THE EFFECTS OF WRITING TO WIN STRATEGIES IN …
THE EFFECTS OF WRITING TO WIN STRATEGIES IN MATHEMATICS
Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my Advisor. This thesis does not include propriety or classified information
___________________________________
Brenice L. Brown
Certificate of Approval:
_________________________
Donald R. Livingston, Ed.D.
Associate Professor and Project Advisor
Education Department
THE EFFECTS OF WRITING TO WIN STRATEGIES IN MATHEMATICS
A project submitted
by
Brenice L. Brown
to
LaGrange College
In partial fulfillment of
the requirement for the
degree of
SPECIALIST IN EDUCATION
in
Curriculum and Instruction
LaGrange, Georgia
July 4, 2011
iii
Abstract:
iv
TABLE OF CONTENTS
Abstract..........................................................................................................iii
Table of Contents............................................................................................iv
List of Tables and Figures...............................................................................v
Chapter 1: Introduction...................................................................................1
Statement of the Problem....................................................................#
Significance of the Problem................................................................#
Theoretical and Conceptual Frameworks............................................#
Focus Questions..................................................................................#
Overview of Methodology..................................................................#
Human as Researcher..........................................................................#
Chapter 2: Review of Literature.....................................................................7
Chapter 3: Methodology.................................................................................16
Research Design....................................................................................#
Setting....................................................................................................#
Sample / Subjects / Participants............................................................#
Procedures and Data Collection Methods.............................................#
Validity and Reliability Measures.........................................................#
Analysis of Data...................................................................................#
Chapter 4: Results..........................................................................................22
Chapter 5: Analysis and Discussion of Results..............................................26
Analysis...............................................................................................26
Discussion...........................................................................................31
Implications.........................................................................................33
Impact on Student Learning................................................................33
Recommendations for Future Research..............................................34
References.......................................................................................................35
Appendixes......................................................................................................38
Appendix A
Appendix B
v
List of Tables and/or Figures
Tables
Table 3.1. Data Shell.............................................................................................19
Figures
Figure 4.1 Title of Figure.......................................................................................23
Chapter 1: Introduction
Statement of the Problem
In math classrooms across the state of Georgia, students have low test scores and lack a deep understanding of mathematical concepts (Beecher & Sweeney, 2008). In response to this problem, Georgia has developed new mathematics standards and curriculum. This pilot study will focus on the Mathematics I curriculum which is organized into four content strands: Algebra I, Geometry, Algebra II, and Statistics. The mathematics curriculum stresses rigorous concept development, presents realistic and relevant tasks, and keeps a strong emphasis on computational skills (Georgia Department of Education, 2010). The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulative and a variety of representations, working independently and cooperatively to solve problems, estimating and computing efficiently, and conducting investigations and recording findings. There is a shift towards applying mathematical concepts and skills in the context of authentic problems and for the student to understand concepts rather than merely follow a sequence of procedures (Georgia Department of Education, 2010).
Significance of the Problem
The Georgia K–12 performance standards in mathematics support a strong, cohesive, and coherent curriculum that provides a clear path to higher mathematics and intelligent citizenship. The curriculum encourages students to reason mathematically, to evaluate mathematical arguments both formally and informally, to use the language of mathematics to communicate ideas and information precisely, and to make connections among mathematical topics and to other disciplines (Combs, 2005).
In mathematics classrooms, students will learn to think critically in a mathematical way with an understanding that there are many different ways to a solution and sometimes more than one right answer in applied mathematics (Georgia Department of Education, 2010). According to Burns (1995), teaching mathematics effectively is too complex for a one-dimensional approach. Mathematics is seen as a subject that communicates through the manipulation of symbols in orderly ways. Through traditional instruction, students learn to compute without understanding and why the computation procedures make sense. Missing from this approach has been attention to students explaining the procedures they use, justifying their reasoning, judging the reasonableness of their solutions and reflecting on their thinking (Burns, 1995). Additionally, this curriculum requires that mathematics classrooms at every grade be student-focused rather than teacher-focused using a balanced approach to instruction. Working individually or collaboratively, students should be actively engaged in inquiry related to real phenomena. Knowledge and procedural skills should be developed in this context (Georgia Department of Education, 2010).
