Implementation and Sustainability of Curricular Change in ...



THE AMOEBA OF SIMULTANEOUS RENEWAL

AND THE RESIDUE IT LEAVES BEHIND

JENNIFER M. BAY-WILLIAMS

Department of Elementary Education, Kansas State University, Manhattan, KS 66506

jbay@ksu.edu

M. GAIL SHROYER,

Department of Elementary Education, Kansas State University, Manhattan, KS 66506

gshroyer@ksu.edu

MELISA HANCOCK,

Teacher-in-Residence, Manhattan/Odgen School District, Manhattan, KS 66506

melisa@ksu.edu

MICHAEL B. SCOTT

Department of Mathematics, Kansas State University, Manhattan, KS 66506

mbscott@ksu.edu

Abstract

This paper outlines the premises of a K-16 simultaneous renewal model. This renewal model involves teachers, mathematics educators, and mathematicians and is based on data analysis of K-16 teaching and learning and K-12 mathematics achievement. Two case studies are used to illustrate how simultaneous renewal impacts all levels of schools. One case study focuses on the improvement in one elementary school and the other focuses on change in the teacher education program. Following the case studies is a discussion of the impact of the model on K-16 teaching and learning.

The Amoeba Of Simultaneous Renewal And The Residue It Leaves Behind

“The initial object of change is not the student, the classroom, or the system, it is the attitudes and conceptions of educators themselves” [1]

Teachers within a school are diverse, schools within a district differ significantly, and districts each take on their own culture. Attempting to address the needs across several district partners while simultaneously improving teacher preparation is a complex and nebulous proposal. The five partners of the Kansas State University Mathematics Teacher Preparation (KSU-MTP) Project include urban schools, rural schools, schools within a University community, and the University College of Education and Department of Mathematics. Each partner has a history and context that is unique. Creating a mathematics team that includes representatives from each with the goal of improving student learning means balancing planned professional development and improvement activities with those that emerge from school-based needs. Planned events for the mathematics team prompted unforeseen projects and initiatives in each partner’s home setting. At times, much activity was happening on a particular topic, such as implementation of standards-based curriculum, and then project activities moved in new directions, such as focusing on teacher content knowledge in geometry. “While schools and teachers approach change in a variety of ways, most experience the process as neither predictable nor orderly but often fitful and pragmatic” [2]. This is the amoeba-like movement of simultaneous renewal, an approach that is responsive to the culture of schools and the needs of students. The movement of an amoeba is not sporadic or disjointed; it moves slowly towards its intended destination, constantly changing its shape, responsive to the external environment and somewhat unpredictable to the observer. While there are boundaries around which the systemic reform occurs, the movement of the group, while together, is somewhat unpredictable. In this paper we discuss the premises for simultaneous renewal and the approach we took towards K-16 improvement in mathematics teaching and learning. Through two case studies, we illustrate the dynamics of planned and emergent professional development and improvement activities and their impact on K-12 schools and teacher education. We conclude with the residue that this process is leaving behind, as well as the new directions the partners are undertaking.

Simultaneous Renewal

Simultaneous renewal is grounded in two basic premises. First, is that lasting change at any level requires change at all levels. This means that if elementary schools have identified that teachers need to develop more effective instructional strategies, then the only way to accomplish this and sustain it is to provide professional development, change programs, and adapt courses so that current teachers in K-12 learn about effective instructional strategies and teacher education courses, field experiences, and content courses are designed so that pre-service teachers develop such skills before entering the teacher workforce. If teachers are not modeling effective instructional strategies, then pre-service teachers are not seeing what they look like in a real classroom. If practicing teachers are using effective instructional strategies and pre-service teachers are not learning about them, they will be unprepared for student teaching or first year teaching and then are at higher risk of leaving the profession.

The second premise is that a problem at any level is the joint responsibility of teachers, district leadership, mathematics educators, and mathematicians. “Collaborative inquiry is the process by which all relevant groups construct their understanding of important problems and potential solutions through asking questions, carefully analyzing all relevant data, and engaging in constructive dialogue with colleagues” [3]. In the example given above one can see that all those involved in K-12 education must participate in reaching the intended goal. If students learn mathematics in a mathematics department in a way that models effective teaching strategies, they begin to see how formulas can be developed, rather than stated. They see that “doing” mathematics is not imitating static steps, but a decision-making process in which various strategies might lead to the correct result. Methodology courses must explicitly address those instructional strategies that enable students to learn mathematics and model such practices. Teachers must use effective instructional strategies and administrators must provide the time and resources for teachers to learn strategies that are not already in their repertoire.

