RME v2n2 5-19-2003
FEATURE
Research Initiative: On Things Rural and Mathematical In this article, our Research Initiative is featured.
“Rural Mathematics Education” is not a field that many people in mathematics education are talking about, studying, or for that matter, doing a great deal of in US schools. That, in a nutshell, is one important reason why ACCLAIM’s Research Initiative exists: to theorize (that is, develop ideas), to study (test ideas by looking at reality), and to develop knowledge of rural, place-based mathematics education.
Lack of knowledge and interest. Lack of knowledge and lack of interest are symptoms that research is necessary. Lack of knowledge is an understandable symptom of the need for study, of course. Lack of interest, however, is more difficult to understand as a symptom that research is needed. Generally, people think that a high level of interest -- “hot topics” or “priority issues” – indicates the need for research. How can a low level of interest indicate such a need? Lack of interest, in this case, needs to be balanced with the understanding that 25 percent of the nation’s population lives beyond the pale of
suburban areas and cities. Lack of interest in this large population is not defensible; instead, lack of interest marks the need to study mathematics education in rural places. (See Edward Silver’s recent editorial in the Journal of Research in Mathematics
Education for an authoritative confirmation of this view.)
Framework as a statement of key ideas across the Center – key ideas for not only the
Research Initiative, but also for the Capacity-Building, Teacher Education, and
Professional Development Initiatives. The Framework is a work in progress, however, and it will change somewhat as the Center develops its ideas and commitments further.
The Research Initiative, then, actually helps to coordinate the various activities, events, and works of the Center. For instance, our staff advises and sponsors a variety of
investigations and discussions (including research symposia and other meetings) that deal with collecting and analyzing data, or that bring people together to talk about and develop unfamiliar or difficult ideas. One example of addressing unfamiliar and difficult ideas is publication of 10 papers from the first ACCLAIM Research Symposium, held at
Ravenwood Castle in very rural Vinton County, Ohio, last November. The papers develop differing perspectives on the ideas, strategies, and tactic to be taken in studying “rural mathematics education.” Notably, the project of rural mathematics education is interdisciplinary, and one of the papers discusses this situation in detail.
Core function. Facilitating scholarship is probably the core function of the Research Initiative. To this end, we encourage research (data-based studies) and theory (think pieces) in many ways.
• We support ongoing studies with funds limited to non-salary research expenses (within and outside ACCLAIM).
• Staff of the Research Initiative engage directly in their own scholarship (both theoretical and empirical) of topics relevant to rural mathematics education.
• Our Research Clearinghouse serves as the Adjunct ERIC Clearinghouse on Rural Mathematics Education through our association with the ERIC Clearinghouse on Rural Education and Small Schools. The Clearinghouse offers all ACCLAIM papers and a wide variety of other resources available, free, worldwide, to anyone interested in rural mathematics education.
• A special section of our website also provides counsel and resources especially to scholars interested in working on research projects with ACCLAIM. We have, for instance, assessed the dissertation literature related to rural mathematics education.
We invite everyone with an interest in ideas about rural mathematics education and in studying data about rural mathematics education to contact any of the following staff members about opportunities to work with the Research Initiative:
• Jim Schultz (740-593-4430) or Craig Howley (740-593-9869), co-directors of the Research Initiative. Jim is Morton Chair of Mathematics Education, and Craig is an Adjunct Professor in the Educational Studies Department.
RURAL DEVELOPMENT
Rural Outmigration, Mathematics Education, and Project HOPE Rural communities tackle youth outmigration
One of the biggest challenges to rural communities is that young people leave as they complete their schooling. This outmigration means that rural communities are not just robbed of their most-schooled residents, but they are robbed of the young families that give them a future. When schools are closed in rural communities, the blow is awful; but when rural schools function to encourage outmigration, they contribute to cultural and economic anemia. Rural community people usually know this is happening: part of the cultural anemia caused by outmigration, in fact, is that communities become alienated from the schools that are supposed to serve them, but instead function to subvert rural communities.
