. Jay handled all of the planning, recruiting, administration, and other management details of the Careers in Math and Math Communities projects. Without Ms. Jay, these programs likely would cease to exist. At Rochambeau, the Lutherie class was the brainchild of a mathematics teacher with a love of and talent for music (he is a mandolin and guitar player who has recorded and sold music locally). He joined with the agriculture teacher who has expertise in crafting wood to create the Lutherie class. Together, the two were able to engage students in the mathematics of crafting ukuleles, from the procurement of the raw materials to the finished product (some of which were then sold to the community to generate ongoing funding for the program). Recently though, the mathematics teacher was promoted to an administrative role that left the agriculture teacher managing the class alone. Though he has had great success motivating a wide range of students to take pride in the production of quality instruments, he disclosed in an interview that: I don’t spend a lot of time teaching math concepts in this class directly. Indirectly, we do it everyday, you know? And the kids don’t even realize that it’s happening. But if a kid has to take a dial caliper and go to the drum sander over there and start with a piece of wood

17 that’s this thick and take it down to eighty-five thousandths, they make—they figure some things out in that process that they’re going to generalize over into their other math classes and everyday life too. The mathematics teacher identified a number of applications of mathematics in making ukuleles, including the acoustic properties of “book-matching” for symmetry on the backs of the resonating chambers and other topics such as the logarithmic layout of the frets. Student informants made mention of these terms, but seemed unable to describe their meaning related to the instruments, indicating that they had discussed those things at the beginning of the year. This would suggest that the absence of the mathematics teacher had an impact on the extent to which mathematical content was studied in conjunction with ukulele production. Nevertheless, students cited measurement and geometry (in particular scaling from blueprints) as the most significant mathematics content that they used in the ukulele class. In his administrative role, the former mathematics teacher is notably able to lobby for the program’s continued existence. This support is likely helpful, given the time demands of the lutherie course: the class meets two hours every day and accommodates only 18 students. The efforts at Green Mountain School and Eastcove are supported by teachers who have graduated from Antioch University’s teacher education program, which promotes place-based education methods. They arguably arrived at their schools prepared to exploit local resources and strengthen community connections. In the case of Green Mountain, the mathematics teacher’s resourcefulness led her to construct curriculum that involves studying the local tract of wooded land owned by the school. Students are given a plot of land (sometimes circular, triangular, or rectangular) and they must profile the available timber (by type, age, etc.) in that plot. Students then construct feasibility studies for the sale of the timber from that plot. This approach is similar

18 to other well documented approaches to place that involve natural resource sampling (Sobel, 2004). Interestingly, this teacher did not graduate from Sobel’s Antioch New England program, but instead seemed to build on her experiences as a child when a student at Green Mountain, as this interchange seems to suggest: Interviewer: Do you remember how you were taught math in 7th grade? Or in middle school area? Or Junior High School or whatever they called it at that point? I mean I. Respondent: I went to The Grammar School. Um…not particularly, but I’m sure... I liked math, I don’t remember specifically. I think we had, for sciences, we had little plots in the woods. I don’t remember. The presence of and interaction with Antioch-trained colleagues would seemingly offer a supportive context for the elaboration of this work. The inspiration, though, seems not only local but specific to this teacher’s childhood in this school. Collegial initiative. The Rochambeau Lutherie class, though supported by the former mathematics teacher and current administrator, is now taught only by the agriculture teacher—he decides and implements the curriculum, and makes decisions about its direction. In contrast, the Eastcove principal hired a consultant from the Island Institute and a new teacher, each of whom graduated from Antioch’s program rooted in place-based methods. Together, they guided the creation of curriculum rooted in local strengths such as “pea-pod” boat designing and building, clamming and lobstering, and the competitive design and construction of an electric automobile. These teachers’ prior training in place-based methods, together with the guidance and support from the principal make Eastcove perhaps the most developed and experienced study site regarding connecting mathematics to place and community. The Eastcove principal is a 34-year

