Innovación Tecnológica
6.2 Caracterización del Sistema Regional de Innovación
What conditions enable and constrain their efforts? The case reports demonstrate a wide variety of affordances and constraints in play. Chief among the affordances are alert and passionate teachers who think for themselves. They are apparently open to a range of productive provocations that goad them to action. They see opportunities and project them, their students, their schools, and their districts into action. Challenges are legion, by contrast: the likelihood that colleagues will embrace the mission is dubious; accountability frenzy is ubiquitous (though not likely significant at Green Mountain); changeable professional norms dictate one-best “best practice” or even miseducative purposes (e.g., global American hegemony); the organizational culture of the school or district might not be propitious for community engagement… and so forth. In these sites, of course, the affordances found a variety of ways past the challenges.
Enumerating such challenges precisely across the sites is a project that awaits further planned attention, but at this juncture, we identify three overarching conditions that seem to govern the emergence of such activity: (1) the imperative to develop community-focused math education, (2) approaches to developing place-based math education, and (3) insights from “middle-class theory.”
The Imperative to Develop Community-Focused Math Education
One might phrase the underlying question in this way: “Do we really need to teach ratios and proportions, elementary and intermediate algebra, geometry, trigonometry, and calculus with any significant connections (e.g., field work) with people or organizations outside the classroom?” If the answer is “yes,” an imperative exists; otherwise not. At the elementary and middle school level (see, e.g., Everyday Math), an affirmative, even in the foregoing cases, was far more likely than at the high school level. What the study seemed to have observed (with the distinct exception of the emergence of the lutherie class at Lafayette) is a consistent negative for “upper math.” The position of the upper-math high school teacher just quoted frames this issue culturally for us (but by no means pedagogically, since the study aims to open up the pedagogical question).
Why is secondary school math so impenetrable, pedagogically speaking? The answer is speculative, a matter of interpretation; one response follows. Upper math is allocated, via the typical mechanisms of American schooling, to deserving students who have proven their capacity for contemplating (Platonic) mathematical objects with patience and forthrightness if
not always curiosity or passion—students for whom the imminence of mathematics is happily associated with just enough fear to keep the intellect alert, and for whom the immanence of mathematics remains unacknowledged, at least until later, when the luckiest will prepare for, and then enter STEM-related careers.
Who might these fortunate math students be? Carr and Kefalas (2009) call them the high-flyers, those most likely to leave a rural community and never return. (Some, like the retired teacher’s son in Lafayette, do, of course, return—as notable and perhaps locally puzzling exceptions.) Almost as a matter of principled local educational practice, then, the local community becomes irrelevant to the probable destinies of such high-flying students and the aspirations that their usually influential parents cherish for them (Carr & Kefalas, 2009). These families want similar destinies for their children as upper-middle class families anywhere else around the nation: footloose professional careers that take them wherever the most lucrative jobs may be; many others have observed that schooling, even rural schooling, seems organized to this end, which is so counterproductive to sustaining the sponsoring community (e.g., Carr & Kefalas, 2009; DeYoung, 1995; Spring, 1988; Theobald, 1997, 2009). True, these students are not always the sons and daughters of local elites, but they generally are (Carr & Kefalas, 2009; Duncan 1999). Thus, engagement with place-based approaches tends to be limited to K-8 settings or, of course, and strongly, to vocational, technical, and agriculture programs—precisely, one might argue, because these settings and programs do not cater to the cadres of high- flyers and their families (Carr & Kefalas, 2009). Seemingly across America, then, the imperative to connect “upper” school mathematics to people and organizations in the community hardly exists,24 not as an oversight, but cleaving ardently to the prevailing purposes of schooling—sorting students, conveying privilege across the generations, and ensuring widespread powerlessness among the losers (e.g., Anyon, 2005; Bowles & Gintis, 1976; Brown, 1991; Duncan, 1999; Spring, 1988).
A psychological prejudice is associated with the social prejudice. The Lafayette case provides evidence that considerable fear surrounds getting local, everyday mathematics into the open. Whereas math indeed may be everywhere, it remains largely unrecognized—what we consider “locally immanent” (indwelling). Few educators anywhere (a few that includes the champions we visited at each site), seem willing to take on the project of disrobing the everyday-ness of mathematics, possibly because it seems an offense to the discipline of mathematics itself, at least as characterized above. One might speculate, then, that the institution of secondary schooling operates so as to widen distance between the curriculum of school math and the applications, including especially the local applications, that affirm math’s utility. It’s too much, on these terms, to expect that bridging the widening chasm would claim any legitimate attention, that is, except from those stalwart teachers thinking otherwise.
