RMEv10n1

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Rural Math Educator

March 2011 Volume 10, Number 1

Sandi R. Mills, Wingate University, Editor 2010-2011

DISCLAIMER. The Rural Mathematics Educator LVSURGXFHGDW2KLR8QLYHUVLW\¶V College of Education and published electronically. The expressions contained in this publication are those of the authors;; these expressions do not necessarily represent the positions or opinions of Ohio University, the College of Education, or anyone else. Postal Address: 207 McCracken Hall, Ohio

PUBLICATION OPPORTUNITIES. Would we be interested in your work?

³<HV´LIWKHZRUGVrural and

mathematics appear often in your manuscript. We welcome distinctive and

non-trendy scholarship. Empirical work (quantitative or qualitative) is a priority, but we will consider theoretical pieces, historical research or biography, and very

ACCLAIM is funded by the National Science Foundation as a Center for Learning and Teaching. The Center is a partnership of the Ken- tucky Science and Technology Corporation (Lexington), Ohio Univer- sity (Athens), the University of Kentucky (Lexington), the University of Louisville (Louisville), the University of Tennessee (Knoxville), and West Virginia University (Morgantown).

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Perceptions and Implementations: A Summary

Sue Nichols

Perception and Implementation of the Ohio Academic Content and Process Standards for Mathematics among Middle School Mathematics Teachers is a dissertation describing the find- LQJVRIDTXDOLWDWLYHVWXG\WRH[DPLQHWKHGLVFRQQHFWEHWZHHQWHDFKHUV¶HVSRXVHGEHOLHIVDERXW

standards-based instruction and classroom practice. The research study consisted of data ob- tained from classroom observations, interviews, and examination of lesson plans, assessments, and classroom materials. Having spent at least thirteen days in each of the twelve classrooms, the data collected provided a consistent and reliable picture of classroom practice for each of the participating teachers. The teachers participating in the study were all middle school mathematics teachers.

Themes

Using a grounded theory methodology, two themes were developed through analysis of the data collected. The first theme was Perception ZKLFK³GHVFULEHVKRZWHDFKHUVSURFHVVDQG DVVLPLODWHWKHIDFWRUVDIIHFWLQJWKHLUUROHDQGUHVSRQVLELOLWLHVDVDPDWKHPDWLFVWHDFKHU´1LFKROV

2010, p. 128) This theme was categorized into three descriptors of perception: (1) compliance, (2) resistance, and (3) performance.

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mathematics. The importance of the Standards is rooted in state mandated achievement tests, and DWHDFKHU¶VHIIHFWLYHQHVVLVGHWHUPLQHGE\WKHVFRUHVRIVWXGHQWVRQWKRVHWHVWV0RVWRIWKHSODQ

ning and classroom practice of teachers who value compliance is carried out with the express purpose of preparing students to pass the achievement test. The test is a part of everyday classroom discourse. Previously released test materials are used to practice for the test and are often the focus of classroom instruction. Compliance-minded teachers establish their feelings of self- efficacy in student test scores. This seems to be exacerbated by administrators who work with these teachers. Teachers who adopt a perception of compliance are doing what is expected of them because it is their job.

Another descriptor of perception is resistance. Teachers who have a resistance perception of mathematics have a romanticized view of education. They long for the days when teachers had more freedom in the classroom to teach what they determine that students need to know. While teachers with a resistance perception demonstrated a limited knowledge of the Standards, they voiced an opinion of the Standards as too numerous, too rigorous, ill-matched to what students need to know, and impossible to cover in the amount of time allotted for instruction. Be- cause of this, or perhaps due to a general decline of personal values, teachers cannot be successful in their teaching (which is, again, determined by student test scores) because students cannot be motivated and just do not care about passing state achievement tests. Teachers with a resistance perception see the standards as a detriment to education.

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grade-level indicators. Performance teachers present mathematics in context and with real world applications. This perception also includes a very positive view of the Standards as a means of accountability for teachers who have not kept up with the changing world of mathematics. Test- ing serves a purpose ± that of making teachers do their job even when they prefer what they have done in the past and what is comfortable.

