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  1. WELCOME Dr. Ruth Ann Meyer KA2P Project Director

  2. First Year in Review • Josh Goss • KA2P Project Graduate Assistant Connie Doorlag KA2P Project Associate Director

  3. Kalamazoo Area Algebra Project A Mathematics/Science Partnership Project

  4. KA2P Partners Western Michigan University Kalamazoo Math/Science Center School Districts in Southwest Michigan

  5. Participating School Districts Albion Athens Bloomingdale Burr Oaks Catholic Schools Centreville Climax-Scotts Comstock Constantine Fennville Gobles Gull Lake Harper Creek Lutheran Schools Kalamazoo Martin Mattawan Parchment Paw Paw Schoolcraft Sturgis Three Rivers

  6. Financing for Project Provided by Mathematics and Science Partnership Competitive Grant Program – Michigan Department of Education

  7. MDE Guidelines state that projects • Have an active and well-defined partnership with STEM staff • Be designed to improve student achievement • Be aligned with the Michigan Professional Development Vision and Standards • Have an evaluation and accountability plan As per 2008 SBE grant criteria

  8. KA2P Project Goal/Objectives • Goal: • Help grades 6-12 teachers improve the teaching and learning of algebra and pre-algebra concepts • Objectives: • Increase mathematics content and knowledge for teaching mathematics of grades 6-12 teachers • Improve articulation and collaboration among grades 6-12 mathematics teachers of participating districts

  9. More Objectives • Establish professional learning communities within participating districts • Provide leadership preparation for teacher facilitators • Improve mathematics achievement of grades 6-12 students • Investigate algebraic misconceptions that interfere with success in algebra courses

  10. Interventions/Activities • PD format: Three Dinner/Dialogues (≈4:00-7:00) • Dinner will be provided and participating teachers will be paid an hourly stipend of $30/hour • Sessions will be facilitated by teacher leaders • Instructional material will be primarily on Interactive DVDs prepared by mathematics and mathematics education professors • Summer Session: Four days devoted primarily to the use of technology to teach algebra

  11. Content Emphasis • Teaching Algebra and Pre-algebra from a function perspective • Addressing Algebra and Pre-algebra Content Expectations • Exploring a variety of strategies/activities for teaching Algebra and Pre-algebra effectively • Including activities that help teachers initiate changes in their classrooms that will support the learning of a more diverse population of students

  12. The Faces of KA2P

  13. KA2P Advisory Committee Dr. Brenda Earhart Director KAMSC Ms. Ruth Rowe Assistant Superintendent, Parchment Dr. Ruth Ann Meyer Director KA2P Dr. Jane-Jane Lo Co-Director KA2P Mrs. Connie Doorlag Associate Director KA2P

  14. Dr. Valentina Aguilar-Zambrano • Visiting Faculty at WMU • Department Chair Universidad San Francisco de Quito: 1997 - 2001 • PhD - Wichita State University • Special Interests: Applied Mathematics, Gender and Mathematics Education • Modules • Differentiated Algebra • Diversity I • Diversity II • Properties of Real Numbers

  15. Daniel Briggs • Mathematics instructor at WMU • Retired high school mathematics instructor • Special interest: Calculus • Modules: • Exponential and Logarithmic Functions • Mathematics Modeling I • Mathematics Modeling II

  16. Dr. Dana Cox • Assistant Professor at Miami University • PhD – WMU • Mathematics Education • Modules: • Function of Proportion • Rate

  17. Dr. Jon Davis • Assistant Professor at WMU • PhD - University of Minnesota • Secondary Mathematics Education • Modules: • Function Representation I • Function Representation II • Rational and Power Functions

  18. Connie Doorlag • KVCC Mathematics Education Instructor: 1990 – 2009 • Masters in the Teaching of Elementary Mathematics • KA2P Project Associate Director • Modules: • Algebraic Reasoning • Systems of Equations • Teacher Facilitator

  19. Dr. Paul Eenigenburg • Emeriti Faculty at WMU • WMU Professor: 1969-2008 • PhD - University of Kentucky • Special Interest: Complex Numbers • Modules: • Complex Numbers • Sequences

  20. Katya Gallegos-Custode • Graduate Student at WMU • Masters in the Practice of Teaching; Intelligence Development and Education • Intellectual Diagnose Specialist • Modules • Differentiated Algebra • Diversity I • Diversity II • Properties of Real Numbers

  21. Joshua Goss • Graduate Assistant M2RI2 • Math Education PhD student at WMU • Focusing on the learning of Pre-Algebra and Algebra • Modules: • Connections • Integers