The purpose of the pilot study is to use Writing to Win strategies in the math classroom to prompt critical thinking skills. Writing is a tool to provide opportunities for students to explore and discover mathematical concepts. Combs (2005) discussed that Writing to Win critical thinking strategies elevate students’ writing about math beyond procedural description and summaries and promote individual ways of organizing math concepts presented in the class.
Theoretical and Conceptual Frameworks
The conceptual framework of this research is aligned with Tenet 2: Exemplary Professional Teaching Practices in the Lagrange College Education Department’s Conceptual Framework (2005). The study focused on the Competency Cluster 2.2: Instructional Skills which states:
• Candidates use effective verbal, nonverbal, and media communication techniques to encourage students’ development of critical thinking, problem-solving, and performance skills.
• Candidates understand and implement effective and appropriate classroom management techniques that promote democratic classroom communities.
This tenet also aligns with several other state and national standards such as domain 3(learning environments) and Domain 5 (planning and instruction) of the Six Domains of the Georgia Framework for Teaching, Element 1c (professional and pedagogical knowledge and skills for teacher candidates) of the Five Elements of NCATE 2000 Standard 1 for Initial Programs, Principle 4 (multiple instructional strategies), principle 5 (learner motivation and behavior) and Principle 6 (inquiry, collaboration, and supportive interaction) of the Ten INTASC Principles for Beginning Teachers, and Proposition 2 (teachers know the subjects they teach and how to teach those subjects to students) of the Five NBPTS Core Propositions for Experience Teachers (Lagrange College, 2005).
The Lagrange College Education Department (2005) explained how educators should develop instructional skills that are based on “constructivist teaching principles that emphasize the need to teach for conceptual understanding, before content information is presented to learners” (p. 7). In this research, teachers will be able to develop these skills through the use of the constructivist theory. Bruner (1996), states that constructivism is “an active process in which learners construct new ideas or concepts based upon their current or past knowledge” (p. 30). The constructivist theory is a general framework for instruction based upon the study of cognition. Bruner (1996) also explains that the theory of instruction should address three major principles: (1) Instruction must be concerned with the experiences and contexts that make the student willing and able to learn (readiness), (2) Instruction must be structured so that it can be easily grasped by the student (spiral organization), and (3) Instruction should be designed to facilitate extrapolation and fill in the gaps (going beyond the information given). Bruner’s theory is linked to the child development research of Piaget.
Jean Piaget has contributed to our understanding of the development of learning in students. He suggested many comprehensive developmental theories. According to Piaget, each student has thoughts and feelings of their own. A student brings those feelings and thoughts into the classroom where they will form their own opinions about what and now they learn (Phillips, 1995). Writing in mathematics will provide opportunities for students to develop their thoughts and critical thinking skills. This study will investigate the relationship between writing in mathematics and students’ achievement levels through the constructivist theory and the development of teachers’ instructional skills.
Focus Questions
In mathematics, it is important that educators provide all students access to an engaging, stimulating, and enriched learning environment. Therefore, the research question asks “How can educators use Writing to Win strategies to prompt critical thinking in mathematics?” This study focused on three specific areas: advanced content knowledge, affective assesssment and school improvement. The first focus question asks “How do Writing to Win strategies in mathematics affect student achievement levels”? The second focus question asks “How do Writing to Win strategies affect students’ attitudes towards mathematics. The third focus question asks “How will writing in mathematics affect the attitudes of educators”? This will provide opportunities to change the remedial instruction and stress students’ strengths as a means to improving student learning and closing the achievement gap.
Overview of Methodology
The pilot study is an action research study which is undertaken in a local county high school setting located in southwestern Georgia. Action research is used to search for solutions to everyday real problems experienced in schools, or looking for ways to improve instructions and increase student achievement. The process of action research assists educators in assessing needs, documenting the steps of inquiry, analyzing data, and making informed decisions that can lead to desired outcomes need an action research citation here. The subjects are ninth grade students. Three Math I classes were used in the study. The first focus question (How does Writing to Win strategies in mathematics affect student achievement levels?) will be measured by using assessments. A comparison between last year and this year’s End of Course Test will be analyzed using a independent t-test to measure the significance of the data. Student attitudinal pre and post surveys will be used to measure the second focus question (How does Writing to Win strategies affect students’ attitudes towards mathematics?). The survey consists of ten questions using the Likert scale. They were examined using a dependent t test, the chi square test, the Cronmbach Alpha test, and look for categorical and repeating data. Finally, the third focus question (How does Writing to Win strategies impact the overall school improvement plan?) will be determined by an interview by the principal and a focus group of six math teachers. The interview and focus group will be coded for themes on the attitudes and opinions about Writing to Win strategies in mathematics.
