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Transcript of Dr. Ruth Ann Meyer KA 2 P Project Director. Josh Goss KA 2 P Project Graduate Assistant Connie...
WELCOMEDr. Ruth Ann MeyerKA2P Project Director
Josh Goss KA2P Project Graduate Assistant
First Year in Review
Connie DoorlagKA2P Project Associate Director
A Mathematics/Science Partnership Project
Kalamazoo Area Algebra Project
Western Michigan University
Kalamazoo Math/Science Center
School Districts in Southwest Michigan
KA2P Partners
AlbionAthensBloomingdaleBurr OaksCatholic Schools
CentrevilleClimax-ScottsComstockConstantineFennvilleGobles
Gull LakeHarper CreekLutheran Schools
Kalamazoo MartinMattawanParchment Paw PawSchoolcraftSturgisThree Rivers
Participating School Districts
Mathematics and Science PartnershipCompetitive Grant Program –
Michigan Department of Education
Financing for Project Provided by
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
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
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
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
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
The Faces of KA2P
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
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
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
Assistant Professor at Miami University
PhD – WMU Mathematics Education Modules:
◦ Function of Proportion◦ Rate
Dr. Dana Cox
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
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
Emeriti Faculty at WMU WMU Professor: 1969-2008 PhD - University of Kentucky Special Interest: Complex Numbers Modules:
◦ Complex Numbers◦ Sequences
Dr. Paul Eenigenburg
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
Graduate Assistant M2RI2 Math Education PhD student at
WMU Focusing on the learning of Pre-
Algebra and Algebra Modules:
◦ Connections◦ Integers
Joshua Goss
Associate Professor at WMU PhD - Florida State University Elementary Mathematics
Education Co-director KA2P grant project Module:
◦ Function of Proportion
Dr. Jane-Jane Lo
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
Professor at WMU PhD – University of Michigan Special Interest: Graph Theory Module:
◦ Permutations, Combinations, Pascal’s Triangle, and the Binomial Theorem
Dr. Allen Schwenk
Emeriti Professor at WMU WMU Professor: 1997-2008 PhD - University of Bucharest Modules:
◦ Absolute Value ◦ Linear Programming◦ Conic Sections
Dr. Radu Teodorescu
Graphing Calculators
TI-84 Plus Silver Edition
TI-Nspire with CAS
Fathom 2 and TinkerPlot software
Technology Emphasis
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
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
Catholic Schools of Greater Kalamazoo FacilitatorMolly Williamson
Comstock FacilitatorsMargo Command-HeymanMarla Reed
Kalamazoo FacilitatorTina Tribu
District Experiences
Dr. Wendy TackettKA2P Project Evaluator
Evaluation Update
Dr. Jane-Jane Lo KA2P Project Co-Director
Research Component
Goal
Investigate the common student strategies and misconceptions about selected algebraic ideas across grade levels.
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.
How many dots will be in the 100th picture? Show your work.
#1 #2 #3 #4
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%
What patterns did students notice?
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?
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?
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
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
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 …
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
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.
Future Plans
Connie DoorlagKA2P Project Associate Director
Josh GossKA2P Project Graduate Assistant
Modules already developed for next year:
New Modules
Absolute Value Functions
Dr. Radu TeodorescuProfessor of Mathematics,
EmeritusDepartment of Mathematics Western Michigan University
Algebraic Misconceptions
Dr. Ruth Ann MeyerProfessor of Mathematics, Emerita
KAAP Project DirectorWestern Michigan University
Differentiated Instruction in Algebra
Valentina Aguilar, Ph.D. Applied MathematicsDepartment of MathematicsWestern Michigan University
Katya Gallegos, SpecialistTeaching, Learning and Educational StudiesWestern Michigan University
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
Linear InequalitiesLinear Programming
Dr. Radu Teodorescu, Professor of Mathematics,
Emeritus
Department of Mathematics, Western Michigan University
Permutations, Combinations, Pascal’s Triangle, and the
Binomial Theorem
Dr. Allen SchwenkProfessor of Mathematics
Department of Mathematics,Western Michigan University
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
The following topics are in the process of being developed:
Also Being Developed
Dr. Radu Teodorescu, Professor of Mathematics, Emeritus
Department of Mathematics, Western Michigan University
Conic Sections
Exponential and Logarithmic Functions
Daniel BriggsWestern Michigan University Instructor
Retired High School Math Teacher
Function Basics
Dr. Ruth Ann MeyerProfessor of Mathematics, Emerita
Western Michigan University
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
Integers
0-1
-2
12
3
3210
-1-2-3-4
Joshua GossResearch Assistant
Department of MathematicsWestern Michigan University
Rate
Dr. Dana CoxDepartment of Mathematics
Miami University
Rational and Power Functions
Dr. Jon DavisAssistant Professor
Department of Mathematics Western Michigan University
Sequences
Dr. Paul EenigenburgProfessor Emeritus
Department of Mathematics
Western Michigan University
T1 T2 T3 T4 T5
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
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
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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