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Transcript of Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie...
![Page 1: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/1.jpg)
WELCOMEDr. Ruth Ann MeyerKA2P Project Director
![Page 2: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/2.jpg)
Josh Goss KA2P Project Graduate Assistant
First Year in Review
Connie DoorlagKA2P 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
KA2P Partners
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AlbionAthensBloomingdaleBurr OaksCatholic Schools
CentrevilleClimax-ScottsComstockConstantineFennvilleGobles
Gull LakeHarper CreekLutheran Schools
Kalamazoo MartinMattawanParchment Paw PawSchoolcraftSturgisThree Rivers
Participating School Districts
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Mathematics and Science PartnershipCompetitive Grant Program –
Michigan Department of Education
Financing for Project Provided by
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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
![Page 8: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/8.jpg)
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
KA2P Project Goal/Objectives
Goal:
◦ Help grades 6-12 teachers improve the teaching and learning of algebra and pre-algebra concepts
![Page 9: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/9.jpg)
More Objectives
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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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
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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
Content Emphasis
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The Faces of KA2P
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KA2P Advisory Committee
Dr. Brenda EarhartDirectorKAMSC
Ms. Ruth RoweAssistant
Superintendent, Parchment
Dr. Ruth Ann MeyerDirector
KA2P
Dr. Jane-Jane LoCo-Director
KA2P
Mrs. Connie DoorlagAssociate Director
KA2P
![Page 14: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/14.jpg)
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
Dr. Valentina Aguilar-Zambrano
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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
Daniel Briggs
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Assistant Professor at Miami University
PhD – WMU Mathematics Education Modules:
◦ Function of Proportion◦ Rate
Dr. Dana Cox
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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
Dr. Jon Davis
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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
Connie Doorlag
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Emeriti Faculty at WMU WMU Professor: 1969-2008 PhD - University of Kentucky Special Interest: Complex Numbers Modules:
◦ Complex Numbers◦ Sequences
Dr. Paul Eenigenburg
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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
Katya Gallegos-Custode
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Graduate Assistant M2RI2 Math Education PhD student at
WMU Focusing on the learning of Pre-
Algebra and Algebra Modules:
◦ Connections◦ Integers
Joshua Goss
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Associate Professor at WMU PhD - Florida State University Elementary Mathematics
Education Co-director KA2P grant project Module:
◦ Function of Proportion
Dr. Jane-Jane Lo
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Emeriti Faculty at WMU WMU Professor: 1976-1999 PhD - University of Wisconsin Mathematics Education Director KA2P grant project Modules
Dr. Ruth Ann Meyer
oAlgebraic MisconceptionsoAlgebraic ReasoningoFunction BasicsoSystems of EquationsoTeacher 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
Dr. Allen Schwenk
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Emeriti Professor at WMU WMU Professor: 1997-2008 PhD - University of Bucharest Modules:
◦ Absolute Value ◦ Linear Programming◦ Conic Sections
Dr. Radu Teodorescu
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Graphing Calculators
TI-84 Plus Silver Edition
TI-Nspire with CAS
Fathom 2 and TinkerPlot software
Technology Emphasis
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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
Project Components
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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
![Page 29: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/29.jpg)
Catholic Schools of Greater Kalamazoo FacilitatorMolly Williamson
Comstock FacilitatorsMargo Command-HeymanMarla Reed
Kalamazoo FacilitatorTina Tribu
District Experiences
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Dr. Wendy TackettKA2P Project Evaluator
Evaluation Update
![Page 31: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/31.jpg)
Dr. Jane-Jane Lo KA2P Project Co-Director
Research Component
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Goal
Investigate the common student strategies and misconceptions about selected algebraic ideas across grade levels.
![Page 33: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/33.jpg)
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.
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How many dots will be in the 100th picture? Show your work.
#1 #2 #3 #4
![Page 35: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/35.jpg)
Results of the Written Test
G6 G7 G8 A1 A2
% of correct responses for each grade/course
4.5% 0% 7.7% 11.1% 27.5%
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What patterns did students notice?
