# Relationship of mathematics curriculum on student achievement as related to instructional leadership

Table of Contents

List of Figures............................................................................................................ xii List of Tables............................................................................................................. xiii Chapter 1: Introduction to the Problem..................................................................... 1 Introduction.................................................................................................... 1 No Child Left Behind and Accountability.......................................... 1 Curriculum and Instruction............................................................... 2 Role of the Leader and the Teacher in Curricular Decisions............ 4 Role of the Math Teacher in Curricular Decisions........................... 7 Mathematics Curriculum................................................................... 8 Statement of the Problem............................................................................... 9 Research Question......................................................................................... 10 Definition of Terms........................................................................................ 11 Educational Significance............................................................................... 12 Summary........................................................................................................ 14 Chapter 2: Review of Related Literature................................................................... 15 No Child Left Behind and Accountability...................................................... 15 Curriculum and Instruction........................................................................... 18 Historical Impact............................................................................... 22 Role of the Leader and the Teacher in Curricular Decisions........................ 25 Distributed and Transformational Leadership.................................. 25 Teacher Leadership........................................................................... 31 ix

Professional Development................................................................. 32 Instructional Leadership.................................................................... 33 Summation.......................................................................................... 34 Role of the Math Teacher in Curricular Decisions....................................... 37 Mathematics Curriculum............................................................................... 39 Traditional Mathematics.................................................................... 41 Standards-Based Mathematics........................................................... 43 Balanced Mathematics....................................................................... 46 Summation.......................................................................................... 48 Summary........................................................................................................ 50 Chapter 3: Method..................................................................................................... 53 Participants.................................................................................................... 53 Research Design............................................................................................ 53 Procedures..................................................................................................... 54 Instrumentation.............................................................................................. 58 Data Analysis................................................................................................. 59 Summary........................................................................................................ 60 Chapter 4: Results...................................................................................................... 61 Statistical Analysis......................................................................................... 62 ANOVA............................................................................................... 62 Descriptive Statistics.......................................................................... 63 Cumulative Logit Model.................................................................... 66

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Chapter 5: Conclusions and Recommendations........................................................ 69 Conclusions.................................................................................................... 69 Recommendations.......................................................................................... 71 References.................................................................................................................. 74 Appendices................................................................................................................. 82 Appendix A – IRB Request for Exemption Approval .................................... 82 Appendix B – Survey Cover Letter................................................................. 83 Appendix C – Mathematics Curriculum Survey............................................. 85

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List of Figures Figure Page 1. Mathematics Performance Level Mean Percents By Year............................ 65 2. Mathematics Curriculum Performance Level Mean Percents By Year......... 66

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List of Tables Table Page 1. Multivariate Tests of Between and Within Subjects Effects of Mathematics Achievement by Mathematics Curriculum, Proficiency Level, and Time............................................................................................. 62 2. Univariate Tests of Within Subjects Effects of Mathematics Achievement by Time, Math Curriculum by Time, and Level Within Math Curriculum by Time.......................................................................................................... 63 3. Means and Standard Deviations of Mathematics Benchmark Scores for 2005, 2006, and 2007 by Math Curriculum................................................... 64 4. Ordinal Model with Cumulative Logits for Mathematics Benchmark Percents for 2005, 2006, and 2007................................................................. 68

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1 CHAPTER 1 Introduction to the Problem

Introduction No Child Left Behind and Accountability No Child Left Behind (NCLB) mandates that every child shall achieve high standards, but this is not a one-size-fits-all law. The act intends that educators individualize instruction to meet the unique needs of each student. NCLB, enacted in 2002, demands that all schools test students annually in reading and math, and break down the test results by racial and income groups. Schools where too few students reach state established targets for proficiency face penalties, ranging from paying for private tutoring to reopening the school under new management (Schemo, 2007). Beginning in 2007, some states started tracking individual student progress from year to year. These states can give schools credit if students are within sight of achievement goals, rather than only if they reach them. Students are within sight of achievement goals if they are making progress from below basic or basic classification towards proficiency classification. Tracking individual students is known as the growth model and is intended to improve academic achievement for our nation’s students and quicken the closing of the achievement gap (Schemo, 2007). The renewal of NCLB needs to shift the focus away from test scores to the support of teachers (Leonard, 2007). Scores are important, but only viewed in context of

