Data Analysis
43model used in vocational programs across the U.S Because such programs
often emphasize career development and life adjustment, thereby preparing students to participate in the local workforce, they often incorporate learning experiences that entail authentic engagement with community businesses. One example of how this approach was used in the Collaborative involved the instruction of the Industrial Technology students in the operation of a computer-controlled lathe similar to one used in a local manufacturing company. The purpose of the training was, ostensibly, to prepare students for work in that company, but the schools were preparing many more students than were likely to be needed as local lathe operators. Interestingly, however, the teacher reported that the mathematical principles needed for understanding this complex equipment were not, in fact, “lower level.” Another example of meaningful place-based math instruction with a vocational focus also came from the Industrial Technology class. The teacher, who had been teaching a unit on mass production for 25 years, involved his students in the manufacture of signs for local businesses and government agencies:
What we do is we bring the business community into it. I have business people come and give talks about how to issue stock, and Mr. P. can show you the stock that we issue. We issue stock … we produce the product, and then we manufacture the product, and we have an open house, and we sell it, and the kids reap their money after their expenses, and get their money back. So, this is one of the few classes where a student can walk out a class with 25 bucks in their pocket. (Industrial Tech Teacher)
The entrepreneurship program at Roosevelt High School also benefitted from an inventive teacher with a long-term commitment to local enterprise. This teacher had recently helped students establish an EBay business that served local community members who wanted to sell items but did not want to handle the transactions themselves. The start-up of a new community-based effort during a period in which the Roosevelt district was facing increasing threats to its existence attests to both the dedication of the teacher and the generative quality of this instructional approach. As the teacher noted,
It’s been a very good experience. We’ve had a few stumbles along the way, but since this is our first year, next year should run a whole lot smoother. But … it’s very good for us and for the school to be out and in the community.
Through the auspices of the business education program, some students also participated in “co-op” arrangements, working in local companies in order to prepare for the transition between school and the workplace. In addition to these initiatives, the teacher invited members of the community to come into the class on a regular basis, in part to convince students that academic study was relevant to career preparation:
We have the community members come in, and when they’re talking about their business and how important education is, and especially basic education…so, mathematics is a function that they need to leave the school with, that they have to be well-versed and well-prepared. (Roosevelt Business Teacher)
Whereas the vocational teachers recognized that place-based activities contributed to instruction in applied mathematics, some of the teachers of college-preparatory classes did not credit these activities as legitimate parts of the mathematics curriculum, despite the complexity of the math used. These teachers saw mathematics instruction, particularly in upper-level classes, as abstract and theoretical, with little need to make connections to local places or to community issues. As one such teacher remarked,
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…. Probability-are we really going to put that in a place? The only way that’s going to happen is through some sort of block scheduling. I’m not sure that the upper math classes (maybe [students from] a lower-income average are going to need that), but my upper math classes—I don’t know that they’d benefit a whole lot (Springfield-Elm HS Math Teacher) Some teachers had similar things to say about instruction in other academic subjects. The following quote, for example, contrasts a science class in the “general” track with the chemistry class in the “college-preparatory” track:
It’s actually called, “Community Chemistry.” I feel it’s more a community science…just because of the curriculum that we have. It’s more of a general class than a specific chemistry class. Usually, [it’s for] the students who didn’t want to be in chemistry. We’re throwing in a little bit of chemistry with environmental and, just, some good science review in the 11th grade year is basically what it is. (Springfield Elm-Roosevelt HS Science Teacher)
The generative possibilities of place- and community-based math. In contrast to the elitist sentiments of some high school teachers, most students and school-level administrators saw value in a more inclusive and practical approach to mathematics instruction. As one of the high school principals reported,
