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Dr. Ruth Ann Meyer KA 2 P Project Director

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Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director

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A Mathematics/Science Partnership Project Kalamazoo Area Algebra Project

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Western Michigan University Kalamazoo Math/Science Center School Districts in Southwest Michigan

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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 Schoolcraft Sturgis Three Rivers

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Mathematics and Science Partnership Competitive Grant Program – Michigan Department of Education

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As per 2008 SBE grant criteria 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

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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 Goal: ◦ Help grades 6-12 teachers improve the teaching and learning of algebra and pre-algebra concepts

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

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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

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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

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Dr. Brenda Earhart Director KAMSC Ms. Ruth Rowe Assistant Superintendent, Parchment Dr. Ruth Ann Meyer Director KA 2 P Dr. Jane-Jane Lo Co-Director KA 2 P Mrs. Connie Doorlag Associate Director KA 2 P

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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

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Mathematics instructor at WMU Retired high school mathematics instructor Special interest: Calculus Modules: ◦ Exponential and Logarithmic Functions ◦ Mathematics Modeling I ◦ Mathematics Modeling II

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Assistant Professor at Miami University PhD – WMU Mathematics Education Modules: ◦ Function of Proportion ◦ Rate

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Assistant Professor at WMU PhD - University of Minnesota Secondary Mathematics Education Modules: ◦ Function Representation I ◦ Function Representation II ◦ Rational and Power Functions

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KVCC Mathematics Education Instructor: 1990 – 2009 Masters in the Teaching of Elementary Mathematics KA 2 P Project Associate Director Modules: ◦ Algebraic Reasoning ◦ Systems of Equations ◦ Teacher Facilitator

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Emeriti Faculty at WMU WMU Professor: 1969-2008 PhD - University of Kentucky Special Interest: Complex Numbers Modules: ◦ Complex Numbers ◦ Sequences

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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

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Graduate Assistant M 2 RI2 Math Education PhD student at WMU Focusing on the learning of Pre- Algebra and Algebra Modules: ◦ Connections ◦ Integers

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Associate Professor at WMU PhD - Florida State University Elementary Mathematics Education Co-director KA 2 P grant project Module: ◦ Function of Proportion

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Emeriti Faculty at WMU WMU Professor: 1976-1999 PhD - University of Wisconsin Mathematics Education Director KA 2 P grant project Modules o Algebraic Misconceptions o Algebraic Reasoning o Function Basics o Systems of Equations o Teacher Facilitator

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Professor at WMU PhD – University of Michigan Special Interest: Graph Theory Module: ◦ Permutations, Combinations, Pascal’s Triangle, and the Binomial Theorem

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Emeriti Professor at WMU WMU Professor: 1997-2008 PhD - University of Bucharest Modules: ◦ Absolute Value ◦ Linear Programming ◦ Conic Sections

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GGraphing Calculators TI-84 Plus Silver Edition TI-Nspire with CAS FFathom 2 and TinkerPlot software

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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

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131 participants 24 facilitators 23 districts 40 schools 48 Dinner/Dialogs held 297 dinners purchased 936 hours spent in professional development

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Catholic Schools of Greater Kalamazoo Facilitator Molly Williamson Comstock Facilitators Margo Command-Heyman Marla Reed Kalamazoo Facilitator Tina Tribu

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Dr. Wendy Tackett KA 2 P Project Evaluator

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Dr. Jane-Jane Lo KA 2 P Project Co-Director

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

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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.

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#1#2#3#4

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G6G7G8A1A2 % of correct responses for each grade/course 4.5%0%7.7%11.1%27.5%

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Verbal Description: Start with 3 dots; then add one group of 2’s each time. Challenge: How many groups of 2’s?

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Verbal Description: Start with 1 dot; then add one group of 2’s each time. Challenge: How many groups of 2’s?

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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

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

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x1234… y35911…

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x = the number of the picture, y = the number of dots in that picture

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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.

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Connie Doorlag KA 2 P Project Associate Director Josh Goss KA 2 P Project Graduate Assistant

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Modules already developed for next year:

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

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

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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

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Dr. Jon Davis Assistant Professor Western Michigan University Department of Mathematics af(a) 11 24 39 416 525

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

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Permutations, Combinations, Pascal’s Triangle, and the Binomial Theorem Dr. Allen Schwenk Professor of Mathematics Department of Mathematics, Western Michigan University

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Properties of the Real Number Set Valentina Aguilar, Ph.D. Applied Mathematics Department of Mathematics, Western Michigan University Katya Gallegos, Specialist Teaching, Learning and Educational Studies, Western Michigan University

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The following topics are in the process of being developed:

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Dr. Radu Teodorescu, Professor of Mathematics, Emeritus Department of Mathematics, Western Michigan University

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Daniel Briggs Western Michigan University Instructor Retired High School Math Teacher

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Dr. Ruth Ann Meyer Professor of Mathematics, Emerita Western Michigan University

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Dr. Jon Davis Assistant Professor Western Michigan University Department of Mathematics af(a) 11 24 39 416 525

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0 -2 1 2 3 3 2 1 0 -2 -3 -4 Joshua Goss Research Assistant Department of Mathematics Western Michigan University

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Dr. Dana Cox Department of Mathematics Miami University

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Dr. Jon Davis Assistant Professor Department of Mathematics Western Michigan University

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Dr. Paul Eenigenburg Professor Emeritus Department of Mathematics Western Michigan University T1T1 T2T2 T3T3 T4T4 T5T5

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Calculator Workshops TI-Nspire TI-84 June 21 – 24 June 28 – July 1 Middle School: Rood Hall, Rm. 3302 Middle School: Everett Tower, Alavi Commons High School: Everett Tower, Alavi Commons High School: Rood Hall, Rm. 3302 8:30 a.m. – 3:00 p.m. Can earn 2 SB-CEU’s for full attendance Earn a TI-Nspire or a TI-84 Plus calculator for full attendance Continental Breakfast and Buffet Lunch provided Free parking in Lot 61

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Calculator Follow-Up Workshops ◦ One in the fall; one in the spring ◦ Tentatively on a Friday or Saturday Professional Development Choices ◦ Six 3-hr DVD Dinner/Dialogs (DD’s) $30/hr stipend $10 dinner provided ◦ Five 3-hr DVD DD’s and four 1-hr Professional Learning Communities (PLC’s) $30/hour stipend for DD’s with $10 dinner provided $30/session stipend for PLC’s

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Statistics Training TinkerPlots – Middle SchoolFathom II – High School http://www.keypress.com/x5715.xmlhttp://www.keypress.com/x5656.xml 3 day workshop Earn single-user software for full attendance Continental breakfast and lunch provided

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Comments? Questions ? Concerns? Suggestions?

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