The second theme developed from the study was Purposeful Practice. Purposeful Prac- WLFHDVDWKHPHLVGHVFULEHGDV³DWHDFKHU¶VLPSOHPHQWDWLRQRILQVWUXFWLRQDOVWUDWHJLHVWKDWEHVW

compliment the relationship between perception and teaching practices which allow teachers to IXOILOOWKHLUUROHVDQGUHVSRQVLELOLWLHV´1LFKROVS:KDWWHDFKHUVXOWLPDWHO\GRLQWKH

classroom is a conscious decision derived from their perception of their role as a mathematics teacher and the desire to efficaciously fulfill their responsibility to students, administrators, and stakeholders. Teachers who use student test scores to determine their effectiveness will teach in a way that brings about higher test scores. While mathematics reform and standards-based instruction call for a more student-centered approach to teaching, it has been suggested that traditional instruction is quite effective for test preparation for standardized tests (National Research Coun- FLO5RVVHWDO7HDFKHUV¶SUDFWLFHLVSXUSRVHIXO²being highly reflective of their

perception.

Short Answers to the Research Questions

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Content Standards for Mathematics?

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mathematical processes. Standards are viewed as a checklist of things to teach. Some content is more important than others and the importance of the content is determined by the amount of coverage a concept has on state achievement tests. Process standards are more or less ignored.

For fewer teachers, the Standards represent the least students should know. They serve the purpose of being a foundation on which professional educators build a comprehensive, cohe- sive curriculum of mathematics which has real world applicability. Teaching is planned with a bigger picture of mathematics in mind.

Research Question 2: How do teachers translate Standards into classroom practice?

The majority of participating teachers taught in a strictly traditional manner. Because few teachers seemed to place value on process skills, mathematics content, most of which was taught procedurally, was the focus of instruction. Following a behaviorist approach, procedure with re- petitive practice was the dominant teaching strategy. The reliance on checklists of grade-level indicators was evident in most classrooms.

Research Question 3: If teachers truly support the Standards and standards-based instruction, to

what extent is this evident in their classroom practice?

What was anticipated to be a simple straightforward question became the most difficult to answer. Nearly all of the participating teachers expressed support of the Standards and reported classroom practice that included doing standards-based instruction. Observations of classroom instruction clearly determined this not to be the case.

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varying degrees of support that may or may not be separable from purpose and value. It would appear from this study that most teachers support the Standards. The basis for that support may not be consistent with the goals of the Standards document, however. Some teachers support the Standards as defining the expected outcomes of their job which is to teach certain mathematical concepts. Their perception of the Standards does not move them beyond that level of support. Other teachers have a good understanding of not just the content standards but the interrelationship between the content standards and the process standards as well as the goals that brought about a need for standards. (Nichols, 2010, p. 155)

Is there a disconnect between what teachers say²i.e., they are doing standards-based instruction²and what teachers actually do? Many teachers view and define standards-based instruction as teaching the standards,IDWHDFKHU¶VXQGHUVWDQGLQJRIVWDQGDUGV-based instruction is limited to the standards as content and they are teaching the content, there is no disconnect between espoused beliefs and practice. Compliance teachers all fell into this category.

On the other hand, teachers with a performance stance espouse support of the standards DQG\HWDQREVHUYHURIWHQVHHVDQHSLVRGHLQWKHVHWHDFKHUV¶FODVVURRPVWKDWH[KLELWVYHU\WUDGL

tional structure on the surface. Performance-minded teachers, however, were able to take what appeared to be direct instruction and change it to standards-based instruction by use of process standards and skillful incorporation of reasoning, representation, communication, and connec- WLRQVWRPRYHSUDFWLFHIURPWUDGLWLRQDOWRPRUHOHJLWLPDWHO\³VWDQGDUGV-EDVHG´

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these teachers are ill-prepared to teach mathematics. Therefore, they tend to rely on test preparation materials to try to help students pass the achievement test. Standards-based instruction is not evident in their classrooms.

Research Question 4: What conditions influence teachers enacting standards-based instruction

in their mathematics classroom?

While not the conditions cited by teachers, according to data collected, the most common condition influencing whether teachers are using standards-based instruction in their classrooms is an incomplete or inaccurate understanding of the Standards and standards-based instruction. Teachers themselves, on the other hand, identified lack of time and a preponderance of students who lack prior knowledge as barriers to using standards-based instruction.