2 what teachers know about what is happening in their classrooms. For teachers to be accountable, they must disaggregate data and make instructional changes, as necessary, to meet the needs of students and ensure student growth from year to year. Supporting teachers requires more money for salaries, staff development, and programs to make sure teachers develop the skills to engage students to choose to become knowledgeable in a variety of areas, and to become responsible citizens (Leonard, 2007). Providing support to teachers may diminish the intensity of teaching to the test. Teachers face a significant challenge to ensure they leave no child behind, cover the curriculum mandated by state standards, and differentiate instruction based on learners’ specific interests and needs (Wiske, 2004). NCLB revealed a deficiency in mathematics education, especially at the 8 th grade level. As noted by Greenes (2006), the achievement gap in mathematics performance between American students and those in other countries, as well as among various ethnic and socioeconomic groups within our own country, has been the reason for many proposed changes in the mathematics curriculum and the way in which mathematics is taught. Educators are beginning to understand the impact of factors outside of school that affect how children perform academically. Therefore, curriculum and instruction must be centered on the whole child to ensure increased student achievement for all students (Noddings, 2005). Curriculum and Instruction A school’s curriculum and instruction either transmits, or conditions students to conform to, the official version of knowledge and values, or challenges them to think on their own (Gutek, 2005). It is important to be aware that every decision made in regard to curriculum and instruction will impact all students in one way or another. An educator’s

3 job is to make sure that each individual child is taught in a way to encourage success in school and in his/her life ahead. Curriculum is an important part of educational leadership and teachers should play an integral part in developing the curriculum. Critical thinking about instruction must take place in the developmental, implementation, and evaluation stages. Curriculum is the backbone of instruction since it is what is actually being taught in the classroom, school, or district. An aligned curriculum allows a teacher to help every student progress toward meeting the expectations of their school (Barr & Parrett, 2003). Students “need to understand what is expected of them and how and why it connects with their lives” (Barr & Parrett, 2003, p. 357). Various instructional strategies, both vertically and horizontally aligned, should be included in every curriculum in order to provide students with a continuous transition from one grade level to the next. Curriculum and instruction in the twenty-first century has changed significantly from the past. In society today, there is a demand for men and women who can think, reason, and use their minds well to solve problems arising around them (Schlechty, 2002). “Teaching and learning require that both the teacher and the students are mutually engaged in constructing knowledge through critical dialogue” (Gutek, 2005, p. 435). Cooperation among all stakeholders is fundamental to the idea of being lifelong learners. In educational practice, leaders must encourage all of their colleagues to be lifelong learners and educators must focus on inspiring students to achieve their maximum potential. Educational leaders and teachers should prepare students to be able to solve problems through critical thinking.

4 Role of the Leader and the Teacher in Curricular Decisions As educational leaders, it is absolutely necessary that we give teachers a vision of effective instruction to help them in planning and implementing their lessons. Student achievement begins and ends with the quality of the teacher, the instructional program, and its leadership (Gabriel, 2005). When teachers accept common goals for students and complement each other’s teaching, and when supervisors work with teachers in a manner consistent with the way teachers are expected to work with students, then a school reaches its goals (Glickman, Gordon, & Ross-Gordon, 2004). Marzano (2003) defines an expert teacher as one who has acquired a wide array of instructional strategies along with the knowledge of when these strategies might be the most useful. Marzano (2003) suggests providing teachers with an instructional framework for units that use research- based strategies, as defined by Marzano (2001). The framework would include clear learning goals, experiences, expectations, applications, and assessment goals. An effective school leader provides supervision that engages teachers reflection on their practices and encourages a teacher to strive to be the best that they can be; with a continued focus on student achievement at the forefront. An effective leader must be professional at all times. Administration and faculty should feel ownership for what takes place in the school building, with accountability at its highest and everyone sharing responsibility for student learning. The administrator should be aware of and willing to find all resources necessary to provide a comprehensive education for all students. An effective leader should know the strengths of each staff member and bring those strengths together to form a united building (Ubben, Hughes, & Norris, 2001).

5 One of the primary roles of an educational leader is instructional leadership. The leader must identify various instructional strategies that are effective in relation to identified instructional goals and individual students (Glickman, Gordon, & Ross- Gordon, 2004). Effective instruction is seen as the ability of the teacher to use various modes of teaching according to a variety of learning goals and student learning styles (Glickman, Gordon, & Ross-Gordon, 2004). Improved student achievement is the ultimate goal and this focus should guide all educational decisions. Supervisors must encourage teachers to research and to implement successful instructional strategies to meet the needs of all students. A large part of instructional or distributed leadership is empowerment. Ubben et al. (2001) defined empowerment as “to enable”. It is important to create a school climate that allows risk taking, personal contribution, and challenge so that all individuals and organizations are enabled to reach and maximize their highest, unique potential. The principal is in the position to facilitate staff development, orchestrate time, and schedule factors so that teachers have opportunities to work together to solve instructional and curricular problems (Ubben, Hughes, & Norris, 2001). An educational leader should be in every classroom on a regular basis in order to be aware of what is actually taking place in each classroom. It is important to be knowledgeable of each subject area, remaining current in research to improve instruction. The administrator must be aware of many different instructional strategies to meet the unique needs of each individual learner. Teachers will appreciate any assistance in this area because they want what is best for their students (Glickman, Gordon, & Ross- Gordon, 2004).