Simultaneous renewal is aligned with philosophies of systemic change. Ball argues that the state and national standards are not programs to be implemented, but are visions for improving mathematics. Her interpretation of systemic reform is much more interactive: “Rather than asking, ‘How might we help more teachers implement the reform?’ I want to ask, ‘How might we engage a wider community in developing and enhancing reform?”[4]. Efforts to reform education should be well planned, and well aligned. “Both horizontal and vertical structures must be considered. Anything less than a systematic approach will find the fabric of change unraveling at one end even as it is being woven at the other end” [5].

The systemic change warranted in simultaneous renewal is fundamental change. In this definition, the assumption is that the problems of change cannot be addressed within the given system, thus systemic change involves changing the system. The goal of systemic reform efforts is to replace the fragmented, multi-layered education system and align policy to a coherent system of instructional guidance [6]. Simultaneous renewal seeks to blur the lines between K-12 schools and higher education, to blur the boundaries of Colleges of Education and Departments of Mathematics, and to encompass all these educators in the responsibility of improving student learning.

Each of the two premises will be further illustrated through the two cases we share in this paper. Each case is an example of a collaborative effort to identify and prioritize the needs of K-12 students and the response of all stakeholders in attempting to meet those needs. The events described in the cases illustrate that while there is planned professional development to identify needs, the projects and professional development to meet those needs emerge in unpredictable ways. This is the amoeba of simultaneous renewal. Before sharing the cases, we discuss the project goals and the planned efforts to identify school needs.

Project Goals

KSU-MTP Project developed goals to guide the direction of simultaneous renewal. While each goal targets a different element of the K-16 continuum, each level supports the improvement of the other levels. Our goals included, (1) To enhance collaboration, coordination and alignment in the KSU mathematics teacher education program to address K-12 school needs while simultaneously improving teacher quality; (2) To extend, assess, and institutionalize a variety of recruitment initiatives aimed at increasing the number of students entering K-12 mathematics teacher education; (3) To collaboratively redesign KSU mathematics teacher preparation; (4) To provide enhanced and sustained professional development for all project participants; (5) To institutionalize a model induction program to provide mentoring for early career teachers to increase retention of qualified mathematics teachers in the profession. The following discussion focuses predominantly on simultaneous renewal to address goals 1, 3, and 4.

KSU-MTP Partners

While we all share common concerns of improving student achievement for all students, improving teacher quality, and aligning curriculum with standards, the challenges within each school differed significantly. Teachers in all partner schools faced challenges resulting from serious discrepancies on test scores for minorities, children from poverty, and students with limited English proficiency. Though common to all districts, the extent of the problem varied greatly. Kansas City, Kansas, located in an urban Empowerment Zone, struggles with tremendous poverty (67% disadvantaged), diversity, teacher turnover, and a rapidly expanding population with limited English proficiency. Geary County (59% disadvantaged) and Manhattan-Ogden (32% disadvantaged) are located in rural regions adjacent to the Ft. Riley Military Installation and near Kansas State University. Garden City is a fast growing rural community in western Kansas with a rapidly expanding population of English Language Learners. All partners needed to align mathematics teaching with National and State standards, including university courses aligned to the MET expectations.

Data-Driven Professional Development

Across teachers, schools, and districts, each individual has different notions about the need for change. There are teachers within the same school who believe the way students are learning mathematics is already the best it can be, while others believe that urgent change is needed. A careful study of data serves to (1) raise awareness that change is needed, (2) provide a rationale for change, and (3) provide a target for change (e.g., to raise student achievement and to align teaching with standards). National reports, such as the Adding it Up [7], How People Learn [8], and Principles and Standards for School Mathematics [9] provide compelling evidence that mathematics teaching must change, as well as guidance on how that change can occur and what effective teaching practices are. State data are important to teachers and schools, as high stakes tests are at the state level. Analyzing state standards for students as well as for teacher licensure can identify content gaps in curriculum, as well as illuminate pedagogical issues. Finally, teachers’ self analysis of school needs is essential in identifying both what most needs to be improved and how it can be accomplished in their individual setting. All three levels (national, state, and local) of data analysis are important in making changes that reflect best practices and are responsive to local needs.