Human as a Researcher
I am a graduate of Tuskegee University and have an undergraduate degree in mathematics. I recently received my Masters degree in Curriculum and Instruction from at LaGrange College. I have been teaching for two years as a 9th-10th grade math teacher in the Troup County School System. Prior to this position, I taught two years in Peach County School System as a 9th-12th grade math teacher.
In this pilot study, the goal is to find that writing in the mathematics classroom improved students’ achievement and understanding. I wanted to able to see a significant difference in the last years and this year’s End of Course Test scores. I feel that writing in math is an effective learning technique. Through surveys, I hoped to find that students enjoyed writing in math class and felt it was an effective learning tool. Through teacher interviews, I hoped to find that teachers believed that writing in the mathematics classroom was effective and beneficial to students. Hopefully, they will begin to implement some strategies of writing in their own classrooms.
Chapter 2: Review of the Literature
Improving student achievement in mathematics
Since the No Child Left Behind Act (NCLB) was passed in 2001, the focus on the achievement gap has intensified specifically among culturally, linguistically, ethnically and economically diverse groups (Beecher & Sweeny, 2008). This posed a great concern to educators and policy makers. One major symptom of the problem involves the adoption of high-stakes testing to measure achievement and evaluate school effectiveness. Beecher and Sweeny (2008), explains that the educational literature is replete with recommendations for improving student achievement and closing the achievement gap; however, research suggest that the gap remains. Factors that affect overall student achievement include the rigor of the curriculum, the experience, quality and commitment of the teachers, the learning environment, including safety and expectations of students and class size (Beecher & Sweeny, 2008).
Reshaping School Mathematics, the framework for curricular revision by the Mathematical Sciences Education Board, states that to know mathematics is to investigate and express relationships among patterns (Countryman, 1992). Mathematics teaching must reflect an active, constructive view of learning. Through the constructivist approach, writing can provide opportunities for students to construct their own knowledge of mathematics (Countryman, 1992). Incorporating writing into math class adds an important and valuable dimension to learning by doing (Burns, 1995). Writing encourages students to examine their ideas and reflect on what they have learned. It helps them deepen and extend their understanding. When students write about mathematics they are actively involved in thinking and learning about mathematics (Combs, 2005).
Research has consistently shown that an emphasis on teaching for meaning has positive effects on student learning and achievement (Kilpatrick, 1992). An important factor in teaching for meaning is connecting the new ideas and skills to students’ past knowledge and experience (Hiebert, 1997). According to Burns (1995), teaching mathematics effectively is too complex for a one-dimensional approach. Mathematics is seen as a subject that communicates through the manipulation of symbols in orderly ways. Through traditional instruction, students learn to compute without understanding and why the computation procedures make sense. Missing from this approach has been attention to students explaining the procedures they use, justifying their reasoning, judging the reasonableness of their solutions and reflecting on their thinking (Burns, 1995). However, a balance is needed between the time students spend practicing routine procedures and the time which they devote to inventing and discovering new ideas (Cobb, Yackel, & Wood, 1992).
Improving students’ attitudes toward mathematics
Over the directions of research in mathematics education, there is a growth in the attention paid to the role of attitudes of students. In the field of mathematics education, research on attitude has been believed that student’s attitude towards a subject determines their success in the subject. A student’s constant failure in mathematics can make a student believe that they can never do well in mathematics. On the other hand, a student’s’ successful experience can make them develop a positive attitude towards mathematics. The definition of attitude is described as “the positive or negative degree of affect associated with a certain subject” (McLeod, 1992, p. 576). According to this point of view, mathematics is seen as good if ‘you get it right’ (Tapia & Marsh, 2004). Students who claim not to like mathematics tend to describe incidents from their past. This suggests that negativity is based on established patterns from the past supported by justifying stories (Mason, 1994).
