# Challenges to reform: an overview of the study.

In 1997, the Department of Education of a mid-western state contracted with a Canadian university to coordinate research on school change initiatives. By spring of 1997, twelve schools from a sample of 500 nominated schools were selected for study. The selection process occurred in three stages.

In stage one, nominations were solicited from the State Department of Education personnel who were familiar with reform initiatives in the state's schools. Over 500 schools were nominated. Nominations were corroborated from at least one other source who had first-hand knowledge of these schools. Demographic information was compiled on each nominated school in order to provide a broad range of school communities. At the end of stage one, 30 schools were under consideration.

In stage two, 45-60 minute interviews were conducted with principals and/or assistant principals. Interviews targeted core areas of study. Principals were asked to describe characteristics of their school community and how these characteristics emerged and changed over time. Principals were also asked to discuss what factors inhibited or enabled a reform agenda.

In stage three, information was organized by: 1) school level (elementary, middle and secondary), 2) location (rural, suburban and urban), 3) school improvement initiative, and 4) focus/status of the change process. Final selection concentrated on schools that had made significant progress toward implementing school change. From the group of 30 schools, twelve were chosen to participate in the cross-case analysis-five elementary schools, three middle schools, and four high schools.

The twelve schools were assigned professors from five local universities. These university researchers were responsible for writing and designing a case study for each school. At each school, a research team was formed consisting of several educators and one or two university professors.

From spring of 1997 through spring of 1999, research teams collected and reviewed documents of student work, observed and participated in classroom instruction, and interviewed teachers, parents, community members, and district administrators. Research teams also met with coordinators from the Canadian university four times during the research process to share information about their individual schools and the school-university research collaboration.

The first two thematic research reports that follow this overview are focused on one of the five elementary schools selected for this cross-case study. It is a K-4 school with 525 students. Sixty-five percent of the students were African-American, 30% were white, and 5% were multiracial or "other." The school is in a suburb whose boundaries are contiguous to a large metropolitan city. The school district has a long tradition of educational excellence. About 97% of its students graduate from college, with many attending prestigious universities.

Historical Perspective

In order to understand the nature of the reform in this school it is important to know the history of the reform; how it evolved and the pivotal events that shaped the reform process. Prior to 1989, the school principal and a handful of teachers recognized the problematic nature of direct, behaviorist theory based instruction for mathematics. They searched for alternatives. After the publication of the NCTM Standards (1989), these educators embarked on a path of mathematics reform that would eventually require them to radically change their teaching and understanding about mathematics. To support reform efforts, the principals wrote a series of grants (1989 - 2000) that totaled approximately $300,000.00. These funds were used to purchase teacher resources and contract with university and secondary mathematics educators to conduct professional development and action-research. Grant funds also supported teachers as instructional writers and designers. Early in the reform, few mathematics textbooks adequately a ddressed the NCTM Standards. Therefore, teachers at this school wrote mathematics lessons and designed what they needed for classroom instruction. Most did not use mathematics textbooks. The major writing effort has provided, to this day, the foundation for professional development in mathematics at this school.

Instructional Challenges

Although the Standards clearly articulated the need for conceptual understanding of mathematical contents such as number and operations, algebra, geometry, measurement, data analysis, and probability, problems emerged about how to effectively implement such a major instructional change. Implementation was problematic because it required elementary educators to acknowledge their lack of content knowledge. It was evident that the Standards report required a different perspective about how individuals learn. In other words, the Standards called for a shift from current learning and teaching practices to practices that reflected constructivism. According to constructivist perspective, cognizing students build all knowledge when they participate in and contribute to the activities of the classroom community (Bauersfeld, 1988; Cobb, Wood & Yackel, 1990; Cobb & Yackel, 1996; Cobb & Bowers, 1999; Wheatley & Reynolds, 1999).

Shifting from direct teaching to active, interactive instruction was a nonlinear process for teachers. Teachers initially were reluctant to implement a different learning theory in mathematics and change their traditional, practices. They were more familiar with textbook tests and workbook pages.

Teachers' reluctance to change instructional practices forced the principal and the assistant principal to create a situation that perturbed the teachers' thinking. For example, fourth grade teachers attended a professional development session where the assistant principal and a university professor "interviewed" a class about the measurement of angles. All students had previous experiences with this topic. During the course of the interview, students were asked to identify angles that the assistant principal formed using a large wooden compass. A student correctly identified and defined a right angle. The teachers were pleased. But when the compass was reversed and the students agreed that the angle was now a left angle, the teachers looked surprised. The assistant principal continued to rotate and flip the right angle. Students renamed the angles as left, upside down angle and a right, upside down angle. When the assistant principal held the angle at the vertex, the students saw the letter V. Teachers were perturbed by these student responses.