Outmigration and mathematics education. What’s the connection to mathematics education? First, doing well in mathematics correlates with doing well in school, and doing well in school correlates with migration out of rural areas. Second, the
Does rural schooling have to act like an extraction industry? Many people working in rural economic development and in rural education don’t think so. They see alternatives in community-based development activities. This sort of community development is different from lots of government-sponsored efforts because it is rooted in local circumstances and issues — and is powered by local people.
One such effort is the Center for Rural Affairs’ Project Hope. Established in 1973,the Center for Rural Affairs is a private non-profit organization working to strengthen small businesses, family farms and ranches, and rural communities. The Center sponsors avariety of programs that address addressing social, economic, and environmental issues. One such program sponsored by the center is Project HOPE (Hope and Opportunity for People and the Environment).
Project Hope. The project’s purpose is to create new markets, greater income and new leadership opportunities for rural communities. Rural communities face crises of population loss, infrastructure decline, economic erosion, and lack of leadership.
assistance for business owners, those forming cooperatives, and those practicing alternative agricultural production, leadership and advocacy training. Six communities benefit from the project: they and their residents gain access to needed resources, learn to lead others, help to have a direct influence in policy, start creative and innovative
community projects, develop a vision for the community, start new ventures within the community, and build support for the area and community.
Residents of these communities want stability, family farms, small businesses, and local schools. Leadership development and community participation in community projects keep these issues in the forefront as top priority, achievable goals.
According to one community member: “In the beginning, my goal was to work to
improve the economic development in the area so that young people will have a reason to stay here and to return if they have left. Our children should be able to live and raise their own families in the environment in which they themselves were raised.” Leadership and policy training help community members realize this common (and commonly neglected) aspiration of rural communities. Educational issues are at the forefront of rural
community-based development efforts like Project Hope.
The Glass Wall: Why Mathematics Can Seem Difficult ( Frank Smith)
Reviewed by Craig Howley and Melissa Gholson (RME Editor)
The Glass Wall is an accessible book about the problems so many people have with mathematics. It’s not about “math phobia,” however. It’s about the nature of mathematical thinking—what’s similar to thinking with words, and what’s different. Howley and Gholson provide two somewhat different perspectives.
Howley
Frank Smith is well known for his works on the various manifestations of language: reading, writing, and thinking, in roughly that order over the span of his career. Smith was originally a reporter, and so, unlike most academics he can actually write as if he wants to be read. It came as a pleasant surprise that he’d written something on mathematics. And it roused my curiosity.
The intended audience seems to be precisely those people who think they understand language (conversation, stories, novels, histories, and poems) but to whom mathematics does seem difficult. What’s the rural angle here? There is a rural angle, but it’s not
One place to begin the unpacking is with my own colleagues in rural education. Most of them probably belong to the intended audience for this book, and that’s why I’ve wanted to review it. Rural context is a realm of meanings, and it’s not especially useful as an analytic category or a locale variable in a quantitative study. Many of us (in rural education) recognize this fact, and that recognition underscores the important role of qualitative research, and of language in rural education work.
There is much here that might be news to some teachers of mathematics, but not, I think to many mathematics educators, with whom Smith, as a dyed-in-the-wool
“constructivist,” is clearly a fellow-traveler. That is, Smith takes understanding (not just skill development) as the aim of learning. The role of understanding as the main game also indicates the critical need to understand the means and end of education. In other words, if you don’t understand (and debate) the proper aims of education, you won’t be able to put understanding at the center of learning.
That position has always made sense to me as well, though strictly speaking I don’t identify myself as “a constructivist.” Maybe Smith wouldn’t either; his writing is remarkably free of both jargon and in-your-face ideology (political, curricular, or sociological).
Reading, writing, thinking, and mathematics – this might be a logical progression not only in the author’s career, but in understanding as well, and, in particular, the
language. For Smith’s main point is that for mathematics not to seem so difficult, a person needs to understand that mathematics is mostly self-referential. To put this in language as simple as Smith’s own: the meanings of mathematics proceeds from discovery of relationships among numbers. People who like mathematics, I suspect, understand this quality very, very well. For such people, numerical relationships are a rich fountain of meanings. This means (quite simply) that mathematics is not inherently boring – for that, we need schools (and impoverished versions of teaching).