This process must be collaborative. Love [10] offers a framework for collaborative inquiry focused on student learning as a vehicle for systemic reform.

[pic]

Figure 1. Love’s [10] Model for Collaborative Inquiry into Student Learning

Love bases this model on eight basic principles. Among these is that school reform is fueled by inquiry, that the inquiry must be data-driven, focused on student learning, and collaborative. Collaboration within the framework of simultaneous renewal goes beyond involving all K-12 stakeholders, which means including mathematicians and mathematics educators who participate in the preparation of teachers. Grounded in the basic principles of Love’s collaborative inquiry and the premises of simultaneous renewal, the KSU-MTP project identified a data-driven collaborative approach to include all partners. A mathematics team was developed including lead teachers from each partner district (though not every school), mathematics educators, and mathematicians. Through the collaborative analysis of national, state, and local needs focused on student learning, each school developed a unique action plan to improve student achievement in their setting (see figure 3).

KSU-PDS Partnership School Improvement Action Plans

School: District: QPA Cycle:

Identified Improvement Area:

Rationale for selecting this area:

Targeted Partnership Goal:

Evidence of Partnership Impact: How will you know when you have achieved your goal? What are your indicators of student achievement? Who will be responsible for monitoring your progress?

Strategies: How do you plan to use KSU students and faculty resources to help achieve your goal?

Teacher Involvement: How will the teachers in your building be involved in the process?

Resources: What resources do you plan to use to accomplish your goal?

Timeline: What is the timeline for activities and results?

Wish List: What resource needs will you have to accomplish your plans?

Figure 3. School Action Plan Protocol.

The development of the action plans was the “point of departure” from pre-planned collaborative discussions with teacher-leaders, to emergent school-wide professional development and improvement activities responsive to the needs of each site. To illustrate the implementation of an action plan, we share one school’s story, a school that was one of the poorest and lowest performing in the state of Kansas.

Case 1: Supporting Teacher and Student Understanding in K-12 Schools

One elementary school, one middle school, and one high school in Kansas City, Kansas became KSU Professional Development Schools in 2001. Teacher leaders from the elementary and middle schools wrote mathematics school improvement action plans based on the data-driven discussions of the mathematics team. They were asked to identify weak areas and resources needed to address these weaknesses. It was from these action plans that teachers began developing a new language to describe what was possible. Phillip Schlechty [11] calls this "invention"--the invention of new ways of thinking and of organizing so that students can be reached more effectively. Such invention cannot be a collection of sporadic and disjointed efforts. Rather, it is "steady work" that is inclusive, broad-based, and grounded in the day-to-day realities of school life [12]. Through our partnership, a supportive environment was formed, that encouraged teachers to work together and the "steady work" began.

A series of activities, one leading to another was set into motion. Initially, Kansas City invited three members of the mathematics team (a teacher, a mathematics educator, and a mathematician) to meet with the district leadership about how to improve mathematics teaching. A question arose in the conversation about the curricula used in another PDS, which was standards-based. The result of the conversation, and several follow-up meetings, was to consider using these two schools as pilot sites to explore standards-based curricula. This led to a PDS exchange in which Kansas City teachers visited Manhattan/Ogden to observe and meet teachers implementing reform curriculum and conceptual mathematics lessons. It was from these observations, reflections and analysis of their mathematics data that lead teachers to realize that their curriculum was not aligned with the state mathematics standards and that expectations of their students were too low. Teachers, school improvement facilitators, clinical instructor, central office personnel and Kansas State University educators came together to rethink curriculum and instruction and attend to the needs of both teachers and students. Two representatives of the math team (the teacher-in-residence and a mathematics educator) offered a summer institute at the elementary school to showcase Investigations in Number, Data, & Space. At that meeting, teachers at each grade level made decisions about the extent that they would use units from this curriculum in the upcoming school year. Similarly, the middle school invited these two representatives to showcase selected units from Connected Mathematics Project (CMP). Both schools became pilot schools for Investigations and CMP. During this pilot, a peer counseling model was adopted and teachers from Manhattan, who were familiar with this reform curriculum, became coaches to the KCK teachers. Observations of teachers using this curriculum continued as well as model teaching at all grade levels in Kansas City. In addition to the peer coaching and model teaching, teachers requested unit-studies. Teachers from another PDS, who were teaching at the appropriate grades, offered grade-specific unit studies to help teachers understand the goals and activities of upcoming units. Professional Development focused on student learning and implementing the reform curriculum.