6 An administrator must always be approachable in a manner that teachers do not feel intimidated. To be an effective leader, one must support teachers, staff, and students. Leadership should encompass a common vision, communication, and collaboration, with every district, school, and classroom fostering a climate and culture of learning. Educational leaders can influence the school, district, and community with their actions. Administrators and teachers should be appropriate role models for students. The school climate must be positive and safe, supplying efficient learning environments to promote academic success. High expectations and standards should be the norm in every school. A child will typically give only what is expected of him or her; educators must expect the best from each individual (Ubben, Hughes, & Norris, 2001). An educational leader must guide teachers to become student leaders. Teachers should guide the students to discover their own learning styles in a way that will benefit the child for sustained learning. An effective administrator will encourage teachers to have high standards for themselves and their students and their knowledge base should be expansive, including all types of strategies. Leaders and teachers must work together to determine the most effective course of action to improve student achievement (Glickman, Gordon, & Ross-Gordon, 2004). Teachers must treat all students with fairness and equality, which should be modeled by the educational leader. Teachers must be committed to continuing education for themselves, as well as for their students. A teacher fills many, diverse roles; the challenge for a leader is to support teachers to take on these roles with excitement. Students have the right to an education that prepares them to be life-long learners. Every child should leave the school building equipped with the knowledge to be productive

7 members of society. It is the job of educators to accomplish this incredible task; all must work together to impact student learning (Cunningham & Cordeiro, 2003). Role of the Math Teacher in Curricular Decisions As a math educator, it is important to realize that mathematics builds upon previously learned concepts, i.e., a spiraling of the curriculum. Students learn at different paces and mature mathematically at different ages. It is important that students are placed according to their level of knowledge. “Math teachers are intuitively skeptical of assigning students who cannot do basic arithmetic to the same classes as students ready to solve complex algebra problems” (Stevens, Jr., Wood, & Sheehan, 2002, p. 95). Parents and teachers are receiving mixed messages on what constitutes quality instruction in mathematics (Confrey, 2006). In mathematics education, teachers have always been faced with the challenge of meeting the varying needs of all students in their classrooms. There is a tough road ahead in mathematics education today. Many elementary teachers currently are using a standards-based approach to teaching mathematics. A standards-based approach allows students to focus on discovering the mathematical concepts being introduced. However, the connection to the algorithms, or the step-by-step processes intended to make mathematical concepts more efficient, is not being made. Most secondary teachers are currently using algorithms to solve problems in the most efficient manner. Students may be confused about what is expected of them and where they are headed. As mathematics frameworks are revised, schools must take another look into the K-12 mathematics curriculum. Curriculum teams should be established to revise the current curriculum and stay abreast of current research. State frameworks provide

8 guidance to ensure the standards are being met at each grade level. Teachers must, also, begin to talk about their instructional practices and reach a balance of standards-based and traditional approaches to mathematics education. Improved student achievement is the ultimate goal, and must guide curriculum development. Mathematics Curriculum A mathematics curriculum is an operational plan for instruction that details what students need to know, how students are to achieve the identified curricular goals, what teachers are to do to help students develop their mathematical knowledge, and the context in which learning and teaching occur (Commission on Standards for School Mathematics, 1989). As applications expand the variety of roles for mathematics, and as technology reduces the role of routine calculations, the balance and connections among different aspects of mathematics will change significantly (Mathematical Sciences Education Board National Research Council, 1990). Mathematical ideas must be linked to and built on one another so that students’ understanding and knowledge deepens and their ability to reason and to apply mathematics expands (National Council of Teachers of Mathematics, 2000). The dawning of the information age caused a shift in theories of learning mathematics (Goldsmith, Mark, & Kantrov, 1998). Three types of theories have emerged. One type is the traditional theory, using textbooks as the primary resource. A second type is the standards-based theory, that is, using investigations to learn concepts. A third type is the balanced theory, using both traditional and standards-based theories together (Goldsmith, Mark, & Kantrov, 1998). As testing pressures continue to increase, educators