24Except, of course, as the cheer, “Math is everywhere!” At this writing that phrase yields over 10,000 hits in Google searches. A typical connection follows: “Hundreds of students from Western New York middle schools
compete in ‘Math is Everywhere,’ a math-based contest initiated to raise student awareness about the many applications of math to their every-day lives.” At this event, middle-school students competed in teams, using written problems. (Source: http://www.eng.buffalo.edu / mathiseverywhere/ Math_Is_Everywhere_Intro.htm ).
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Such speculations help explain the strange claim that “the side of math you don’t see every day is the everyday math.” Given (non-educator) adults’ testimony that more application is desirable, empirical investigations into the possible ways and reasons that the practice of school math obscures the utility of mathematics (everyday math, and mathematics in biology, sociology, history, and engineering) would surely be a fruitful realm of inquiry. Perhaps the central challenge for a place-based math practice is in the “seeing” of applications rather than the “connecting” of curriculum to community.
Developing Place-Based Math Education
The truly daunting challenges of practicing community-based mathematics instruction per se explain why readers might judge the results of this study disappointing. An appreciation of the purpose of place-based efforts can help readers understand the challenges much better.
Once again: Place-based education concerns the sustainability of rural places—rural communities, whether towns or informally existing enclaves. Place-based mathematics is by no means a quaint or backward cousin to project-based learning or culturally responsive pedagogy. It harbors an educational agenda as fine as culturally relevant pedagogy and community- based learning, and surely the preservation of community itself, as a practice and as an ideal toward which neighbors strive is an aim worthy of struggle (Theobald, 1995).
A great deal of rural education research suggests rather strongly that the sine qua non of sustainability in rural places is the continued existence of a school, and the most accessible study of this relationship is the late Tom Lyson’s (2002) study of rural towns and villages in New York. Places where schools had closed did less well. Less generalizable quantitative studies show that rural people attribute their towns’ sustainability to the continued existence of the school (DeYoung, 1995; Peshkin, 1982), and contributing authors to this study have reported this finding from their other qualitative work as well (e.g., Howley & Howley, 2006).
The stories we heard in the present work also included examples of sites where sustaining the rural community was foremost in the minds of formal and informal leaders: Eastcove, Confluence Collaborative, Lafayette, and Magnolia. But had we dug deeper (going outside the research mission of the study), we would probably have found such claims and concerns at every site. Remarkably in a study of mathematics education, however, the concern surfaced in these four sites without prompting. This eventuality is perhaps an indication that this study’s outlook on place-based education is about right.
At any rate, in these four sites educational leaders and practitioners shared a collective priority that had little to do, on the surface, with mathematics education—especially not mathematics education as typically practiced and conceived at the secondary level (as we heard in Magnolia, with self- deprecating irony: “I’m the typical, shut-in math teacher.”).
If the interpretations in this concluding section have some truth, then, an additional challenge of developing a place-based mathematics education might concern “seeing” the mathematics of the everyday (or injecting the mathematics of, say, differentiation, into the everyday) in combination with envisioning the future role of locally possessed mathematical knowledge in sustaining the local rural community. This sort of application of mathematics25 might strike even applied mathematicians as peculiar; after all, it’s rather like using music to reinforce school spirit—an analogy that also suggests that the seemingly peculiar application is not actually arcane. Are these misuses of music and mathematics? Perhaps; one doesn’t know about the music, but since mathematics is indeed applied to produce all sorts of good (including great private wealth, as for instance in the derivatives market), the collective usage for the public good would be more than arguably legitimate, but necessary—unless rural community were not, indeed, regarded as legitimate. One must wonder, here in America. Can high school math teachers be found or cultivated to embrace this mission? We have at least the examples of Eastcove and Lafayette as existence proofs. Moreover, it’s clear from the Magnolia, Confluence, and Eastcove sites that formal and informal arrangements do support place- based education efforts to good effect on qualities related to community sustainability.
These reflections about community-based mathematics instruction have shown where one challenge lies—simply seeing the local math and the possibilities for mathematizing the local everyday. Addressing that challenge well seems a logical first step on the way to developing a real praxis of rural (place-based) mathematics education.