Situations like the above episode were critical turning points in the reform process. Teachers saw vividly that what they taught was not how the students built their understanding of the lesson. Slowly, over time, teachers began implementing mathematics dialogues to gather information and assess student understanding by actively listening to students' voices.

The principal and assistant principal evolved into new roles with the reform process. They emerged as passionate visionaries with a strong commitment to restructuring and reculturing mathematics education. They often expressed the need for hiring and involving teachers who wanted to pursue higher academic and intellectual achievement. For example, three educators from this school, including the assistant principal, earned their doctorates during the ten-year reform process.

The principals also became adult learners, and they spent much extra time on weekends and during summers to develop instructional activities and facilitate professional development activities. They emerged as lead teachers and mentors, taking on the responsibility of tutoring potentially underachieving students and modeling a constructivist classroom. They tutored before school and on Saturday mornings to prepare potentially underachieving students for state mandated tests in mathematics.

Structural Challenges

The instructional shift provoked structural changes in the following areas: 1) extended instructional time, 2) roles and relationships, 3) assessment and instructional practices and 4) parental involvement.

Shifting from behaviorist to constructivist teaching required more time for student interactions and communications. In addition, school leaders recognized that major change in mathematics teaching required much more planning and instructional time for mathematics lessons. Daily state requirements of 45 minutes for mathematics were not sufficient to develop deep understanding of mathematical concepts and application of skills. Therefore, the principals and teacher-leaders established a mandate of 90 minutes of teaching for mathematics each day.

Traditional roles and relationships were also restructured. A teacher-leadership team was initiated. Seniority status was not one of the criteria for selection as a teacher-leader. Teachers were selected on their ability to conduct action-research and implement reform in the classroom. These teacher-leaders created and designed instruction and assisted the principals in making instructional decisions. When the district adopted a new mathematics textbook for students, the teacher-leaders advocated against the use of it at the school and the book was not ordered. Teacher-leaders worked with principals, university professors, and secondary mathematics educators to restructure mathematics curriculum around key ideas and topics. They also developed new assessment practices in problem-solving that valued students' illustrated solutions and their written explanations or defenses of mathematical strategies (Wheatley & Reynolds, 1999). These problem-solving assessments were collected and saved for five years in order to capture growth in understanding of major mathematical concepts.

Assessment practices encouraged more parental participation. Teacher-leaders conducted "student-led" conferences where students demonstrated their strengths and weaknesses to parents and teacher. Students also collaborated with parents and teachers to establish appropriate learning goals.

Parent participation began to focus more on issues about learning. Parent-Teacher Organization (PTO) meetings highlighted instructional practices in classrooms that were changing. Parents enthusiastically supported many of the changes in mathematics instruction and requested special "math nights" to "relearn" mathematics in order to assist their children at home.

In the midst of all the reform efforts, the state instituted a fourth grade mathematics proficiency test. The school's low scores (67% passage rate) in mathematics for three years from 1996 to 1998 refocused the reform on how to improve achievement on this instrument. The principal felt that the extended time in the classroom was not sufficient for underachieving students. Therefore, more time for mathematics was created in morning tutoring, after-school Kumon mathematics (an adopted Japanese project), Saturday School, and a tuition-free six-week summer school. After the school provided 200250 extra hours of mathematics to at-risk students, the state test scores radically improved from a 67% passage rate in 1998 to a 90% passage rate in 1999 and 2000.

External Challenges

The teachers and principals at this school confronted two external challenges: 1) a continuous media debate about the nature of mathematics instruction, and 2) the political turmoil surrounding state testing.

Educators in this school were often subjected to local and national media information that probably confused and distorted the fundamental issues of mathematics instructional reform. National newspapers and national news magazines created a "math war' The national debate focused on direct teaching of basic mathematics calculation skills versus mathematics problem-solving within a constructivist learning environment. Constructivist theory and problem-solving were nicknamed "fuzzy math."

Through their action-research, educators at this school began to understand constructivist teaching and learning as a movement beyond basic calculation skills. They began to understand that the either-or mentality of basic skills versus problem-solving was an erroneous dichotomy. These educators understood mathematics as both basic calculations skills and problem-solving. They realized that to teach both skills and problem-solving required more instructional time.