Grounded Theory: Perspective

Perspective is the capacity to view things in light of relative importance. Mathematics teachers value mathematics and take their jobs seriously. Through this study, it became clear that teachers viewed mathematics teaching from two different perspectives. One perspective, the As- sessed Curriculum Perspective, holds a view where, in the relationship between school mathe-

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The other perspective, School Mathematics Perspective, holds a view where school mathematics is of utmost importance and the Standards are viewed as a tool that organizes the various mathematics topics. Teachers for whom performance is most important tend to have this perspective. They translate Standards into classroom practice by looking at the big picture in mathematics.

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of school mathematics as opposed to the importance of the value of the assessed curriculum to teaching practice positions their perspective as a central belief in the psychological structure of RQH¶VEHOLHIV\VWHP*UHHQ(YHU\RWKHUEHOLHIDQGGHFLVLRQLVEDVHGXSRQWKDWSHUVSHF

tive.

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Implications

With the adoption of Common Core Standards, more changes are coming in mathematics education. It is apparent that practicing teachers do not have a thorough understanding of current standards. If mathematics reform is to be effective, it is important to help teachers value mathematics above test scores and provide teachers ample opportunities to gain a deep and meaningful understanding of the new standards. It is also important to change the message in education that high test scores alone are the indicator of successful teaching.

References

Green, T. F. (1971). The activities of teaching. New York: McGraw-Hill.

Hiebert, J., & Stigler, J. W. (2000). A proposal for improving classroom teaching: Lessons from the TIMSS video study. Elementary School Journal, 101(1), 3.

National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. Washington DC: Author.

Nichols, S. (2010). Perception and implementation of the Ohio Academic Content and Process Standards for Mathematics among middle school teachers. Ph.D. dissertation, Ohio Univer-

sity, United States -- Ohio. Retrieved January 22, 2011, from Dissertations & Theses @ Ohio University. (Publication No. AAT 3423503).

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Review of Hands On Earth Math: Digging Deeper into Environmental Topics (Rydberg, V., 2008)

What are book reviews for? One idea is that they help prospective readers learn enough about a book to decide if they want to buy it. So a review, looked at this way, is a sort of mar- NHWLQJSOR\7KDWZRQ¶WZRUNKHUH7KLVFXUULFXOXPLVKDUGWRJHWEXW,¶GEHWFRSLHVDUH

still available if you write to the author, who now works for the outfit that funded its development²the Wisconsin Department of Public Instruction. Victoria Rydberg reports that (as of early September) she had fewer than 50 copies left and no funds for shipping.

Victoria Rydberg and her seven co-authors put this curriculum of nine units together explicitly for 7th_{and 8}th_{VWXGHQWV7RP\WKLQNLQJWKRXJKDQGIRUWKLVUHYLHZZKDW¶VPRVWH[}

citing is the example this curriculum provides for the possibility of a place-based form of math HGXFDWLRQDWDOOOHYHOV,W¶V³VWDQGDUGV-EDVHG´ORFDOO\JURXQGHGDQGZLUHG,WVSHFLILHVREMHF

tives, materials (some it provides), and assessments;; it gives clear lesson plans written in good (QJOLVKVRPHWLPHVWKDW¶VDQLVVXHZLWKORFDOO\SURGXFHGPDWHULDOV7KHOD\RXWLVDWWUDFWLYH

and practical. The lessons get students outside and working on projects. The production values are professional, in short.

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one another. The project assistant, Brittany Roberts, is the daughter of the author of the first unit, Mary Roberts. It bears the marks of community, of people immediately available to one another.

7KHZRUNFRPHVRXWRI5\GEHUJ¶VDVVRFLDWLRQZLWKRiver Crossing School, a Wisconsin

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students in 11 schoolsDQG1&(6FODVVLILHVWKHGLVWULFWDV³WRZQGLVWDQW´,QVKRUW3RUWDJHLVD rural town, and both Rydberg²who now works for the SEA herself²and her (at the time) un- dergraduate project assistant grew up in rural places.