Out of each of these encounters, new dilemmas gave rise to new priorities and the need for new supports and actions. For example, the extremely high teacher turnover rate common to urban schools, resulted in a need for new-teacher sessions that equip teachers new to the school with the rationale and approach for using Investigations. Additional sessions continue to emerge, addressing issues such as English Language Learners (ELL) (which are 70% of the school population), consistent use across grades, developing colleagueship, and expanding responsibilities for teachers and students. The comprehensive approach to change that this school proposed was complex work, and we had no road maps to guide us. It was through our partnership and the focus on learning, not only of teachers, but students as well, that these two schools truly became professional development schools. Peer coaching, model teaching, summer institutes and professional development during the school year continues, as the achievement of students in this high needs area, continue to increase.

Change at one level requires change at all levels (premise #1 of simultaneous renewal). As this elementary school entered into its implementation of standards-based mathematics instruction, it was also beginning to provide field experiences for math methods students and student teachers. Consequently, math methods faculty increased their attention on standards-based curriculum and asked all methods students to teach at least one lesson from an NSF-funded project. Math content course faculty began to use various problems from standards-based middle school programs. The student teachers placed at this elementary school were instrumental in supporting the implementation of the program. In addition, some of these student teachers became first year teachers at the school in following years. Changes in K-12 schools prompted change in teacher education, while changes in teacher education supported the change in K-12 schools.

Case 2: Supporting Student Understanding in Teacher Education

In our second case, we place teacher education in the forefront, and illustrate the impact it has had on simultaneous renewal. The same national, state, and local data served as a launching point. Through the data-driven discussions, a common theme surfaced: teachers (both preservice and inservice) lack the conceptual understanding necessary to teach standards-based mathematics. The specific planned activities are shared here, as well as the efforts that emerged to improve teacher education.

Peer Consultation. Bernstein’s model of peer consultation was a second form of initial, planned, collaborative professional development [13]. In this process, team members compared syllabi, visited other’s classrooms, and discussed student learning in those classrooms. University faculty visited K-12 classrooms, and methods and content instructors at the university discussed syllabi and visited each other’s classrooms. This prompted individual or paired initiatives, as well as math team meeting discussions. A first grade teacher paired with a mathematician. Their exchange had a positive impact on both of them, as noted in the teacher’s journal:

I observed in David's (pseudonym) Math for Elementary School Teachers class. I was surprised by the empty seats - students not attending class. In first grade parents call or e-mail when absent or the office calls and checks. When students miss class I have to "catch" them up/teach the material missed. How do pre-service teachers get "caught up" on material missed? How does that affect their interning and their later teaching? David was the one in charge of the chalk and the board. Students were very comfortable asking questions and sharing their solutions in class, but David always did the writing on the chalkboard. As we visited after class I asked him, as a new Dartmouth graduate, if he ever planned to share the chalk with the students in his class. He liked the idea and said he planned to try it the next semester.

I learned from David that in his higher-level math classes at Dartmouth that the professor would walk into class, present a problem and then walk out. The students quickly gathered and shared the solving of the problem as a group. Ideas were shared, new learning had to have occurred. I tried to remember these things as I worked with first grade mathematicians--I needed to share the chalk. In Investigations we were working on "combinations" and I had students at the chalkboard sharing their ideas for combinations. Students will learn from each other as well as from me.

David also visited the teacher’s classroom and was surprised by the collaborative, problem solving approach he saw, noting it was much different than the way he had remembered elementary school. In sharing their exchange with the rest of the mathematics team, important issues arose, such as whether elementary school is to learn basics in order to later solve problems, or if, in fact, students should solve mathematics via problem solving right from the beginning.