Student beliefs and attitudes have the potential to either facilitate or inhibit learning. In a comparative study, researchers found that there is a direct link between students’ attitudes toward mathematics and student outcomes (Burstein, 1992). Gibbons, Kimmel and O’Ssheal (1997), suggests that students’’s attitudes about the value of learning mathematics may be considered as both an input and outcome variable because their attitudes toward the subject can be related to educational achievement in ways that reinforce higher or lower performance. In other words, students who do well in mathematics, generally have more positive attitudes towards mathematics, and those who have more positive attitudes towards mathematics tend to perform better in mathematics (Gibbons, Kimmel, & O’Ssheal, 1997).
This suggests that students attitude towards mathematics could be enhanced through effective teaching strategies (Akinsola & Olowojaiye, 2008). Educators must be open to different instructional techniques such as writing to reach these students and encourage a more positive attitude toward mathematics.
Organizational change
In order to succeed, efforts to improve instruction must focus on the existing knowledge base in respect of effective teaching and learning. The practice identified reflects a mixture of emerging strategies and practices in long-term use. The strongest possibility of improving student learning emerges where schools implement multiple changes in teaching and learning activities affecting the daily life of students (Mason, 1994). For example, if the aim is to improve students the school might plan to introduce new strategies such as Writing to Win. The value of a teacher focusing more attention on teaching for meaning may not be demonstrated if student assessments concentrate on rote recall of facts and proficient use of isolated skills. The practices are not mutually exclusive but are complementary (Mason, 1994). Teachers must ensure that students are given the opportunity to learn important content and skills. If students are to compete effectively in a global, technologically, oriented society, they must be taught the mathematical skills needed to do so (Phillips, 1995). It is important to note that opportunity to learn is related to equity issues.
The book, Using Equity Audit to Create Equitable and Excellent Schools, discussed education equity, the educational policies, practices and programs necessary to eliminate educational barriers and provide equal educational opportunities. Chapter 10 discussed how to develop nine high-quality teaching skills. It is essential that math educators incorporate all nine of these skills in the classroom because it will ensure that students are learning and deeply understanding the mathematical concepts. In this pilot study, consistent and reliable classroom procedures and routines and communicating high expectations will be implemented. Skill 4 says that “students are actively, cognitively engaged if they are thinking” (Skrla, McKenzie, & Scheurich, 2009, p. 99). This skill ties in with the one of the purposes of writing in math class. Writing strategies will prompt critical thinking. In the math classroom, teachers are often fooled about the level of active cognitive engagement. The reason for this is because some teachers are only using a traditional approach to teaching which causes students to lose interest and eventually become un-engaged. Teachers need to structure learning so that they monitor students’ active cognitive engagement. Writing will allow an opportunity to catch a misunderstanding or a lack of understanding early enough to prevent a gap and ensure equity.
Chapter 3: Methodology
Research Design
A combination of an action research design and an evaluation research design was used for this project. To define the action research design, Charles and Mertler (2002) stated that the action research is used to search for solutions to everyday, real problems experienced in schools, or looking for ways to improve instruction and increase student achievement. The process of action research assists educators in assessing needs, documenting the steps of inquiry, analyzing data, and making informed decisions that can lead to desired outcomes (Charles & Mertler, 2002). Moreover, this method specifically refers to a disciplined inquiry done by a teacher with the intent that the research will inform and change his or her practices in the future.
On the other hand, evaluations research design is involved in making judgments about the value of merit of a program. This method is used to analyze the impact of a particular program on a certain social problem. The process of evaluation research includes comparative content analysis, resultant student achievement, teacher acceptance, student acceptance, observations and interview, and analysis of theoretical tenets (Charles & Mertler, 2002). The overall goal of the project used an action research design that developed something new and an evaluation research design that appraised the quality of the innovation.
Setting
The location of this study is in southwestern Georgia at a local high school. The high school enrolls 784 high school students from grades 9-12, which is a medium sized city with a median household income of $27,976. The large faculty and staff, including fifty-four full-time teachers, serves the student body with an average class size of 14.5. The majority of students enrolled are White, making up about fifty-three percent of all students. Forty-three percent are Black, 1% Asian, 1% Hispanic, and 2% Unknown. The students’ eligible for free lunch is forty-two percent and 9% are eligible for reduced lunch. There were several steps taken to gain access to conduct the study. Permission was given from the principal of the high school, the local county board of education, and the Institutional Review Board.