The second challenge for principals and teacher-leaders was the complexity and political pressure of state mandated testing. Numerical data from state mathematics tests became the sole indicator of effective mathematics instruction. Teachers and principals confronted the dilemma of teaching to the test or teaching for mathematical understanding. They decided to do both by expanding instructional time for underachieving students. They could not underestimate the political impact of state testing. These educators had to deal with the state test successfully. Local property values, school choice decisions, racially balanced enrollment, and the socioeconomic level of the community could all be potentially affected by state test results.

The following three thematic papers discuss: 1) the challenges of restructuring and reculturing mathematics instruction at the K-4 level, 2) authentic assessment, and 3) implications of these challenges for teacher education programs.

The first paper explains the complex and dynamic process of changing from a behaviorist learning theory to a constructivist learning theory for mathematics instruction in a K4 school. The paper also discusses new roles for principals, teachers and students as they change learning environments and create more time for instruction.

The second paper focuses on how assessment practices in the same school were changed to capture students' growth in understanding and applying mathematics. It also describes the difficulties educators encountered after the initiation of state testing. The paper recounts the impact of high-stake tests on a decade of instruction reform.

The third paper explores how instructional reform in mathematics education might affect teacher preparation programs. This research report was conducted in a different setting in the Midwest. The report focuses on an urban elementary school with a student population that is nearly all African-American. It describes how preservice teachers began their college mathematics methods course with an uncertainty about how to teach mathematics and dissatisfaction about how they were taught mathematics as young students. The mathematics methods course challenged their prior beliefs and provided an alternative pedagogy. However, during their practicum/student teaching, when they were faced with reality of classroom situations, preservice teachers moved back to conventional methods. The study also reveals the impact of state mandated tests on teachers' instructional decision-making and the challenges that state testing may bring for teacher preparation programs.

REFERENCES

Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In T. Cooney & D. Grouws (Eds.), Effective mathematics teaching (pp. 2746). Reston, VA: NCTM.

Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives in theiry and practice. Educational Researcher, 28(2), 4-15.

Cobb, P., Wood, T., & Yackel, E. (1990). Classroom as learning environments for teachers and researchers. Journal for Research in Mathematics Education, 4, 25-146.

Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychology, 31, 175-190.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics K-12. Reston, VA: NCTM,

Wheatley, G.H., & Reynolds, A.M. (1999). Coming to know numbers. Mathematics Learning, Tallahassee, FL.

In stage one, nominations were solicited from the State Department of Education personnel who were familiar with reform initiatives in the state's schools. Over 500 schools were nominated. Nominations were corroborated from at least one other source who had first-hand knowledge of these schools. Demographic information was compiled on each nominated school in order to provide a broad range of school communities. At the end of stage one, 30 schools were under consideration.

In stage two, 45-60 minute interviews were conducted with principals and/or assistant principals. Interviews targeted core areas of study. Principals were asked to describe characteristics of their school community and how these characteristics emerged and changed over time. Principals were also asked to discuss what factors inhibited or enabled a reform agenda.

In stage three, information was organized by: 1) school level (elementary, middle and secondary), 2) location (rural, suburban and urban), 3) school improvement initiative, and 4) focus/status of the change process. Final selection concentrated on schools that had made significant progress toward implementing school change. From the group of 30 schools, twelve were chosen to participate in the cross-case analysis-five elementary schools, three middle schools, and four high schools.

The twelve schools were assigned professors from five local universities. These university researchers were responsible for writing and designing a case study for each school. At each school, a research team was formed consisting of several educators and one or two university professors.

From spring of 1997 through spring of 1999, research teams collected and reviewed documents of student work, observed and participated in classroom instruction, and interviewed teachers, parents, community members, and district administrators. Research teams also met with coordinators from the Canadian university four times during the research process to share information about their individual schools and the school-university research collaboration.

The first two thematic research reports that follow this overview are focused on one of the five elementary schools selected for this cross-case study. It is a K-4 school with 525 students. Sixty-five percent of the students were African-American, 30% were white, and 5% were multiracial or "other." The school is in a suburb whose boundaries are contiguous to a large metropolitan city. The school district has a long tradition of educational excellence. About 97% of its students graduate from college, with many attending prestigious universities.

Historical Perspective

In order to understand the nature of the reform in this school it is important to know the history of the reform; how it evolved and the pivotal events that shaped the reform process. Prior to 1989, the school principal and a handful of teachers recognized the problematic nature of direct, behaviorist theory based instruction for mathematics. They searched for alternatives. After the publication of the NCTM Standards (1989), these educators embarked on a path of mathematics reform that would eventually require them to radically change their teaching and understanding about mathematics. To support reform efforts, the principals wrote a series of grants (1989 - 2000) that totaled approximately $300,000.00. These funds were used to purchase teacher resources and contract with university and secondary mathematics educators to conduct professional development and action-research. Grant funds also supported teachers as instructional writers and designers. Early in the reform, few mathematics textbooks adequately a ddressed the NCTM Standards. Therefore, teachers at this school wrote mathematics lessons and designed what they needed for classroom instruction. Most did not use mathematics textbooks. The major writing effort has provided, to this day, the foundation for professional development in mathematics at this school.