Middle-Class Theory
Although the selected communities certainly exhibited some variability, it seems that all of them enjoyed substantial or considerable local resources. In this sense, perhaps, the Green Mountain case (our one private-school site that accepted public-sector tuition students) appears not to be the outlier one might otherwise judge it to be (i.e., as a New England private school): Household income distributions for all sites are given in Figure 5 (US Bureau of Census, 2000). The data displayed in Figure 5 for five sites represent school-district-level data from Census’s school district tabulations. Green Mountain data are also from the 2000 census, but represent the town in which the school is located and obviously not any public school district. Magnolia, the other exception, is part of a district with several high schools whose circumstances varied, and it seemed more accurate to use the available separate 2000 census data for the town of Magnolia. On the basis of these data, Magnolia seems to be by far the least well- resourced site in the study. The work in Magnolia, however, benefitted from a long association with a leading place-based education program that specifically designed its assistance for small, remote, and impoverished
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63 Alabama schools. This work has been reported impressionistically in the
national literature, and is widely admired, but has never been formally studied according to the program’s founder.
Magnolia’s involvement in the relevant work was as seemingly durable as that at Eastcove Island, though a Maine island and a southern Alabama rural town are in many ways polar opposites in terms of local economy, history, and culture. Race relations, for instance, do not manifest themselves in the Maine transcript data, nor do the Census statistics provide evidence of racial diversity there. Evidently, however, they do share commitments and a legacy of action on behalf of local place.
Figure 5 also shows a couple of other things. First, on the basis of household income data, none of these communities can be called affluent. Green Mountain is the predictably most affluent, but not by much (16% of households reporting incomes above $75,000 as against Meriwether Lewis’s 14%). Except for Magnolia, all the districts exhibit middle-income bands (2000 household income from $25,000 to $74,999) varying from 32% to 43% of households. Second, in four of these seven sites (Green Mountain, Confluence Collaborative, Meriwether Lewis, and Eastcove), the middle-income band is the modal band.26 Such a shared circumstance might be merely fortuitous, but it’s worth observing that sociologist Cynthia Duncan (1999, 1996) holds that a prevalent middle class helps sustain rural communities politically, economically, and culturally. The influence of the
middle class is regarded, in this view, as salutary both in the schools and in the community. The income distribution tables in Worlds Apart (Duncan, 1999) very clearly illustrate this principle, and we offer Figure 5 to suggest this theory, which we both appreciate and find doubtful.
Doubts stem from our appreciation of the distinction between the fading petty-bourgeois “middle class” and the now more common corporate- professional “middle class.” Citizens, politicians, and scholars alike too rarely distinguish what they really mean by the term, but as Flora, Flora, Spears, and Swanson (1992) have suggested, the interests and commitments of these two sorts of “middle classes” are very, very different. In rural places, in particular, it seems that a devotion to place might linger a bit longer even among local-origin inductees to the more corporate-leaning professional middle class (e.g., teachers). This issue cannot be addressed adequately in this study, but readers should be aware of its salience. Perhaps in most of these towns, both the necessary material conditions and the sufficient professional interest co-existed. The case of Magnolia, however, would seem to demonstrate that being largely “middle class” is not actually a necessary condition but only a helpful one. Whether or not a corporate-professional middle class is unhelpful must await other studies, but the negative influence of corporate orientation is actually well known from a half-century of study in agriculture (e.g., Goldschmidt, 1947; Green, 1985; Lyson, Torres, & Welsh, 2001).
26With 67% of households reporting incomes less than $25,000, only Magnolia might be judged “impoverished.” On their visit to Magnolia, the lead authors drove through the surrounding countryside and around
the town of Magnolia on several occasions. The town and the local countryside could be described as much healthier than many rural towns in the remote and not-so-remote parts of Appalachia with which the lead authors are familiar.
SITES 1 :: Magnolia, 2 :: Green Mountain, 3 :: Lafayette, 4 :: South Valley, 5 :: Merriweather-Lewis, 6 :: Confluence, 7 :: Eastcove
1 2 3 4 5 6 7 80% 67% 20% 5% 26% 36% 16% 44% 34% 9% 41% 32% 9% 34% 36% 14% 36% 43% 7% 34% 36% 11% 70% 60% 50% 40% 30% 20% 10% 0%
FIGURE5 //Household Income Distribution Across All Sites
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