Smith is insistent: numbers are not quantities of objects. “What is it about numbers that makes them numbers independently of any use to which they might be put? The answer is that numbers are relationships. Relationships with what? With other numbers.... Numbers don’t get their meaning from anything except each other” (p. 37). For mathematicians and mathematics educators, this statement might be contestable in various ways, but it would nonetheless seem obvious, perhaps shallow. I believe, however, that it is a profound insight, and one that I can remember discovering quite clearly in moving (about the age of 12) from arithmetic to algebra. It’s summed up by the idea that a number can be written in many ways – and this, I think, was a principle articulated at some length in my algebra text (new math) circa 1962. It was a memorable idea.
instance, or acing all tests) hardly ever leads to understanding. Nearly everywhere, mathematics is taught not only as if it were disconnected from the “real world,” but it’s taught to intimidate, confuse, or bore. Much of this result is not intentional on the part of teachers or administrators, but has to do with the culture of schooling in general, and the special honor reserved for mathematical talent as the special domain of “really smart” kids. Baloney!
So much of schooling (and this is a battle for caring and concerned teachers) is about reproducing the inequities of the real world. These prevalent inequities reinforce each other, and schooling is part of the system of reinforcement. Poverty, for instance, correlates with low achievement. It also correlates with poor school funding, the assignment of teachers, and the nature of curriculum, and the quality of teaching. Again: in some (too many) situations, mathematics actually is taught to intimidate, confuse, or bore children, and this instructional regimen is a particularly vicious turn of the screw for poor children. This sort of mathematics instruction is not good, in fact, for anyone. One of the commitments of the NCTM Principles and Standards—and of many members of the organization for several decades—is that everyone can learn
mathematics. The public should not abandon the knowledge of mathematics to “really smart” kids. Those kids grow—they are us. A mathematically ignorant nation will quickly have its democratic aspirations surgically removed (by really smart kids who have been schooled to greed rather than justice). Why? questions of economics, politics, and equity cannot be adequately understood without, say, a real facility with ratio
Mathematics can be taught with equity prominently in mind. And this is precisely where the rural connection with Smith’s ideas comes in. Equity implements a concern for students’ lives – their actual circumstances outside of school. Those circumstances for rural kids are hardly ever understood, honored, or cultivated by the institution of schooling, and this is arguably more true in mathematics than in other subjects. The argument is that math teaching is about skills and not about understanding.
Skills are cultivated not principally for the benefit of the one who might (with luck, in some school settings) become skilled, but for future purchasers of skilled labor. In the culture of schooling, these purchasers are almost always imagined as remote national or transnational corporations. The watchword for these purposes is “competitive workforce development.” That is, national economic purposes displace rural purposes (including the accrual of benefits to local rural economies, instead of mostly to national and transnational corporate structures).
and bore students so that they will not raise politically inconvenient objections or occupy places in the economy normally taken by kids from affluent circumstances (aka “really smart” kids). The barriers confronting this sort of education are very high.
There are nonetheless some examples of this vision. Jerry Lipka and colleagues at the University of Alaska in Fairbanks have created supplementary instructional materials based on Yupik cultural practices. Eric Gutstein has described his teaching of
mathematics for social justice in a recent series of articles in the Journal of Research in Mathematics Education.
Gholson
Smith argues that two different worlds exist: the physical world (a familiar world of objects and events) and the world of mathematics (a completely different domain of experience). These two worlds are separated by a glass wall, which exists because the language used to talk about them is not the same; many people find themselves on the outside looking in. This analogy plausibly explains why math is difficult for so many people. Yet while the recognition and acknowledgement that a wall exists between these two worlds is refreshing, it seems to take a very simplistic view of a much more complex problem.
world, but from something in our mind, and from the world of mathematics that minds have created”(p. 35). Smith says, and I agree, that when the learner begins to construct in the mind this mathematical world, he or she either develops mathematically or else becomes walled off from mathematical understanding. This wall goes unchallenged and unrecognized by the mathematically wise inside it and the mathematically challenged outside. Smith effectively brings this dilemma to light.