Instructional Challenges

Although the Standards clearly articulated the need for conceptual understanding of mathematical contents such as number and operations, algebra, geometry, measurement, data analysis, and probability, problems emerged about how to effectively implement such a major instructional change. Implementation was problematic because it required elementary educators to acknowledge their lack of content knowledge. It was evident that the Standards report required a different perspective about how individuals learn. In other words, the Standards called for a shift from current learning and teaching practices to practices that reflected constructivism. According to constructivist perspective, cognizing students build all knowledge when they participate in and contribute to the activities of the classroom community (Bauersfeld, 1988; Cobb, Wood & Yackel, 1990; Cobb & Yackel, 1996; Cobb & Bowers, 1999; Wheatley & Reynolds, 1999).

Shifting from direct teaching to active, interactive instruction was a nonlinear process for teachers. Teachers initially were reluctant to implement a different learning theory in mathematics and change their traditional, practices. They were more familiar with textbook tests and workbook pages.

Teachers' reluctance to change instructional practices forced the principal and the assistant principal to create a situation that perturbed the teachers' thinking. For example, fourth grade teachers attended a professional development session where the assistant principal and a university professor "interviewed" a class about the measurement of angles. All students had previous experiences with this topic. During the course of the interview, students were asked to identify angles that the assistant principal formed using a large wooden compass. A student correctly identified and defined a right angle. The teachers were pleased. But when the compass was reversed and the students agreed that the angle was now a left angle, the teachers looked surprised. The assistant principal continued to rotate and flip the right angle. Students renamed the angles as left, upside down angle and a right, upside down angle. When the assistant principal held the angle at the vertex, the students saw the letter V. Teachers were perturbed by these student responses.

Situations like the above episode were critical turning points in the reform process. Teachers saw vividly that what they taught was not how the students built their understanding of the lesson. Slowly, over time, teachers began implementing mathematics dialogues to gather information and assess student understanding by actively listening to students' voices.

The principal and assistant principal evolved into new roles with the reform process. They emerged as passionate visionaries with a strong commitment to restructuring and reculturing mathematics education. They often expressed the need for hiring and involving teachers who wanted to pursue higher academic and intellectual achievement. For example, three educators from this school, including the assistant principal, earned their doctorates during the ten-year reform process.

The principals also became adult learners, and they spent much extra time on weekends and during summers to develop instructional activities and facilitate professional development activities. They emerged as lead teachers and mentors, taking on the responsibility of tutoring potentially underachieving students and modeling a constructivist classroom. They tutored before school and on Saturday mornings to prepare potentially underachieving students for state mandated tests in mathematics.

Structural Challenges

The instructional shift provoked structural changes in the following areas: 1) extended instructional time, 2) roles and relationships, 3) assessment and instructional practices and 4) parental involvement.

Shifting from behaviorist to constructivist teaching required more time for student interactions and communications. In addition, school leaders recognized that major change in mathematics teaching required much more planning and instructional time for mathematics lessons. Daily state requirements of 45 minutes for mathematics were not sufficient to develop deep understanding of mathematical concepts and application of skills. Therefore, the principals and teacher-leaders established a mandate of 90 minutes of teaching for mathematics each day.

Traditional roles and relationships were also restructured. A teacher-leadership team was initiated. Seniority status was not one of the criteria for selection as a teacher-leader. Teachers were selected on their ability to conduct action-research and implement reform in the classroom. These teacher-leaders created and designed instruction and assisted the principals in making instructional decisions. When the district adopted a new mathematics textbook for students, the teacher-leaders advocated against the use of it at the school and the book was not ordered. Teacher-leaders worked with principals, university professors, and secondary mathematics educators to restructure mathematics curriculum around key ideas and topics. They also developed new assessment practices in problem-solving that valued students' illustrated solutions and their written explanations or defenses of mathematical strategies (Wheatley & Reynolds, 1999). These problem-solving assessments were collected and saved for five years in order to capture growth in understanding of major mathematical concepts.

Assessment practices encouraged more parental participation. Teacher-leaders conducted "student-led" conferences where students demonstrated their strengths and weaknesses to parents and teacher. Students also collaborated with parents and teachers to establish appropriate learning goals.

