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INTEGRATED COLLABORATIVE MATHEMATICS Charity M - INTEGRATED COLLABORATIVE MATHEMATICS Charity M Tanaleon B.A., University of California, Davis, 2002 PROJECT Submitted in partial satisfaction of the requirements for the degree of MASTER OF ARTS in EDUCATION (Curriculum and Instruction) at CALIFORNIA STATE UNIVERSITY, SACRAMENTO SUMMER 2009 C 2009 Charity M Tanaleon ALL RIGHTS RESERVED ii - INTEGRATED COLLABORATIVE MATHEMATICS A Project by Charity M Tanaleon Approved by: Committee Chair D/ Julta Lambating au¢t~ .2 6(, 024 q Date 6/ iii L I *Student: Charity M. Tanaleon I certify that this student has met the requirements for format contained in the University format manual, and that this project is suitable for shelving in the Library and credit is to be awarded for the Project. 3raduate Coordinator . Julita Lambating Date v Department of Teacher Education iv Abstract of INTEGRATED COLLABORATIVE MATHEMATICS by Charity M Tanaleon Currentmathematical instructionalpractices remain unchanged, allowing educational practicesand curriculum to remain shallow, undemanding and diffuse in content coverage (NationalResearch Council, 2001). The standardizedmath curriculums are basal programsthat utilize a spiral approach to instruction, often presenting concepts as isolatedor unrelated skills. These concepts present themselves too quickly and in a specified order with educatorsfocusing on basic skills due to the amplified stress of high stakes testing and accountability. These curriculums lack relevance to students' lives, inhibitingeffective brainfunctioning and covering more math topics than other countries. The sources of data used in this project include achievement comparisonsfrom internationalassessments such as the Programfor InternationalAssessment (PISA) and Trends in InternationalMathematics and Science Study (TIMSS). This project grounds itself in constructivist theories of Piaget, Dewey, and Vygotsky, as well as brain research and observational studies examining variationsof problem based learning (PBL) incorporatedinto the classroom. This project provides gradefive teachers with a supplementary math curriculum entitled, Integrated CollaborativeMathematics (IC Math). This is a separate curriculumthat incorporateslessons and songs into an individualize unit and is versatile, allowing teachers the V opportunity to extrapolate individual lessons or songs to supplement the particularmath concept currently taught. IC Math integration of gradefive mathematics and language arts helps students practice these skills while minimizing teacher's time teaching individual standards. Collaborationengages students toward solving real life scenarios as they engage their prior knowledge, and realize that math is relevant to their lives. IC Math attempts to help students gain flexible knowledge, self-directed learning skills, and higher order thinking skills that are necessary to be successful. Committee Chair Datea vi I DEDICATION I dedicate this project, to my family and friends who supported me through this endeavor. Especially my parents for their assistance on this academic journey; Marie and Grace for being a sounding board to my ideas; and to Renee, whose love of math, interest in social justice, and thought provoking ideas helped inspire me to create IC Math. vii h ACKNOWLEDGEMENTS I appreciate the support and encouragement I received from the faculty at CSU Sacramento. Especially, Dr. Julita Lambating, for her patience, understanding, and guidance that helped me focus my ideas and complete this project. I would like to acknowledge Dr. Forest Davis in his assistance toward developing the title, and thank Dr. Frank Lilly for encouraging me to pursue and include my passion for music in this project. Dr. Lilly, your advocacy for Universal design and enthusiasm to enhance students' ability to think critically and evaluate evidence inspires me to become an agent of change. I would like to thank eight-year old, gentleman Oman, for continuously cheering me on through this process. Finally, a special thanks to Renee and Sabrina for their willingness to be my other editors. I appreciate your constant encouragement, motivating words, good food, positive energy, and your unwavering belief in me. viii TABLE OF CONTENTS Page Dedication.............................................................................................................................. vii Acknowledgments..............v.................................................................................................... viii List of Figures ................ x Chapter 1. INTRODUCTION..............................................................................................................1 Overview .................................................................................................................... 1... Purpose of the Project .... 2..............................2 Statement of the Problem ................................... 4 Significance of the Project .................................. 5 Limitations..................................................................................................................6 Definitions of Terms .... 7..............................7 Organization of the Project .................................. 9 2. REVIEW OF RELEVANT LITERATURE .................................. 10 History of Problem Based Learning .................................. 10 Constructivism .................................. 11 Brain Research .................................. 14 Educational Discrepancy .................................. 17 Math Curriculum .................................. 23 21st Century: Skills that Matter .................................. 24 Summary................................................................................................................... 25 3. METHODOLOGY........................................................................................................... 27 Introduction............................................................................................................... 27 ix Integrated Collaborative Mathematics .......................................... 27 Implementation......................................................................................................... 31 Summary................................................................................................................... 31 4. SUMMARY, LIMITATIONS, RECOMMENDATIONS .......................................... 36 Summary................................................................................................................... 36 Limitations................................................................................................................ 37 Recommendations..................................................................................................... 39 Appendix A. Grade five California Subject Standards ..................... ..................... 41 Appendix B. The Restaurateur Unit .......................................... 53 Appendix C. Math Songs .......................................... 111 References .......................................... 121 x LIST OF FIGURES Page 1. Figure 1: Math and language arts standards .............................................. 33 2. Figure 2: The Restaurateurunit overview and integrated standard .................... 34 3. Figure 3: Note/example illustration .............................................. 35 xi 1 Chapter 1 INTRODUCTION Overview Current educational practices focus on academic achievement, especially with the goal of all students demonstrating proficiency in math and reading-language arts by 2014 (Yell, 2006). Bush's 2001 educational legislation, No Child Left Behind (NCLB), set this precedent. Unfortunately, the emphasis to achieve this goal diminishes time spent on problem-solving, critical thinking and enrichment activities, especially in urban schools where procedural computations and obtaining the correct answer is the sole focus (Sutton & Kruger, 2002). Teachers are under tremendous pressure to get students performing at proficient levels. Yell (2006) emphasizes that "100% of a state's students must reach 100% proficiency in both reading- language arts and math by the 2013-2014 academic year" (p. 192). NCLB transformed standardized tests, designating them as the force behind instructional practices; instead of a guiding tool to supplement curriculum standards. Many states and school districts spend more time focusing on NCLB tested areas - reading and math, as well as testing strategies that may give students an advantage during the test (Abrams & Madaus, 2003). Even though the United States (U.S.) focuses on academic achievement through test score improvement, its students continually perform below average on the Program for International Student Assessment (PISA). The Pisa is an assessment that examines a student's ability to understand concepts and apply them to various situations within the subject. The 2006 PISA results reveal that U.S. students performed below the 498 Organization for Economic Cooperation and Development (OECD) average. These students performed behind 31 European and Asian countries in math literacy. Even isolating U.S.'s high achieving students 2 still left the U.S. trailing behind 29 of the 51 participating countries. No measurable changes occurred from the prior 2003 PISA results (Baldi, Jin, Skemer, Green, & Herget, 2007). U.S. students may be capable of solving straightforward computational procedures; however, they lack math literacy. Students are unable
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