Smith identifies four essential conditions that, if they prevail, would allow anyone to learn, understand, and enjoy mathematics: Educators must present mathematics in an interesting and comprehensible manner; learners must approach mathematics without fear; and both must allow adequate time. Here Smith is too simplistic. The reality is that, for many reasons, many students find math neither interesting nor comprehensible. Language barriers, a lack of attention to details, poor pedagogy, and a wide array of other variables all can lead students to learn errors. An emphasis on teaching “technique
Even many educators accept the notion that fear, stress, or inadequacy in math are natural and inevitable, perpetuating the myth that mathematics is attainable for some but not all. Smith argues that all learners are capable of truly understanding mathematics (p.134). Under circumstances that allow individualized instruction tailored to each learner – certainly the best practice in an ideal world – Smith is no doubt correct. In our current educational environment, with its focus on state standards, pedagogy and curriculum, Smith’s ideals seem far out of reach. Until our educational system comes to focus on the learner, to set as it goals comprehension and understanding, and to allow sufficient time for students to achieve those goals, the glass wall will will persist as a barrier to
mathematical achievement for many.
RESOURCE REVIEW National Rural Educators Association ( NREA) A National Voice for Children in Rural Schools
The National Rural Education Association is the oldest established national organization of rural school administrators, teachers, board members, parents, regional service agency personnel, researchers, and business and industry representatives. NREA seeks to provide services to enhance educational opportunities for rural schools and their
communities. The NREA is an open membership organization. The Rural Educator is a nationally recognized publication from the NREA that features timely and informative articles written by leading rural educators. The NREA promotes research in to rural education and provides a wide variety of awards and grants. The organization is actively involved in legislation at the federal level. The NREA opposes mandatory school
consolidation. It also supports suspension of No Child Left Behind unless and until it is changed and adequately funded so rural districts can comply with it. For more
information go to www.nrea.net. The NREA is currently seeking a permanent editor for its primary journal and is calling for proposals for hosting the editorial functions of The Rural Educator. If you are interested, contact Dr. Bob Mooneyham, Executive Director: [email protected]. The NREA invites membership and announces the 95th Annual NREA Conference to be held October 22-25, 2003 in Kearney, Nebraska. This year’s topic: “Rural Education: Meeting the Challenges of NCLB.”
US Department of Education proposes abolishing small schools clearinghouse
Washington, DC. April 11. The U.S. Department of Education has announced its attention to eliminate the ERIC Clearinghouse on Rural Education and Small Schools (ERIC/CRESS). The elimination is part of the Department’s plans to restructure the national ERIC system. All 16 ERIC clearinghouses would be closed.
The restructuring would eliminate t immensely popular ERIC publications like ERIC Digests – developed for parents, teachers, and administrators. It would also end the free online question-answering service called AskERIC, used each year by millions of people across the nation.
The change would predictably make it more difficult for rural voices to be heard, not only by policymakers and administrators but by one another. ERIC/CRESS helps rural educators stay in touch with one another.
To see what will be lost, consult the ERIC/CRESS homepage. It, and its content, would disappear; worse, the development of similar new materials would cease as well. There are implications for ACCLAIM, as well, since ACCLAIM operates the Adjunct ERIC Clearinghouse on Rural Mathematics Education.
Troublesome as the implications for rural education and ACCLAIM may be, it will likely be worse for American Indian education, which is covered by ERIC/CRESS. The reason is that the applicable law (NCLB) does not specifically include Indian education as part of ERIC. The draft procedures are available online.
Suggested links . . .