This review discusses (1) where Hands On Earth Math came from and why it exists, (2) the nature of the engagement with mathematics, (3) the question of rural context and content, and (4) it includes an incredibly brief and succinct explanation of why rural math education is so difficult.

Why This Curriculum?

I was able to track Victoria down at her new job, and got the full story. In 2002 she was employed, in her first real teaching job, as the one teacher at River Crossing. Even today the school enrolls only about 20 kids (according to NCES, the district also maintains a 9-12 public charter school enrolling 20 kids). The school was established with progressive commitments that would be rare in some parts of the nation: no textbooks, classroom without walls, weekly field H[SHULHQFHV0V5\GEHUJZURWH³3HRSOHZHUHZRUULHGWKDWZHZHUHQ¶WKLWWLQJWKHULJKWFRQFHSWV

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two-year grant, part 1 of which concerned explaining the school, which resulted in a book and short video, and part 2 of which resulted in this curriculum. Rydberg was suitably modest in

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center, and more complex organization. The very existence of Hands On Earth Math is some- thing of a miracle²and the quality of these materials is high.

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done this way.´

Getting to the Math

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saw nothing like this developed curriculum at any of the study sites, and none of our 60 national QRPLQDWRUVSXWIRUZDUGWKH5LYHU&URVVLQJVFKRRO%XWGXULQJWKHVWXG\,¶GZRQGHUHGLIDQ\

such materials existed aside from those produced by <XS¶LNSURMHFWRXWRI)DLUEDQNV.

So where and what is the math in Hands On Earth Math? There is real math in every unit: the Appendix shows the connections to the Wisconsin math standards for each lesson in HDFKXQLW,QHYHU\VWDWHLQWKHQDWLRQWKDW¶VVXIILFLHQWZDUUDQW

For instance, the unit on prairies deals with patterns in natures, and naturally enough, in- FOXGHVWKH)LERQDFFLVHTXHQFHVDPSOLQJSUDLULHVSHFLHVXVLQJµTXDGUDWV¶VDPSOLQJVRLOS+

constructing 3D scale models, estimation, and graphing data.

The unit on the home environment focuses on fractions and ratios²perhaps the critical DQWHFHGHQWWRµDGYDQFHG¶PDWK²in consideration of kilowatt wattage, lumens, volume of water

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Each unit is loaded with such connections, and with ample prompts for discourse, practice, and projects. Units do vary in the amount and character of practice and discourse, no doubt reflecting the experience and dispositions of the authors;; the variation strikes me as simply KHDOWK\,W¶VDQH[DPSOHLQLWVHOIRIDZD\QRWWRstandardize standards-EDVHGVFKRROLQJ,¶PQRWD

fan of how standards are used, but it looks like they exerted a productive influence on this cur- ULFXOXP7KHXQLWVDUHQ¶WWKHFUHDWXUHVRIIHDU-of-VWDQGDUGVEXWRIWKHLUDXWKRUV¶LQKHUHQWVHQVHRI

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are concerned elsewhere to make connections to their local natural places and communities.

Getting to the Rural

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anywhere except in the bios of Rydberg and her assistant. Is this a rural education curriculum? No, but some of the units are clearly tied to the Portage locality, and most of them concern the natural world: the curriculum is very much in the tradition of outdoor environmental education. Most of the authors profess a love for the outdoors and for the natural world. In rural places, the (humanly modified) natural world is most of what one encounters outside. The rural influence is YHU\FOHDUKHUHGHVSLWHWKHORZLQFLGHQFHRIWKHH[DFWWHUP%XWLW¶VVWLOOQRWUXUDOSHUVHDQG

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be a covert aim. These people in Portage seem pretty scrappy and well-informed.

Getting to Rural Math Education

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First, rural is context, and context is just FRQWH[W:KDW¶VPRVWLPSRUWDQWWRPRVWSURIHV sionals is the math, or the environmental learning, or the what-have-you at the center of instruction. Context is, by definition, outside that center. Rural is outside such conventions.

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actually teach in real credit-bearing courses that there are two big and persistent issues: (1) con- solidation and (2) youth-outmigration. The agenda is implicit in those issues;; it arises from them as matter of course if one cares about rural places RWKHUZLVHQRWDQGRIWKHQDWLRQLVQ¶W rural).