  22. Dr. Jane-Jane Lo • Associate Professor at WMU • PhD - Florida State University • Elementary Mathematics Education • Co-director KA2P grant project • Module: • Function of Proportion

  23. Dr. Ruth Ann Meyer • Emeriti Faculty at WMU • WMU Professor: 1976-1999 • PhD - University of Wisconsin • Mathematics Education • Director KA2P grant project • Modules • Algebraic Misconceptions • Algebraic Reasoning • Function Basics • Systems of Equations • Teacher Facilitator

  24. Dr. Allen Schwenk • Professor at WMU • PhD – University of Michigan • Special Interest: Graph Theory • Module: • Permutations, Combinations, Pascal’s Triangle, and the Binomial Theorem

  25. Dr. Radu Teodorescu • Emeriti Professor at WMU • WMU Professor: 1997-2008 • PhD - University of Bucharest • Modules: • Absolute Value • Linear Programming • Conic Sections

  26. Technology Emphasis • Graphing Calculators TI-84 Plus Silver Edition TI-Nspire with CAS • Fathom 2 and TinkerPlot software

  27. Project Components • Professional development for grades 6-12 mathematics teachers – during the school year and the summer • Informational sessions for administrators • Preparation of teacher facilitators/leaders • Professional learning communities • Technology/Materials • Research/Evaluation

  28. KA2P by the Numbers (Spring 2010) • 131 participants • 24 facilitators • 23 districts • 40 schools • 48 Dinner/Dialogs held • 297 dinners purchased • 936 hours spent in professional development

  29. District Experiences • Catholic Schools of Greater Kalamazoo Facilitator Molly Williamson • Comstock Facilitators Margo Command-Heyman Marla Reed • Kalamazoo Facilitator Tina Tribu

  30. Evaluation Update Dr. Wendy Tackett KA2P Project Evaluator

  31. Research Component • Dr. Jane-Jane Lo • KA2P Project Co-Director

  32. Goal Investigate the common student strategies and misconceptions about selected algebraic ideas across grade levels.

  33. Preliminary Report • A written test was administrated to 169 students in grades 6-8, Algebra 1 and Algebra 2. • Individual interviews were conducted with 24 selected students.

  34. How many dots will be in the 100th picture? Show your work. #1 #2 #3 #4

  35. Results of the Written Test

  36. What patterns did students notice?

  37. How many dots are in the 100th picture? Verbal Description: Start with 3 dots; then add one group of 2’s each time. Challenge: How many groups of 2’s?

  38. How many dots are in the 100th picture? Verbal Description: Start with 1 dot; then add one group of 2’s each time. Challenge: How many groups of 2’s?

  39. How many dots are in the 100th picture? Verbal Description: In picture #1, there are 1 dot and 2 dots; in picture #2, there are 2 dots and 3 dots….. So in picture #100, there are 100 dots and 101 dots. Answer: 201

  40. General Rules? Number Sentences: (add 2, 99 times) (add 2, 100 times) General Rules: y = 3+2(x-1) = 1+2x y = 1+2x y = x+(x+1)= 2x+1 x = the number of the picture, y = the number of dots in that picture

  41. Table x = the number of the picture, y = the number of dots in that picture

  42. Graph x = the number of the picture, y = the number of dots in that picture

  43. Conclusions • Geometrical Pattern problems are accessible to both the middle school and high school students. • Increasing the experience with complex numerical expressions in middle school may facilitate the learning of symbolic expressions in high school. • Increasing attention to the connections among multiple representations in high school will solidify student reasoning with patterns.

  44. Future Plans Josh Goss KA2P Project Graduate Assistant Connie Doorlag KA2P Project Associate Director

  45. New Modules Modules already developed for next year:

  46. Absolute Value Functions Dr. Radu Teodorescu Professor of Mathematics, Emeritus Department of Mathematics Western Michigan University

  47. Algebraic Misconceptions Dr. Ruth Ann Meyer Professor of Mathematics, Emerita KAAP Project Director Western Michigan University

  48. Differentiated Instruction in Algebra Valentina Aguilar, Ph.D. Applied Mathematics Department of Mathematics Western Michigan University Katya Gallegos, Specialist Teaching, Learning and Educational Studies Western Michigan University

  49. Function Representation Translations via Technology:A Pathway toward Deeper Function Understanding Dr. Jon DavisAssistant ProfessorWestern Michigan UniversityDepartment of Mathematics

  50. Linear InequalitiesLinear Programming Dr. Radu Teodorescu, Professor of Mathematics, Emeritus Department of Mathematics, Western Michigan University