I do think we do math across the curriculum … we offer a program called Electric Power Car competitions, where the kids do a lot of math. When we started a few years ago with the electric car process, and kids really had to get into the math, because they had to draw their plans up, for this electric car. They had to build it from scratch, that’s all electric- powered from batteries, and they had to know how much it would pull—how many amps it would pull for how long…. And, so, when they got into the math part, I think they started to enjoy that…. They saw the value of the math, where some kids [say] (and you’ve heard it before too) “where will I ever use this?” …. And, I do know that in our sciences, of course, we have a lot of math in science. (Roosevelt HS Principal) Students across the curriculum tracks not only appreciated large-scale projects that enabled them to learn and apply math, they also enjoyed instruction in which teachers used authentic examples to illustrate math concepts. Describing one of the math teachers, a student commented,
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Well, she is so math-y. She relates everything to math in her life. So, then, she’ll always get these little stories, like, she was grocery shopping, and she thought of this, or something. And, so, each day, basically, she has something that relates to our lesson that she thought of, or something. (Springfield-Elm 11th and 12th grade Focus Group)
The schools also used service-learning projects as a way to link academic instruction to the needs of the local communities. Participants described various such initiatives in which students learned mathematics through their participation in construction projects:
We’re just building a shed. It’s like an 8-by-10 shed, and I figured the angle for the rafters and everything like that. So, that was a lot of math, I guess, related to…something that would be part of the community, I suppose. (Springfield HS 11th and 12th Student Forum)
They’ve built some things for the city, along the walking trail. And, like I said, they built some garages. We usually build two or three sheds a year, where people will come in and say, you know, “I’d like a garden shed for my backyard,” or something. So, we go out and see, ok, “How big is your backyard; what dimensions do you think you’d like this?” And, then, we come back and some of our math kids will sit down and start plotting, drawing it out. The kids really enjoy that hands-on, get out of the building. (Springfield-Elm HS Principal)
Science classes also gave students the chance to learn mathematics through engagement with place and community. At Springfield-Elm High School, the science program had a research focus, which provided learning experiences that were both technologically sophisticated and attentive to local issues. Testing water quality, for example, was one way that students could connect realities of large-scale agriculture to significant environmental concerns.
I have some … probes that people will stick into a solution that helps them visualize the type of mathematics that’s possible on a local basis. Like, we test for nitrates in the water or things like that. And, you can look with your eye-it looks like an iced tea solution, so you can sort of see a spectrum of how many parts per million might be in something. And, you can actually, physically, guess close and then you put it in an instrument and it will shoot this beam of light through it, and tell you what amount of light is actually going through the material, compared to a standard. And, that’s all that those machines (spectrophotometers) are, which is really a big link between math and science, because it shows you how the probe can fit into that, to tell a mathematical reading. So, there’s math in both—and math in all kinds of things. (Springfield HS Science Teacher)
Whereas in the higher grades educators saw community as the context for connecting students with vocations and as a way to increase curricular relevance, at the elementary level, educators treated the community as an affective touchstone, sometimes in the superficial ways described above, but sometimes in deeper and more generative ways. Because each community served as a source of support and meaning for its residents, it lent emotional force to what the school was trying to accomplish. In the following quote, for
example, a math teacher from one of the middle schools revealed her belief that connection with the community would increase students’ appreciation for mathematics as a subject:
But, it is important that we try to build a relationship between the community with math as a subject…. They built a new pool, and so I took the grades 3 through 8, but we studied perimeter and area and volume, and did those. We measured the new pool and so on, and so forth…. We studied stuff in math at a community place, you know, if that makes sense. (Roosevelt MS Math Teacher)
A math teacher from a middle school in one of the other communities also shared the view that grounding in the familiar—students’ homes and places of residence—would help them see math as a purposeful part of daily life:
We’ll talk about the carpenters in town or the computer place, or the local businesses, that way. And, they’re able to connect to those people because they know those people. Or, they’ll bring in their own parents’ positions, and maybe reflect, “My dad’s a business owner. What does he do? What does he do mathematically?” (Springfield-Elm MS Math Teacher)
Using problems and examples with local relevance was, in fact, something that math teachers at all grade levels tried to do. The math teacher at Pioneer and Homestead, for instance, reported, “When I think about instruction, especially story problems, I like to include something, for instance, agriculture. For instance, if we’re doing mixture problems, possibly relate it to herbicide or something like that.”