19 veteran teacher on the island. Originally an off-islander, he learned about the community and its needs through long experience; arguably, this experience educated him to the role: Teachers came and went so frequently that kids and parents wouldn't develop close relationships with them, because they were always afraid that teachers would up and leave. You know, and so, it was really a testing thing. You know: "are you going to stay?" You know, if we're rude to you, if we're...you know...will you still stay? Will you still like us enough to stay? And so teachers would leave, they wouldn't stay. And that went on for a long time. And, really, I became principal because I was sort of the last person standing. I was the, you know, the pers...just by virtue of my persistence, you know, that I'd stayed that long. And, I had this-- by then I'd been for eighteen years, and I'd been...I had been-- you know, I had this institutional memory of, of, of what went on. And I didn't have any aspirations to be principal, but I really did care about the school. I thought it was a great school, I just thought people didn't understand how good and important it was. And, becoming principal gave me the opportunity to sort of impose my...educational philosophy on the place. And, which is what I had wanted. And tried to do for a long time. The forms of initiative observed above involve educators marshalling resources to make decisions that create and sustain efforts to connect mathematics—or all of schooling, as in the case of Eastcove—to community. The testimony of the Eastcove principal seems to warrant the relevance of local conditions—especially the need to understand deeply the inauspicious conditions.

20 Further initiatives include raise support in the community and in the form of time, money, and sympathy for the efforts. Additionally, administrative colleagues defend the projects’ existence in light of possible opposition, as in the case of Rochambeau. Support. Support of the community, parents, foundations, educators, students, and the teachers perhaps constitutes a recurrent theme in the data. Schooling is a public function and, as mentioned above, a core part of the identity of many smaller communities. In Meriwether Lewis, for instance, a grant from the Salmon Falls Educational Foundation paid members of the community for their participation. Eastcove’s principal, responsible for initiating the place-based approaches there, had to convince dubious members of the community of the worth of the field trips and other projects and was even fired and then re-instated as a result of first backlash from a portion of the community, and then the rallying of student and community support for him. On the view from the Eastcove data, securing community support—and engagement—is a arguably a form of struggle, and not a mere arrangement. This surmise is perhaps warranted by the conditions in Great Plains. This site, in fact, figures in a number of existing studies of place-based education. It has received external support in the past from a variety of sources, some of them national. At present, however, support from the community and from the teachers seemed dubious on our reading of the transcripts. Whereas in Eastcove the struggle seemed successfully concluded, in Great Plains the struggle was clearly not concluded. The following remarks from Great Plains math teachers illustrate the point quite well: Teacher One: We don’t really do anything in places. We don’t really do any of that. I would say, maybe, the shop class is where you’re going to find that. The closest we’re going to come to that is just story problems.

21 Teacher Two: Well, I don't do much in the way of pulling in outside things, really. Um, I work basically from the textbooks and from, um, oh, a few things that I've pulled together, but it's from other sample texts, and that. You know, I really haven't done a lot as far as trying to pull something from the community in, and use it. So. Teacher Three: Currently I probably don’t actually contact any places in the community, but we might draw on what they do, as far as when we refer to story problems or try to bring it to reality for them when they ask, “Well, how can I ever use this?” Teacher Four: I’m not sure what’s all around to actually take them out to where they’re supposed to go. Like we were talking about um, recycling, for instance. Laurel has a great recycling place where you can go in and drop off everything. I wanted to take them there but I just didn’t know how – how to get that going and it kind of got too late. Praxis of the Real Many of the sites studied connected mathematics to community through a focus on “applying” mathematics to “the real world.” Such “real world” connections or contexts, in particular the reality of the present, are far from a given in making connecting mathematics to community. Eglash (1999) has studied the Chokwe people’s sona sand drawings and the ways in which children are taught to draw what amount to Eulerian graphs that connect to stories of Chokwe spiritual legacy. As the children mature, the story and the drawings gain more points of complexity. While the “reality” of the cultural connection is arguable, the mathematics is used to communicate and represent a shared part of the community and culture.

22 Though the majority of informants studied here saw making connections as “making it real,” some disagreed. One upper-level high school math teacher at Great Plains described teaching with applications as more important for lower-SES or lower achieving students: I teach upper math, so I don’t know. I teach Trig and Calculus. So I doubt if we do any Calculus in local places around here. I don’t know how we have time to do that. I am not sure that the upper math classes – maybe a lower income average are going to need that, but my upper math class. I don’t know that they would benefit a whole lot. I think because my kids that I teach now are interested ‘in the math.’ I don’t have to make it flowery, I don’t have to make it enjoyable, I don’t have to make it fun, they just want to know, what’s the math, the theory behind it. So, that’s why I wonder about the upper math. I know you could argue engineering is going to need on-site things, but the Calculus? I don’t know how you are going to do that. Given the nature of the study, and the sampling of sites that were engaged in place-based approaches, such perspectives were rare, but important in that they revealed the tensions that accompany this work. The role of the “real world” differed at different sites. At Eastcove, the realities of living on a small, unbridged island are important to schooling. For instance, the principal commented that, “Of all the islands in [the state], there are only three left...and, so, we feel like we've got to work hard to keep this community going, and part of it is connecting the kids with the community all the time in whatever ways we can.” The realities of island lifeways motivate this approach to education. The realities that the mathematics connects to involve building pea-pod boats, designing new rooms for the school building, seafood harvesting tools and techniques, and