9 debate which is the better way to teach math: through traditional memorization and worksheets or through discovery hands-on exploration. Some teachers contend the best approach is a mix of the two (ASCD Smart Brief, 2005). Different students learn mathematics differently. Confrey (2006) discusses the need to improve in how the subject is taught to students on a daily basis in the majority of classrooms. If teachers incorporate different styles/approaches into a math lesson, students will build in computation skills, explanations and proofs, collaboration and real- world application, and non-routine problem solving (Strong, Thomas, Perini, & Silver, 2004). The need to be able to think and reason mathematically has become essential for everyday life (National Council of Teachers of Mathematics, 2000). Technology has become an integral part of mathematics classrooms. New technologies make learning interactive, engaging, collaborative, and linked to the world outside the classroom (Wiske, 2004). Computers, computer software, databases and spreadsheets, digital cameras, SMART boards, graphing calculators, calculator-based laboratories (CBLs), and Navigator systems are just a few of the new technologies available to mathematics classrooms. Teachers are able to approach topics from different angles than a traditional textbook would allow. No common instructional method is found in the highest achieving countries’ mathematics classes; however, technology is a common tool found in international educational settings (Educational Research Newsletter, 2004). Statement of the Problem There is a real problem in mathematics instruction for all children, referred to as “snapshot mathematics” by Jacobs (Perkins-Gough, 2004). Early childhood curriculum

10 maps reflect little conceptual work in developing the skills of addition, subtraction, metrics, and telling time. Teachers need a chance to teach a more solid, language-oriented math curriculum (Roseman, Kulm, & Shuttleworth, 2001). To be literate in math, students should be able to listen and speak mathematically (Perkins-Gough, 2004). Today teachers cover too many topics without developing any of them well (Roseman, Kulm, & Shuttleworth, 2001). High-stakes accountability in mathematics is real. Instructional leadership must be at its highest level to ensure teachers are provided the resources needed to educate students (Gabriel, 2005). The purpose of the study will be to examine the relationship between math curriculum and student achievement, controlling for technology, socioeconomic background, and teacher experience for 8 th grade students at Arkansas middle or junior high schools. Two independent variables will be examined, namely math curriculum, with three levels, traditional, standards-based, and balanced, and proficiency level, with four levels, below basic, basic, proficient, and advanced. One repeated measure dependent variable will be examined, the mathematics student achievement on the ACTAAP 8 th grade Benchmark exam for three years. Three controlling variables will be included, technology, socioeconomic background, and teacher experience. Research Question The study is designed to answer the following research question: 1. What is the relationship of the math curriculum taught, i.e. traditional, balanced, or standards-based, on student achievement on the 8 th grade Arkansas Mathematics Benchmark exam over a three year period?

11 Definition of Terms For the purpose of the study, the following terms must be defined. Balanced Mathematics – A balanced math program would combine computational skills, conceptual understanding, problem solving, and mastery of basic facts (Ainsworth & Christinson, 2000). Balanced mathematics combines traditional and standards-based instructional strategies to teach mathematical concepts. Curriculum – “Curriculum is at the core of any educational system because it defines what schooling should accomplish; it specifies in what content areas no child is to be left behind” (Schmidt, 2004, p. 7). Three types of curricula are the intended curriculum, content specified by the state, district, or school to be taught in a particular course or grade level; the implemented curriculum, content actually delivered by the teacher; and the attained curriculum, content actually learned by students (Marzano, 2003). Mathematics Curriculum – A mathematics curriculum is an operational plan for instruction that details what students need to know, how students are to achieve the identified curricular goals, what teachers are to do to help students develop their mathematical knowledge, and the context in which learning and teaching occur (Commission on Standards for School Mathematics, 1989). No Child Left Behind (NCLB) – NCLB, enacted in 2002, demands that all schools test students annually in reading and math, and break down test results by racial and income groups. Schools where too few students reach state established targets for proficiency face penalties, ranging from paying for private tutoring to reopening the school under new management (Schemo, 2007).