Center for Rural Entrepreneurship
The Center for Rural Entrepreneurship is a Rural Policy Research Institute. Its goal is to stimulate and support private and public entrepreneurship development in communities throughout rural America. The center is committed to generating expanded information about rural landscapes, people, communities, economies, and issues. It produces
monographs focusing on federal, state and community policy, policy maker briefings, and organizes jurisdictional groups. The website is dedicated to sharing research, work and policy information. Website: www.ruraleship.org
Organizations Concerned about Rural Education
Organizations Concerned About Rural education (OCRE) is a coalition of more than two dozen organizations dedicated to improving public education and economic development in rural America. The website offers news and contact information, resources, and a “take action” toolkit. Website: http://www.ruralschools.org
The Handbook of Mathematical Discourse
This online handbook available for download ( 200 pages) is a compilation of
mathematical education. Discussion groups, mailing lists, papers, links to authors’ websites and other sites of interest are available. Website:
www.cwra.edu/artsci/math/wells/pub/aboutbk.html
Publication Opportunities . . .
ACCLAIM sponsors a Working Paper Series for works-in progress that are relevant to its mission. We welcome distinctive and non-trendy research reports or thoughtful essays that are “all your own.” Contact Craig Howley at [email protected] for more
information on submitting a working paper.
UPCOMING EVENTS National & Regional
June 19-21, 2003 Louisville, KY NCTM Affiliate Leaders Conference www.nctm.org
July 13-16, 2003, Park City, Utah
AASA 2002 Small Rural Schools System Leaders Conference American Association of School Administrators
Promoting Leadership in Rural America www.aasa.org
July 7-25, 2003, Lexington, KY ACCLAIM Leadership Institute
http://www.acclaim-math.org/leadinfo.shtml
International
June 22-27, 2003, Inverness, Scotland International Rural Network Conference
Taking Charge: Rural Community Empowerment
in Rural Development, Rural Health and Rural Education http://www.takingcharge.co.uk
July 27-30, 2002, Montreal, Canada Rural Sociological Society
HERE’S WHAT’S HAPPENING IN OUR NECK OF THE WOODS Capacity Building Initiative
By Vena Long, University of Tennessee ACCLAIM well represented at national meeting
The Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics was well represented at the annual meeting of the National Council of Teachers of Mathematics in San Antonio April 7-12. ACCLAIM doctoral students Julianna Gregory, Craig Green, Brenda Lackey, Brian Boyd, Karla Willis, Christie Perry, Frank Edge and Crystal Rice assisted ACCLAIM professors at the Research Pre-session, a reception for potential doctoral students, a session during the regular conference, and an ACCLAIM breakfast on Friday morning.
Members of the cohort anxiously await their second summer in residence to begin June 29 in Lexington, KY. Along with nine hours of coursework, cohort members will participate in a conference with mentors and in a research conference with doctoral faculty and other graduate students from all participating institutions.
A Masters level course in mathematics entitled “Elementary Analysis” is being offered in June at Marshall University in Huntington, WV.Other masters’ level coursework will begin in the fall.
Professional Development Initiative
Submission by Stephen Henderson, ARSI Program Improvement Review
Using the Mathematics Program Improvement Review for Planning and Evaluation Ron Pelfrey, ACCLAIM Program Improvement Review Coordinator
April 25, 2003
One inherent difficulty in managing a multi-state project is coordinating the planning and evaluation of the various school entities. Each school project needs the autonomy to be able to make its own decisions based upon its individual needs and demographic factors such as size of staff, central office support, existing curriculum documents, type of state assessments, etc. ACCLAIM has chosen the “Mathematics Program Improvement Review (PIR)” as the major process by which mathematics program needs are identified and as a tool to guide program improvement planning.
The mathematics PIR uses a team of mathematics educators to conduct an intensive analysis of the entire mathematics program. The process includes a preliminary
review of the various documents pertaining to the program, such as the curriculum, lesson plans, recent classroom tests, state assessment results in mathematics, and
inventories or bibliographies of library resources: math-related books, videos, periodicals, and inventories of software used by mathematics teachers. On a site visit, the team members observe instruction led by each of the school’s mathematics teachers and
interview the mathematics teachers, the school principal, a random group of students, and a randomly selected group of parents.