23 electric car design competitions. This approach is evident in other subjects at the school and students often find themselves in the community as a result. Magnolia High School’s aquaculture and turf management projects can be seen as similar to Eastcove’s projects in the way in which they appeal to “real world” skills and “applied knowledge.” Like Eastcove, Magnolia plays on community economic strengths. This part of Alabama features golf courses and resorts, so turf science has economic relevance to the region. The aquaculture program is much less a mandate of the area economy, but offers a robust opportunity for student involvement measuring, managing, and solving complex problems related to farming fish. Students in the focus group at Mangolia never specifically mentioned mathematical applications, though most of the teachers acknowledged the ways that mathematics was important to the chemistry and biology applications, especially in terms of formulae used. In this way, the “real life” uses of mathematics often are often subtle, and probably not recognized by the students as mathematics as they’d see it in the classroom. This phenomenon was recognized by the Rochambeau ag teacher who commented that, “I don’t spend a lot of time teaching math concepts in this class directly. Indirectly, we do it everyday, you know? And the kids don’t even realize that it’s happening.” At Meriwether Lewis, the teacher uses community members to convince students of the applicability of mathematics to a variety of careers and hobbies. In a way, it confirms the Rochambeau teacher’s perspective that “we do it everyday,” so much so that people in a variety of careers never imagined to depend on mathematics are nevertheless practicing it every day. Calling the goal “motivational,” Ms. Jay hoped students would see relevance in what they’re learning and that it’s sort of a motivational factor to stay engaged in math and to learn math…. My number one reason for doing it was …‘When

24 are we ever going to have to use this?’ When you’re in a rural area, [the school is] central to our community, and so they just want to be involved. We have such a rich background of people here, and they have so much to offer, and so, [I hoped] they’d just be involved and feel good about what’s going on with their kids. Math Communities, unlike the Careers in Math program, focuses on solving multi-step problems that may or may not be considered applied in any sense. Hence “the real” at Meriwether Lewis is used in the sense of a motivational argument for students to consider the mathematics they study (applied or not) as useful later in life in their careers. Careers in Math has less to do with teaching mathematics than convincing students of its value. Math Communities, on the other hand, has everything to do with the development of mathematical skills under the guidance of parents working with the students in small groups. Discussion As with the foregoing analysis, the present discussion is problematic and tentative. Nonetheless, engagement with data and experience with the sites and the debates in the theoretical, policy, and research literatures enable some observations at this juncture. The teaching of mathematics, a discipline possibly so abstract as to transcend place and community, may strike some observers as ill-suited to instruction in place- or community-based approaches. Nevertheless, current thinking in mathematics education, with its emphasis on the construction of meaning and the application of problem-solving to “real-world” situations, might logically be interpreted as supporting community- and place-based approaches to instruction. This realm is, after all, still the realm of school math as distinct from academic mathematics. Very few students here or anywhere are destined to become “pure” mathematicians.

25 What can be said about what the actors in our seven cases confronted—the nature of their struggles—based on our initial “surmise” findings? Three points connected seem evident at this incomplete stage of our work. First, struggle does prevail across these cases, even in the case of Eastcove, where “placebased education” was, in fact, the pedagogical template. On some views, Eastcove might seem a paradise of place-based learning. But even there, as we learned, some students and families questioned the value of what the school practices so assiduously as place-based education. Indeed, part of the genius of this case (and this place) is that its practices have evolved through stagnation and crisis to the present pitch. Second, nearly everywhere, as both site nominators and the scant relevant empirical literature suggested, mathematics was seldom (not rarely, but at best episodically) taught through community resources, and teachers of mathematics at all grade levels generally reported that “time” constrained their engagement with place and community. The most notable exception, perhaps, was The Green Mountain School’s “tree plot math (and science).” Here a perspicacious teacher, evidently building on her own experience at the school as a student, developed a math (and science) project related to managing the school’s tract of timber. In other places (e.g., Meriwether Lewis, South Valley), individual math teachers developed projects that exhibited different, and perhaps less systematic, connections to place. One must note, with Green Mountain, however, that connections to an authentic community and place were problematic since the school (a private venture serving some public systems) drew students not only from a veritable assortment of towns, but from towns in three states. “Place” thus devolves not to community, but literally to the school itself. One might argue that it’s a strange construction of place that omits local community (we argue that a school is not itself a local community in the