Participants
The participants of the action research study are ninth grade students who have taken Math I for the first time. The average age of the students is fourteen years old. There are sixteen males and twelve females that will participate in the study. There was one Math I teacher whothat was interviewed. The teacher has been teaching for twenty-six years. She now is the math department chair at the high school. This teacher was selected because she taught Math I ninth grade students. She has also implemented Writing to Win strategies in the classroom.
Procedures and Data Collection Methods
The data shell below describes the overview of the research study methodology. It includes three focus questions, literature sources, type of method and data, how and why data are analyzed, rationale, and strengths/weaknesses.
|Focus Questions |Literature Sources |Type of Method |Why these data|How these data |Rationale |Strengths/ |
| | |and Data |provide valid |are analyzed | |Weaknesses |
| | | |data | | | |
|How does Writing to Win|Burns, M. (1995) |Method: |Type of |Quantitative: |Quantitative: |Validity |
|strategies in |Combs, W. (2005) |Assessment |Validity |Descriptive and |Determine if there|Reliability |
|mathematics affect |Countryman, J. (1992) |EOCT Exam |Content |inferential |are significant |Depend-ability |
|student achievement |Enyart, A. M. & Van | |Parallel Test |statistics |differences |Bias |
|levels? |Zoest, L. R. (1998) | | |Dependent T-test | | |
| | | | | | | |
|How does Writing to Win| |Method: |Type of |Qualitative: |Qualitative: |Validity |
|strategies affect |Meaney, T., Trinick, |Student |Validity: |Independent |Look for |Reliability |
|students’ attitudes |T., & Fairhall, U. |attitudinal pre |Content |T-test |categorical and |Depend-ability |
|towards mathematics? |(2009) |and post survey |Construct |Chi Square |repeating data |Bias |
| |Goos, M., Brown, R., |Likerit Scale |Predictive |Crombach Alpha | | |
| |Makar, K., & | | | | | |
| |Mathematics Education | | | | | |
| |Research Group of, A. | | | | | |
| |(2008) | | | | | |
|How does Writing to Win|Whitin, P. & Whitin, D.|Method: |Type of |Qualitative: |Qualitative: |Validity |
|strategies in |(2000) |Principal |Validity: | | |Reliability |
|mathematics affect the |Phillips, D. (1995) |interview |Content |Coded for themes |Look for |Depend-ability |
|attitudes of educators?|Beecher, M., & Sweeny, |Teacher focus |Construct | |categorical and |Bias |
| |S. (2008) |groups |Predictive | |repeating data | |
| | | | | | | |
| | | | | | | |
| | | | | | | |
Table 3.1: Data Shell
How does Writing to Win strategies in mathematics affect student achievement levels?
In order to determine if Writing to Win strategies affect student achievement levels, a comparison method was conducted. The comparison is between Math I students of this year and Math I students of last year. The scores of the End-of-Course exam were analyzed by using an independent t-test. This method determined if there were any significant differences among the two groups.
How does Writing to Win strategies affect students’ attitudes towards mathematics?
Research on attitude has a long history in mathematics education. Research develops more toward the formulation of measuring instruments such as those by Likert. The study adopted the descriptive survey design using frequency and percentages for the analysis. The instrument used was Student Attitude Scale (SAT) which was adapted from the modified Fennema-Sherman Mathematics Attitude Scales (need to refer to appendix to see survey). The survey consists of 6 items which the students were expected to respond by expressing their level of agreement or otherwise on a four-point scale of Strongly Agree (SA) rated 4, Agree(A) rated 3, Disagree(D) rated 2 and Strongly Disagree (SD) rated 1. The instrument was administered to 30 Math I students and the Cronbach alpha, Chi Square, and Dependent T-test are used for the study determine any categorical and repeating data.
How does Writing to Win strategies in mathematics affect the attitudes of educators?