The team leader compiles the accumulated data and produces a report based upon ten standards of best practice and the indicators for these standards: curriculum, instruction, equity and diversity, school climate, usefulness (or applicability), professional
environment (including professional development training), community (including parental involvement), organization and leadership, and continuing assessment and redesign. The report includes a 5-point scoring guide on the indicators for each of these standards.
Recommendations and suggested resources are provided for possible use by the school staff as they plan how they will implement improvements with ACCLAIM support. It is suggested that the staff focus on no more than one or two of the recommendations so that change can be realized within the ACCLAIM time constraints.
Schools that have used the PIR for planning have found it very useful. For example, Lincoln County Middle School in Stanford, Kentucky, initially used the report to brainstorm ideas for emphasis and identified instruction as the key focus standard. The teachers’ first efforts were to purchase Geometer’s Sketchpad, train the teachers on how to use it as an investigatory tool, and integrate it into the geometry instruction in both 7th and 8th grades. As an ACCLAIM Professional Development Team site, Lincoln County has also formed a Leadership Team, which identified estimation as an area of focus within the curriculum and has begun improving instruction in this area.
A new ACCLAIM Professional Development Team school, T. A. Dugger Middle School in Elizabethton, Tennessee, has just completed a PIR. School employees report that the review provided a forum for teachers to discuss in a non-threatening way what they do in their classrooms. The mathematics teachers also report that the PIR findings have
helped the school focus professional development and mathematics education at the school.
For more information regarding the Mathematics Program Improvement Review process, contact Stephen Henderson at [email protected].
Teacher Education Initiative
The first ACCLAIM preservice mathematics teacher conference planned and hosted by the Teacher Education Initiative was held in Huntington, WV on February 21-22, 2003. Comments volunteered by participants and taken from the conference evaluations
indicate that Mathematics Teachers in Appalachia - Future and Present was a resounding success.
The 147 individuals who attended the conference began arriving at the Radisson Hotel at 3:30 PM on Friday to complete the conference registration process. By 5:00 PM shuttles and vans began to move all the participants to the Don Morris Room of the Memorial Student Center on Marshall University's campus for dinner. Karen Mitchell and Thomas Klein welcomed participants.
The primary goal of the conference was to offer the middle and high school mathematics teacher candidates who attended insights into the profession they are preparing to join. All participants were given a table assignment that made it possible for them to have conversations during dinner with preservice mathematics teachers and faculty from other institutions and with mathematics teachers already working at the middle or high school level. After dinner Karen Karp detailed the benefits of being a member of the National Council of Teachers of Mathematics. Following Dr. Karp's presentation, a panel of practicing mathematics teachers who have been recognized for teaching ability answered questions posed by the conference participants. The panel members’ answers were so inspiring that the panel discussion was the best received part of the conference.
On Saturday morning after breakfast at the hotel, participants returned to Marshall University to be welcomed to campus by university president Dan Angel. Four 90-minute concurrent sessions and related 60-90-minute follow-up discussions were conducted in the morning and then repeated in the afternoon after lunch, together with a fifth session and discussion. Participants were able to attend two of the five sessions. Participants were given notes for all sessions, including the ones they did not attend, to encourage conversations among participants from the same institution.
follow-up, Linda K. Griffith provided the participants with examples of different assessment instruments and strategies and their uses and strengths. Thomas Klein concluded the conference with some remarks and a drawing for prizes.
The Teacher Education Initiative is currently preparing for Mathematics Teacher Preparation in Appalachia - Mathematics Content. This conference is designed for college and university faculty who are involved with secondary mathematics teacher preparation. It will be held on August 8-9, 2003 in Huntington, WV. The overarching goal of this conference is to examine the national, regional, state, and local pressures and influences on the mathematics content of mathematics teacher preparation programs in the Appalachian regions of West Virginia, Ohio, Kentucky, and Tennessee.
WHAT TO LOOK FOR
In our next edition, we feature research projects and an article on the Yupik Math project, a review of Stigler and Hiebert’s The Teaching Gap, and an dialogue around a question from an RME reader in Arizona.
