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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