Attitudes to mathematics and its teaching are important contributors to a teacher’s make-up and approach, because of the effect they can have on a student’s’ attitude to mathematics and its learning but ultimately on student achievement in mathematics (Schoenfeld, 2001). Teachers’ attitude towards mathematics itself includes liking, enjoyment and interest in mathematics, teacher’s confidence in his or her own mathematical abilities, teacher’s mathematical self-concept, and the teacher’s valuing of mathematics (Quinn, 1998). In this research study, interviews and focus groups are used to collect information from those individuals participating in the study (administrators and teachers) to learn from them about their experiences. Interviews are valued for their rich descriptive detail which can help clear an understanding of how intervention is being implemented and connecting with people. The data are coded for themes and categorized by topic and repeating data. The records and documents are extremely valuable in providing tangible evidence of implementation and progress and to analyze attitudes and opinions about Writing to Win strategies in mathematics.
References
Beecher, M., & Sweeny, S. (2008). Closing the Achievement Gap with Curriculum Enrichment and Differentiation: One School's Story. Journal of Advanced Academics, 19(3), 502-530. Retrieved from ERIC database.
Bruner, J. (1996). The Culture of Education, Cambridge, MA: Harvard University Press.
Burns, M. (1995). Writing in Math Class. White Plains, NY: Cuisenaire Company of America, Inc.
Burstein, L. 1992: The analysis of multilevel data in educational research and evaluation.
Review of Research in Education; 8, 158-223. Federal Republic of Nigeria 2004: National Policy on Education (Revised), NERC
Cobb, P.,;Yackel, E.,& ;Wood,T. 1992. A constructivist alternative to the representational view of mind in mathematics education. Journal for research in mathematics education (Reston,VA), vol. 23, p. 2–23.
Countryman, J. (1992). Writing in Mathematics: Strategies that Work. Portsmouth, NH: Heinemann.
Enyart, A. M. & Van Zoest, L. R. (1998). Mathematics the Write Way. In L. Leutzinger (Eds.), Mathematics in the Middle (pp.165-169). Reston, VA: The National Council of Teachers of Mathematics, Inc.
Gibbons, S; Kimmel, H and O’Shea, M. 1997: Changing teacher behaviour through
development: Implementing the teaching and content standards in science. School Science and Mathematics; 97(6), 302-310.
Goos, M., Brown, R., Makar, K., & Mathematics Education Research Group of, A. (2008). Navigating Currents and Charting Directions. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (31st, Brisbane, Queensland, Australia, June 28-July 1, 2008). Volumes 1 and 2. Mathematics Education Research Group of Australasia. Retrieved from ERIC database.
Hiebert, J., et al. 1997. Making sense: teaching and learning mathematics with understanding. Portsmouth, NH: , Heinemann.
Kilpatrick, J. 1992. A history of research in mathematics education. In:Grouws,D.A., ed. Handbook of research on mathematics teaching and learning, p. 3–38. New York,
Macmillan.
LaGrange College Education Department. (2009). Conceptual Framework. LaGrange, GA: LaGrange College.
Mason, J.,: 1994, Researching From the Inside in Mathematics Education: locating an I You
relationship, in Ponte, J. and Matos J. (eds), Proceedings of PME XVIII, Lisbon,
Portugal, 176–194.
McLeod, D. (1992). Research on affect in mathematics education: a reconceptualization. In D.Grows (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp.575-596). New York: McMillan Publishing Company.
Meaney, T., Trinick, T., & Fairhall, U. (2009). Learning How to Represent Mathematics on Paper. Australian Primary Mathematics Classroom, 14(1), 21-27. Retrieved from ERIC database.
Phillips, D. (1995). The good, the bad, and the ugly: The many faces of constructivism. Educational Researcher, 5-12.
Quinn, R. J. (1998). Effects of mathematics methods courses on the mathematical attitudes and content knowledge of preservice teachers. Journal of Educational Research, 91(2),108.
Schoenfeld, A. H. (2001). Mathematics education in the twentieth century. In L. Corno (Ed.), Education across a century: The centennial volume. (pp. 239-278). Chicago, Ill.:National Society for the Study of Education, University of Chicago Press.
Tapia, M., & Marsh I, G. (2004). An instrument to measure mathematics attitudes. Academic Exchange Quarterly. 8 (2), 1-8.
Whitin, P. & Whitin, D. (2000). Math is Language Too: Talking and Writing in the Mathematics Classroom. Reston, Virginia: National Council of Teachers of Mathematics.
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