Analysis of Licensure Standards. Through an annual two-week summer institute, the team has analyzed standards for teacher licensure. Teachers who supervise student teachers, methods instructors, and content instructors discussed which standards they addressed in their course, the nature of the activities preservice teachers did to demonstrate their knowledge, and the performance assessments that were in place to assure that pre-service teachers had met these standards before graduation. The matrices that resulted in these discussions highlighted experiences in methods courses, content courses, and field experiences that targeted specific licensure standards. Figure 2 is an example of one such standard.

|Licensure Performance Standard |Courses Where Addressed |Assessment Instruments |Criteria Used in Assessing |

|The teacher uses geometry, measurement, and |EDEL 473: Math Methods | |Lesson observations completed by |

|spatial visualization to explore mathematical | |Prepare and teach geometry|supervisor |

|questions and conjectures, formulate |EDEL 420: Math Clinical |lesson | |

|counterexamples, generalize solutions, select | | |Self-Reflection (scored with |

|and use various types of reasoning and methods | | |rubric) |

|of proof. |MATH 572: | | |

| |Foundations in |Prepare and present proofs|Rubrics and written commentary |

| |Geometry |of theorems | |

Figure 2. One topic from the geometry standard matrix for middle school mathematics licensure.

The creation of the matrices served several purposes. First, as was the original purpose, we were able to determine what standards were not getting taught in our program. Second, each person became much more aware of what is actually taught in various courses. This increased awareness of what was taught led to discussions related to the focus on conceptual and procedural knowledge. Third, discussing how we knew that students learned what we taught prompted rich dialogue about alternative assessments and rubrics as a means for learning more about what students know.

Gateway Exam. In response to earlier discussions of strengthening preservice teacher content knowledge, the KSU-MTP project proposed the creation of a Gateway Exam. Computer Assisted Instruction (CAI) such as a Gateway exam, where online practice is used to supplement a course, is effective in improving student affect and in raising student achievement [14] [15] [16]. The motivation for supplementing the course with a gateway exam is to take most of the computational aspects of the material outside of the classroom, and spend the additional class time focusing on the more conceptual and abstract ideas. We have implemented a web-based gateway exam for the mathematics course required for preservice elementary school teachers at Kansas State University. For each content area, there is an online quiz that students take. Each time they retake the quiz, new items focused on the same concept arise. The KSU-MTP Gateway Exams provide immediate feedback, customized tutorials (if a student misses the same item twice, a tutorial pops up), multiple attempts to be successful, and access to high quality practice problems. Using this model of CAI provides the instructor with an additional tool to monitor student learning. From tracking how students perform on each item, an instructor can modify the course curriculum to be responsive to these weaknesses.

Academic Excellence Workshops. The Academic Excellence Workshops provide enriched supplementary instruction to targeted students enrolled in selected mathematics courses. The workshops are designed to be a support mechanism that empowers students to achieve a high level of mathematical understanding and enhance success. The KSU-MTP has begun discussions on how these workshops, originally aimed at African-American students, might be modified to meet the needs of Hispanic American students. The notion of providing extra support without lowering expectations is critical to all K-16 educators.

Through the creation and analysis of the matrices, the results of the pilot Gateway Exams, the book studies, and the ongoing discussions about school needs, the mathematics team identified geometry as a mathematics standard that needed the most attention. State assessment data of K-12 students supported this conclusion. In addition, we were prompted to act by reports from preservice teachers and practicing teachers citing their lack of confidence in this area, preservice teachers dropping out of a mathematics course in geometry, and an awareness that geometry was the most skipped topic in our PDS elementary schools. This was the point of departure where additional professional development and improvement activities emerged to meet partner needs.

The mathematics lead teachers decided that intensive geometry workshops should be offered in their districts, yet they felt unprepared to offer them. The solution was two-fold. First, many attended an NCTM Academy for Professional Development in order to learn more about geometry and to see how to design professional development around a mathematics standard. Other mathematics team members wrote for additional funding in order to offer a more intensive geometry course in the summer. Lead teachers will participate in this summer institute and prepare their own “mini academy.” Cross-district teams will be available to visit schools and provide these workshops. Methods courses increased the focus on geometry, and the related clinical experience required that pre-service teachers teach one lesson on geometry. The mathematics department is developing a course for teachers that will be project-based and link geometry and art.