Students also were quick to point out their awareness of ways in which mathematics fit with important activities in the community. For some, knowledge about how mathematics was used in the community was grounded in the experience of farming, as the following quote illustrates.
My dad—he put up a new hog unit, and so he was just going over… the money you need to do this stuff, and actually, kind of, the money he brings in, he kind of went over with me about that. And, you don’t really expect that math to be that complicated with a simple hog farm, but it’s more complicated, I think, than people think it is. (Roosevelt HS Student Focus Group)
Other students talked about the math used in various jobs in the community, such as carpentry and the operation of a small business. Some, like the student quoted below, reported about how they had used math in the work required by a summer job or on the family farm.
And, this summer I worked at a trailer manufacturing place, building trailers, so it was huge. Everything’s got to be perfect angles, and everything’s got to match up and be symmetric So, I use it a lot. (Roosevelt HS Student Focus Group)
The parents who were interviewed also expressed the hope that the schools would provide math instruction that showed explicit linkages between academic subject matter and valued community enterprises, particularly farming:
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Well, I’d like to see them [i.e., the teachers]—this is coming from the farm aspect. You know, you have to figure how much chemical to fertilizer and all that. And, my son uses it all the time. I mean, sometimes you want to change the ratio. So sometimes maybe if they would … throw in just a section on figuring—using your math ability to formulate…. Or, sometimes you have to, I mean, teach them how to measure out an acre of farmland, or something, you know, since we are an agricultural community, and if the kids stay around here… (Springfield Parent #1) As the discussion has thus far showed, a number of teachers were dedicated to place- and community-based education and found inventive ways to use it to teach math as well as other subjects. For at least one of these teachers—a teacher who had recently assumed responsibility for educating not only elementary, but also middle school students—connecting math to community life supported the complicated task of teaching math to students at several grade levels.
While appreciating the benefits of place- and community-based methods of instruction, teachers nevertheless recognized that challenges facing the Collaborative sometimes functioned as impediments to the use of such methods. In particular, budgetary constraints and increasing standardization limited the extent to which teachers were able to use these forms of pedagogy. As the math teacher at one of the middle schools noted, “If we could get past (I hate to say it) the standards and that kind of thing, we could…connect math to the real world.” Despite the difficulties, the teachers who were committed to this approach found creative ways to work around the impediments. One science teacher—the same teacher who ran the science research program—had obtained a bus driver’s license, for example. Having the license meant that he no longer needed to forgo field trips but could drive his students to locations in the community where they could test water quality.
The shrinking place for place-based education. Perhaps the word “distance” and the word “place” are, in important ways, opposed. Yet both distance education and place-based education were occurring within the Collaborative at a time when enrollment losses and funding problems seemed to be requiring the former approach to take priority over the latter. As the discussion above showed, parents and administrators preferred any approach—even one where place- and community-based education might be sacrificed—that would allow each community to retain its schools. Their stance resulted not from the belief that distance education is a better pedagogical method than place- or community-based education, but from the strong conviction that survival of the communities was an important aim of schooling in the Collaborative.
Unlike parents and school-level administrators, the superintendent seemed to see the demise of the communities as inevitable, and his comments about the primary aim of schooling—to prepare students for high-paying jobs, most likely jobs beyond the borders of the four communities—motivated his emphasis on educational quality. In his mind, distance education and place- based education could co-exist because both contributed to the academic— and eventual career—achievement of students.
Teachers, by contrast, saw the two approaches as ultimately incompatible. For teachers, the instructional roles required under the two approaches were so significantly different that the (perhaps preferred) option of exposing all students to both approaches seemed already to be out of reach. At the time of the study, the Collaborative appeared to be working out the contradictions in two ways. First, administrators were asking teachers to take on different roles, some of which entailed extensive involvement with distance education and some of which permitted on-going engagement with place- and community-based initiatives. Second, particularly at the high schools, distinctions in curriculum tracks guided the allocation of instructional methods. Distance education, which allowed for the provision of advanced