26 sense that we mean: multi-age, economically functional, real-time neighbors accessible to one another; cf. Buber, 1949). Third, varied affordances stimulate the emergence and maintenance of community connections. In two sites, the most relevant affordances were outright cultural and financial capital—perhaps embarrassingly outright. At Eastcove the district enjoyed the support of offisland homeowners to endow this public school with resources perhaps including the influence some form of high-status cultural capital (e.g., Bourdieu, 1997; Horvat, Weininger, & Lareau, 2003). A Maine lobstering community in contemporary America, without the seasonal occupants, would enjoy a far more stringent economy, with its schools suffering the usual fate in such communities. Instead, island residents met affluent, cosmopolitan off-islanders—and no doubt, often worked for them. But the cosmopolitan seasonal residents also supported the school (as the research team heard) in order to sustain the community. A similar ethos (but with a different local-cosmopolitan balance) seems to have prevailed at Green Mountain. There, the teaching core carried the high-status cultural value and likely the associated privileges—a circumstance uncommon in public education. The school nonetheless enrolled some public school students on a tuition basis, and these students had access to a progressive pedagogy, including “tree plot math (and science).” It’s difficult to judge which of these two sites benefited more directly from the affordance of high-status cultural capital. Eastcove, though, clearly enjoyed a munificence nearly unique in the public sector (a per pupil expenditure of about $27,000), especially for such an (otherwise) impoverished community. The Great Plains Union District (GPUD) presents an entirely different case of an affordance in this, the most complex of our seven cases. In this traditional agricultural area, local community leaders put four separate districts under the superintendency of a single

27 administrator. Though the districts remain separate, the arrangement is thought to make the districts themselves more sustainable in light of Nebraska’s ongoing attempts to close small rural districts. This site lacks the implicit or explicit munificence that characterized Eastcove and Green Mountain—though none of the communities seemed genuinely impoverished, none is by any means affluent. While strategically, community survival and defense motivates the effort strategically, math teachers remain skeptical about how and, and to a somewhat lesser extent, why to develop community connections with the curriculum. What insights might explain this circumstance? We will suggest two possibilities at this time. First, DeYoung’s insights about the disjunction of schooling and community may be relevant, particularly if teachers believe the community-defense affordance displaces or fails to connect with the assumptions of schooling; teachers see more academic value in traditional pedagogy than in any “progressive” place-based pedagogy that honors community. In a sense, they may be seeking to maintain the privileges that devolve to them through the disjunction of academics and community purposes. Second, though the combined superintendency may enhance the odds of survivial for the independent districts, it may not be able to foster the specific affordances that basing an education on place seemingly requires. One should not presume that four districts in the same neighborhood are so similar as to render vacate this insight. Peshkin’s class study, The Imperfect Union, shows that town several miles apart can harbor interests that are wholly incompatible (Peshkin, 1982). One implication of such logic is that place-based education is impractical, as a systemic phenomenon, in districts that cobble together diverse communities. We would prefer to conclude this paper with more synoptic implications or interpretations, or at least with a posting of more definitive insights about the struggle at the

28 center of interest in this study. Such work, however, must await a more complete reanalysis of the full data set.

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APPENDIX A

Interview Schedule: Teachers

1. Our study focuses on mathematics instruction that draws on or makes use of local places and communities. How does what you do with your students fit in with this way of thinking about instruction? 2. What goes into the process of teaching in this way? (Probe: how do you use the textbook(s) you are assigned to teach from?) 3. What are the results of teaching in this way? 4. How has this way of teaching evolved in your own work? In the work of the school in general? (Probe: Do you have colleagues with whom you can talk about this way of teaching? Tell me about what that is like.) 5. What do you see happening with students when you teach in this way? 6. How do other educators in this school teach? 7. What kind of support have you received to help you teach in this way? 8. What forces interfere with teaching in this way? 9. What do you see happening with parents and community members when you teach in this way? 10. What are the future prospects for teaching this way at this school?