12 Socioeconomic Background – The student’s placement as determined by the free and reduced lunch designation, i.e. the percentage of students who are classified as free and reduced lunch recipients. Student Achievement – The percent of students scoring proficient or advanced on the 8 th

grade Arkansas Mathematics Benchmark exam. Standards-based Mathematics – Standards-based mathematics is considered a problem- based, discovery approach to learning. “In a guided-inquiry approach to mathematics instruction, children investigate phenomena or problems and devise multiple problem- solving strategies as well as stunning facility in expressing their mathematical thinking” (Camins & Berman, 1999, p. 102). Teacher Experience – The number of years the teacher has been in the classroom teaching mathematics curriculum. Technology – The use of graphing calculators, computers, and SMART boards in the classroom. Traditional Mathematics – In the traditional mathematics approach, students follow a pattern of teacher lecture, homework, worksheets, and drill and practice (International Center for Leadership in Education, 2000). Educational Significance The National Council of Teachers of Mathematics (NCTM) has shifted the focus of mathematics learning, teaching, and assessment away from memorization and rote application of procedures toward standards for performance that are based on conceptual understanding and reasoning (Goldsmith, Mark, & Kantrov, 1998). The NCTM Standards do not state that computation is unimportant or that students can function without

13 knowing basic number facts and operations. The Standards do state that decreasing the amount of class time spent on the “drill and kill” approach in order to make more room for conceptually-based learning is more beneficial (Goldsmith, Mark, & Kantrov, 1998). As curriculum is developed, student achievement is a primary focus. It is important to know what type of curriculum has the most positive effect on student success. The quantitative research study comparing math curriculum to student achievement is important due to No Child Left Behind legislation that requires accountability measures. The Standards (2000) call for education that will create a positive shift in attitudes about mathematics for all students. Students should be engaged in educational experiences that will enable them to recognize and value the power of their own mathematical thinking (National Council of Teachers of Mathematics, 2000). The emphasis on engaging students in doing mathematics - making connections, problem solving, reasoning, and communicating - is intended to help students understand the why as well as the how of the mathematics they study (Goldsmith, Mark, & Kantrov, 1998). The best math curriculum needs to be used to improve student achievement. Textbook companies could use the results of the research to design a book that meets the needs of teachers to reach the maximum amount of students. Policy makers can relate the findings to state framework revisions. Research exists on traditional methods and standards-based methods (Camins & Berman, 1999; Goldsmith, Mark, & Kantrov, 1998; Marzano, Pickering, & Pollock, 2001). Balanced instructional strategies have been discussed (Ainsworth & Christinson,

14 2000; Lezotte, 2004), but there is little about balanced methods and the effect on student achievement. There is a need in mathematics curriculum education for further research on the topic at hand. Summary “The capacity to establish and maintain a focus on students and the quality of the experiences they are provided, the capacity to maintain direction, and the capacity to act strategically are the most crucial components to be attended to if we are serious about developing an action plan to improve the quality of America’s schools” (Schlechty, 2000, p. 222). No Child Left Behind legislation mandates that the quality of America’s schools will be improved. The question then becomes “What are the needs of students as they assume the responsibilities of full citizenship in the twenty-first century (Cunningham & Cordeiro, 2003, p. 57)?” Curriculum and instruction must be a focus of all schools. Educational leaders and teachers have to work together to provide the best possible education for all students. “Our progress will come to nothing if our schools are not safe places, orderly places where teachers can teach, and children can learn” (Cunningham & Cordeiro, 2003, p. 41). Cunningham & Cordeiro (2003) quote an African proverb “It takes an entire village to raise a child.” “Learning is everywhere; learning is personal; learning is not about memorizing, but about thinking; learning is for everyone; learning is doing real work; learning is about being mindful; learning is problem solving, alone and with others; learning is using the resources and people around you; learning can happen every minute of every day for every person; and learning is a lifelong process” (Littky et al., 2004, p. 39).

15 CHAPTER 2 Review of Related Literature

No Child Left Behind and Accountability “Public schools in the United States today are under enormous pressure to show— through improved test scores—that they are providing every student with a thorough and efficient education” (Noddings, 2005, p. 8). The clearest indicator of what we value is what we test (English, 2000). Teachers assess students using informal and formal methods. The primary high-stakes test in Arkansas is the Arkansas Comprehensive Testing, Assessing, and Accountability Program (ACTAAP) Benchmark. The Benchmark is given in grades three through eight in literacy and math. End of Course exams are given in literacy, algebra, and geometry. In 2007, NCLB forced districts to begin testing students in science in grades five and seven. Schools are held accountable for student achievement. Adequate yearly progress (AYP) is determined for each district. If the district fails to meet AYP two years in a row, it begins year one of school improvement. In the event the district continues to fail the AYP score and remains in school improvement for three years, the district will be taken over by the state department. Districts must determine a way to improve student achievement. Common quarterly assessments should be developed based on the Arkansas Frameworks Standards to help students prepare for high-stakes testing. Quarterly