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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?
![Page 38: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/38.jpg)
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?
![Page 39: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/39.jpg)
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
![Page 40: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/40.jpg)
General Rules?
Number Sentences:
1) (add 2, 99 times)
2) (add 2, 100 times)
3)
3222......2
1222.....2
100101
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
![Page 41: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/41.jpg)
Table
x = the number of the picture, y = the number of dots in that picture
x 1 2 3 4 …
y 3 5 9 11 …
![Page 42: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/42.jpg)
Graph
x = the number of the picture, y = the number of dots in that picture
0
2
4
6
8
10
12
1 2 3 4 5
![Page 43: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/43.jpg)
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.
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Future Plans
Connie DoorlagKA2P Project Associate Director
Josh GossKA2P Project Graduate Assistant
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Modules already developed for next year:
New Modules
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Absolute Value Functions
Dr. Radu TeodorescuProfessor of Mathematics,
EmeritusDepartment of Mathematics Western Michigan University
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Algebraic Misconceptions
Dr. Ruth Ann MeyerProfessor of Mathematics, Emerita
KAAP Project DirectorWestern Michigan University
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Differentiated Instruction in Algebra
Valentina Aguilar, Ph.D. Applied MathematicsDepartment of MathematicsWestern Michigan University
Katya Gallegos, SpecialistTeaching, Learning and Educational StudiesWestern Michigan University
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Dr. Jon DavisAssistant Professor
Western Michigan UniversityDepartment of Mathematics
Function Representation Translations
via Technology:A Pathway toward Deeper
Function Understandinga f(a)
1 1
2 4
3 9
4 16
5 25
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Linear InequalitiesLinear 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 SchwenkProfessor of Mathematics
Department of Mathematics,Western Michigan University
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Properties of the Real Number Set
Valentina Aguilar, Ph.D. Applied MathematicsDepartment of Mathematics, Western Michigan University
Katya Gallegos, SpecialistTeaching, Learning and Educational Studies,
Western Michigan University
![Page 53: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/53.jpg)
The following topics are in the process of being developed:
Also Being Developed
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Dr. Radu Teodorescu, Professor of Mathematics, Emeritus
Department of Mathematics, Western Michigan University
Conic Sections
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Exponential and Logarithmic Functions
Daniel BriggsWestern Michigan University Instructor
Retired High School Math Teacher
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Function Basics
Dr. Ruth Ann MeyerProfessor of Mathematics, Emerita
Western Michigan University
![Page 57: Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie Doorlag KA 2 P Project Associate Director.](https://reader035.fdocuments.in/reader035/viewer/2022081514/56649cda5503460f949a3b89/html5/thumbnails/57.jpg)
Dr. Jon DavisAssistant Professor
Western Michigan UniversityDepartment of Mathematics
Function Representation Translations
via Technology:A Pathway toward Deeper Function Understanding - II
a f(a)
1 1
2 4
3 9
4 16
5 25
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Integers
0-1
-2
12
3
3210
-1-2-3-4
Joshua GossResearch Assistant
Department of MathematicsWestern Michigan University
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Rate
Dr. Dana CoxDepartment of Mathematics
Miami University
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Rational and Power Functions
Dr. Jon DavisAssistant Professor
Department of Mathematics Western Michigan University
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Sequences
Dr. Paul EenigenburgProfessor Emeritus
Department of Mathematics
Western Michigan University
T1 T2 T3 T4 T5
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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 attendanceEarn a TI-Nspire or a TI-84 Plus calculator for full attendance
Continental Breakfast and Buffet Lunch providedFree parking in Lot 61
Summer 2010
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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
2010 – 2011 School Year
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Statistics Training
TinkerPlots – Middle School Fathom II – High Schoolhttp://www.keypress.com/x5715.xml http://www.keypress.com/x5656.xml
3 day workshop
Earn single-user software for full attendance
Continental breakfast and lunch provided
Summer 2011
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