Pre-service teachers are the responsibility of all educators (premise #2 of our simultaneous renewal model). For teachers to become stronger teachers of geometry, preservice teachers must have a stronger background. The methods instructor provided the support for an increased focus on geometry and assisted in the development of geometry lessons. K-12 teachers provided support by observing and providing feedback on a lesson (which in turn helped them see what geometry can be taught their grade level), and the mathematicians developed courses that are designed to meet the needs of teachers, while targeting increased content knowledge. Conversely, the improvement of teacher education impacted K-12 schools. Practicing teachers saw preservice teachers teaching geometry and learned new ideas for their own teaching, and the grant developed to target geometry will include the participation of up to fifty practicing teachers.

The Residue of Simultaneous Renewal

The residue this process leaves behind “stains” those involved. In other words, changes that have occurred and are occurring are sustainable. Some of those are measurable and others not measurable, but observable. In the first case shared above, the urban elementary school, student achievement has continued to improve on the Kansas State Assessment. Over three years, the 4th grade math scores on the Kansas State Assessment increased by 29%! Mentoring was provided for new teachers entering the building, and three teachers applied for National Board Certification (NBPTS). The positive impact of the curriculum adoption prompted a full implementation across the district, using a similar phase-in model. Other KSU PDS have looked to KCK for strategies of effectively improving mathematics teaching and learning, and teachers that have stayed at the school have become local leaders. In the second case of improving teacher education, the content expectations within courses have been altered to better suit the needs of teachers. Instruction in mathematics courses is more focused on conceptual knowledge and standards-based curriculum, the number of middle school mathematics students has continued to increase, and new projects have been developed to better serve students (such as the summer course). In both cases, the residue is an increased awareness of what each person does, the challenges faced at each level, and a greater understanding that we all impact student learning at all levels. Most importantly, the open lines of communication continue to lead to discussions, projects, and professional development that will move the amoeba in a new direction, still moving towards improving mathematics teaching and learning at all levels, but not always predictable.

Summary

Approaching change through responding to local needs is not a new concept. John Dewey wrote, "Schools are social institutions that need to provide mechanisms for exchanging ideas and defining collective visions, always open to negotiating and redefining these visions according to the needs of the community" [17]. The need of our community was to increase student learning. Working under two assumptions, that change at one level requires change at all levels, and that all those involved in teacher education are responsible for change, we formed teams to begin addressing what our exact needs were. From those initial activities, new needs arose and the team was responsive to those individual events. Studies on effective professional development have identified specific “best practices,” in enabling teacher change [18]. Commonly sited are the need for teacher reflection, autonomous decision-making, ongoing implementation support, collaboration, and opportunity to practice what is learned [18] [19] [20]. In our KSU-MTP simultaneous renewal model, it has been clear that these elements must be in place. A long-term plan for professional development is not equivalent to a long-term professional development plan, the former being a model that is responsive to national and state expectations, but also responsive to local needs.

Acknowledgements

KSU-MTP Project, an NSF-supported STEMTP project, includes the following partners: Kansas State University Center for Science Education, College of Education, College of Arts and Sciences, Geary County Unified School District, Kansas City, Kansas Unified School District, and Manhattan-Ogden Unified School District. We would like to acknowledge the commitment to excellence of all project partners.

Author Biographies

Jennifer M. Bay-Williams is an Associate Professor of Mathematics Education. She has written numerous articles on implementation of standards-based mathematics curricula and provides support for schools and districts as they face the challenges of reform.

M. Gail Shroyer, professor of science education, is the Director of the KSU PDS partnership. She has directed numerous collaborative projects involving College of Education, Arts & Sciences and K-12 Schools. Shroyer was a member of the NRC Committee on Science and Mathematics Teacher Preparation.

Melisa Hancock, teacher-in-residence for the KSU-MTP project has taught intermediate grades for 15 years. She has received numerous recognitions including Milken National Education Award, Presidential Award in Mathematics (Kansas), and is currently president-elect for the Kansas Association of Teachers of Mathematics.

Michael B. Scott is a Post-Doc in the Department of Mathematics. Scott teaches mathematics courses for preservice teachers and has developed, piloted, and researched the KSU-MTP Gateway Exam.

References

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[18] S. Loucks-Horsley, P. Hewson, P., N. Love, & K. Stiles, Designing professional development for teachers of science and mathematics. Thousand Oaks, CA: Corwin, 1998

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