Third, for the 20% at risk of caring for rural places, the agenda is this: fostering the health and survival of rural communities. Until recently, such agendas have been a legitimate role for UXUDOVFKRROLQJEXWLW¶VDVRFLDO-MXVWLFHUROHRIWKHVRUWWKDWFRQWHPSRUDU\SROLWLFVMXVWKDWHV,W¶V

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The idea that mathematics teaching and learning could contribute to a thriving rural community is strange and unusual. In the seven-site study we heard in particular from high-school WHDFKHUVRI³DGYDQFHGPDWK´WKDWVXFKDQLGHDZRXOGQRWVLWZHOOZLWKVWXGHQWVRUSDUHQWV7KHVH

high-flyers had, according to these teachers, quite a different agenda.

Let Many Thousand Curricula Bloom

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outside Japan, but I can imagine a form of lesson study that kept such curricula alive once they were created. So much for sustainability.

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instruction more widely, and particularly in rural places, and particularly at the secondary level, including²especially²³DGYDQFHG´PDWKVXFKDVLQWHUPHGLDWHDOJHEUDWULJRQRPHWU\DQGFDOFX lus. The approach of centering content on environmental studies would likely be a promising venue in which to do such work.

Many thousands of small-WRZQDQGUXUDOVFKRROVH[LVWDFURVVWKHFRXQWU\7KDW¶VWUHPHQ dous potential;; only the capacity is dubious. But if Victoria Rydberg is right, the want of that capacity is not the impediment it might seem to be.

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Mike Corbett's ACCLAIM movie: Putting Mathematics in Its Place (streaming video)

ACCLAIM held its seventh Research Symposium recently, with Mike Corbett's presentation the central event. Dr. Corbett is author Learning to Leave: The Irony of Schooling in a Coastal Community;; he teaches at Acadia University in Wolfville, Nova Scotia. His intellectual background is sociology and his practical background is 20 years teaching at the elementary

level...which means he was indeed a teacher of mathematics. In this movie, Mike interviews two mathematics education colleagues at Acadia, framing the conversation with his own reflec- tions...and a bit of tree felling. The movie is about 50 minutes in length;; it's professional quality video work (Mike also teaches videography to teachers);; and he and we are making the movie freely available to the planet. Mike would probably be interested to hear from anyone wanting to create subtitles for it (e.g., our friends in Turkey, Sweden, Germany, France).

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Opportunities for cohort members²ACCLAIM Pre-session at AMTE:

A Short Report

In addition to the wonderful presentation by Michael Corbett at the AMTE ACCLAIM pre-session, there were many other opportunities for ACCLAIM cohort members. First of all, cohort members who have not yet received their doctorates were able to meet with those that had. Their remarks were invaluable as we who are embarking on the dissertation phase begin our journey through the process.

Furthermore, as we have received regular updates on The Seven Site Study in the RME, we were privileged to hear an in-person research report from some of the authors, namely Aimee Howley, Craig Howley, and Bob Klein. As inexperienced researchers, it was extremely benefi- cial to hear the positive and negative aspects of a qualitative study. We were able to ask clarify- ing questions as well as questions about the methods used and the findings made.

Finally, ACCLAIMers were able to pose questions to a panel including management team members and Michael Corbett. General questions about research and roadblocks to pro- gress were addressed along with tips for beginning the dissertation phase.

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Upcoming Conference Information

NCTM 2011 Annual Meeting and Exposition

Indianapolis, IN April 13-16

Geometry: Constructing and Transforming Perspectives

NCTM 2011 Regional Conferences & Expositions

Atlantic City, NJ²October 19±21 St. Louis, MO²October 26±28 Albuquerque, NM²November 2±4

RSS 2011

In conjunction with the Community Development Society, the 74th annual meeting of the Rural Sociological Society will be held in Boise, Idaho, July 27-31 at the Boise Center.

AERA 2011 Annual Meeting New Orleans, LA

April 8-12

Inciting the Social Imagination: Education Research for the Public Good

RMEv10n1

Rural Math Educator

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