Parent participation began to focus more on issues about learning. Parent-Teacher Organization (PTO) meetings highlighted instructional practices in classrooms that were changing. Parents enthusiastically supported many of the changes in mathematics instruction and requested special "math nights" to "relearn" mathematics in order to assist their children at home.

In the midst of all the reform efforts, the state instituted a fourth grade mathematics proficiency test. The school's low scores (67% passage rate) in mathematics for three years from 1996 to 1998 refocused the reform on how to improve achievement on this instrument. The principal felt that the extended time in the classroom was not sufficient for underachieving students. Therefore, more time for mathematics was created in morning tutoring, after-school Kumon mathematics (an adopted Japanese project), Saturday School, and a tuition-free six-week summer school. After the school provided 200250 extra hours of mathematics to at-risk students, the state test scores radically improved from a 67% passage rate in 1998 to a 90% passage rate in 1999 and 2000.

External Challenges

The teachers and principals at this school confronted two external challenges: 1) a continuous media debate about the nature of mathematics instruction, and 2) the political turmoil surrounding state testing.

Educators in this school were often subjected to local and national media information that probably confused and distorted the fundamental issues of mathematics instructional reform. National newspapers and national news magazines created a "math war' The national debate focused on direct teaching of basic mathematics calculation skills versus mathematics problem-solving within a constructivist learning environment. Constructivist theory and problem-solving were nicknamed "fuzzy math."

Through their action-research, educators at this school began to understand constructivist teaching and learning as a movement beyond basic calculation skills. They began to understand that the either-or mentality of basic skills versus problem-solving was an erroneous dichotomy. These educators understood mathematics as both basic calculations skills and problem-solving. They realized that to teach both skills and problem-solving required more instructional time.

The second challenge for principals and teacher-leaders was the complexity and political pressure of state mandated testing. Numerical data from state mathematics tests became the sole indicator of effective mathematics instruction. Teachers and principals confronted the dilemma of teaching to the test or teaching for mathematical understanding. They decided to do both by expanding instructional time for underachieving students. They could not underestimate the political impact of state testing. These educators had to deal with the state test successfully. Local property values, school choice decisions, racially balanced enrollment, and the socioeconomic level of the community could all be potentially affected by state test results.

The following three thematic papers discuss: 1) the challenges of restructuring and reculturing mathematics instruction at the K-4 level, 2) authentic assessment, and 3) implications of these challenges for teacher education programs.

The first paper explains the complex and dynamic process of changing from a behaviorist learning theory to a constructivist learning theory for mathematics instruction in a K4 school. The paper also discusses new roles for principals, teachers and students as they change learning environments and create more time for instruction.

The second paper focuses on how assessment practices in the same school were changed to capture students' growth in understanding and applying mathematics. It also describes the difficulties educators encountered after the initiation of state testing. The paper recounts the impact of high-stake tests on a decade of instruction reform.

The third paper explores how instructional reform in mathematics education might affect teacher preparation programs. This research report was conducted in a different setting in the Midwest. The report focuses on an urban elementary school with a student population that is nearly all African-American. It describes how preservice teachers began their college mathematics methods course with an uncertainty about how to teach mathematics and dissatisfaction about how they were taught mathematics as young students. The mathematics methods course challenged their prior beliefs and provided an alternative pedagogy. However, during their practicum/student teaching, when they were faced with reality of classroom situations, preservice teachers moved back to conventional methods. The study also reveals the impact of state mandated tests on teachers' instructional decision-making and the challenges that state testing may bring for teacher preparation programs.

REFERENCES

Bauersfeld, H. (1988). Interaction, construction, and knowledge: Alternative perspectives for mathematics education. In T. Cooney & D. Grouws (Eds.), Effective mathematics teaching (pp. 2746). Reston, VA: NCTM.

Cobb, P., & Bowers, J. (1999). Cognitive and situated learning perspectives in theiry and practice. Educational Researcher, 28(2), 4-15.

Cobb, P., Wood, T., & Yackel, E. (1990). Classroom as learning environments for teachers and researchers. Journal for Research in Mathematics Education, 4, 25-146.

Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychology, 31, 175-190.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics K-12. Reston, VA: NCTM,

Wheatley, G.H., & Reynolds, A.M. (1999). Coming to know numbers. Mathematics Learning, Tallahassee, FL.

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Title Annotation: | research on school change initiatives |
---|---|

Author: | Svec, Lawrence V. |

Publication: | Focus on Learning Problems in Mathematics |

Geographic Code: | 1USA |

Date: | Jan 1, 2002 |

Words: | 2242 |

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