The East Carolina University Program for Effective Teacher Preparation in Middle School Mathematics Ann Bullock, Ron Preston, Sid Rachlin East Carolina

The East Carolina University Program for The East Carolina University Program for Effective Teacher Preparation in Middle School Effective Teacher Preparation in Middle School

MathematicsMathematics

Ann Bullock, Ron Preston, Sid Ann Bullock, Ron Preston, Sid RachlinRachlin

East Carolina UniversityEast Carolina University

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Middle Grade TeacherMiddle Grade TeacherCertification ProgramsCertification Programs

The Middle Grades The Middle Grades Mathematics Mathematics

Teacher Preparation ProgramTeacher Preparation Program



Excellence Through Excellence Through PartnershipPartnership

What were your What were your expectations expectations for the for the mathematics mathematics concentration concentration and what did and what did you receive?you receive?





The The Middle GradesMiddle Grades Mathematics Mathematics


Partnership Partnership Theory to Theory to

PracticePractice Continuous Continuous

ImprovementImprovement

Builds on the Builds on the three strands of:three strands of:

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The The Middle GradesMiddle Grades Mathematics Mathematics Teacher Preparation ProgramTeacher Preparation Program

Admission criteria Program based on INTASC and

SDPI criteria Professional core of classes

consistent with teacher education Six specific courses with field

based assignments Concentration in mathematics

At A Glance:At A Glance:


PARTNERSHIPPARTNERSHIP



Martin

Beaufort

Onslow

Lenoir

EdgecombeNash/Rocky Mount

Pitt

Carteret

Pamlico

Craven

Wilson

Wayne

JohnstonGreene

Jones





Professional DevelopmentDevelopment School



The Clinical Schools Network The Clinical Schools Network and the Professional and the Professional Development School provide the Development School provide the context for moving fromcontext for moving from

TheorTheoryy

PracticPracticee

toto


Clinical Schools Network Clinical Schools Network Move from a one semester to Move from a one semester to

a year-long internshipa year-long internship Professional Development SchoolProfessional Development School

Development of quality field Development of quality field experiences at the junior experiences at the junior levellevel

THEORY TO THEORY TO PRACTICEPRACTICE

Changes:Changes:


Confidence increased Confidence increased because of longer time in because of longer time in school during senior yearschool during senior year


Impact on Impact on Graduates:Graduates:


InterviewsInterviews ArtifactsArtifacts


Evidence:Evidence:QuickTime™ and a

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Assessment as a Driving ForceAssessment as a Driving ForceTeaching the Diverse StudentTeaching the Diverse StudentBecoming a Reflective Becoming a Reflective

PractitionerPractitionerTeaming and CollaborationTeaming and Collaboration


Four Themes:Four Themes:


ReflectionReflection

CONTINUOUS CONTINUOUS IMPROVEMENTIMPROVEMENT

Emphasized at all Emphasized at all stages of the stages of the programprogram

Connected to field Connected to field experiencesexperiences

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““ReflectionReflection is the process of is the process of assessing information or assessing information or events, thinking about and events, thinking about and analyzing them, and then using analyzing them, and then using the results to change or the results to change or enhance future events" (p. 29).”enhance future events" (p. 29).”


Bullock and Hawk, Developing a Teaching Portfolio: A Guide for Preservice and Practicing Teachers, (2000)



THE REFLECTION THE REFLECTION CYCLECYCLE

DESCRIBDESCRIBEE

PLANPLAN ANALYZEANALYZE



Student’s Reflection on a Math Student’s Reflection on a Math LessonLesson

The lesson was successful because students The lesson was successful because students participated, and through informal assessment, participated, and through informal assessment, students seemed to be understanding the content students seemed to be understanding the content addressed within the lesson. . . the lesson was not addressed within the lesson. . . the lesson was not successful because . . . I also insisted on perfection successful because . . . I also insisted on perfection from students on each aspect of the lesson before I from students on each aspect of the lesson before I was willing to move on . . . I ran out of time before was willing to move on . . . I ran out of time before all content was addressed. Teaching this lesson all content was addressed. Teaching this lesson taught me assessment was necessary, drilling was taught me assessment was necessary, drilling was not necessary, and to set my goals at an achievable not necessary, and to set my goals at an achievable level for students.level for students.



Teaching, Learning & Teaching, Learning & Assessing Content Knowledge Assessing Content Knowledge

The Diverse AdolescentThe Diverse Adolescent Managing and Managing and

Communicating in and out of Communicating in and out of the Classroomthe Classroom

Professional DevelopmentProfessional Development TechnologyTechnology


Five Domains of the Five Domains of the Portfolio:Portfolio:


Implementation of framework for quality reflections

CONTINUOUS IMPROVEMENTCONTINUOUS IMPROVEMENT

Changes:Changes:


““When we heard about the state When we heard about the state licensure portfolio requirements licensure portfolio requirements at our beginning teacher at our beginning teacher meeting, we laughed because meeting, we laughed because we realized how well prepared we realized how well prepared we were for this. The portfolio we were for this. The portfolio we did at ECU really prepared we did at ECU really prepared us.”us.”

CONTINUOUS CONTINUOUS IMPROVEMENTIMPROVEMENTImpact on Impact on

Graduates:Graduates:

Sarah Henderson,2000 graduate, Sarah Henderson,2000 graduate, 11stst year teacher at Selma Middle School year teacher at Selma Middle School




…a teacher at my school who is going through National Board asked me to help her with her portfolio and reflections…this was after she looked at the portfolio I created at ECU…

Tracy Britto, 1999 graduate,

2nd year teacherSouthern Nash Middle

School

Impact on Impact on Graduates:Graduates:



EvidenceEvidence InterviewsInterviews ArtifactsArtifacts




The The Middle GradesMiddle Grades MathematicsMathematics


Partnership Partnership Theory to Theory to

PracticePractice Continuous Continuous

ImprovementImprovement

Builds on the Builds on the three strands of:three strands of:

The Middle Grades The Middle Grades MathematicsMathematics Teacher Teacher Preparation ProgramPreparation Program

Background: Mathematics Preparation Background: Mathematics Preparation Programs as Collections of CoursesPrograms as Collections of Courses

Mathematics Courses for Elementary Mathematics Courses for Elementary TeachersTeachers

Mathematics Courses for Secondary Mathematics Courses for Secondary TeachersTeachers

Mathematics Courses for General CollegeMathematics Courses for General College

PreparationPartnershipsConnection to middle gradesReview of current programs and

courses Impact at ECU: Planning a new

program

The MIDDLE MATH Undergraduate The MIDDLE MATH Undergraduate FacultyFacultyEnhancement Project (NSF #DUE-Enhancement Project (NSF #DUE-9455152)9455152)



MIDDLE MATH Grant: PreparationMIDDLE MATH Grant: Preparation

Study reform documents

Invite speakers to address critical issues

Gather input from middle grades teachers


Mathematics EducatorsMathematiciansSchool of Education

RepresentativeTeachers-in-Residence

MIDDLE MATH: Planning PartnershipsMIDDLE MATH: Planning Partnerships


National Science FoundationNational Science Foundation

NC Statewide Systemic NC Statewide Systemic InitiativeInitiative


MIDDLE MATH: Funding PartnershipsMIDDLE MATH: Funding Partnerships


NC State Department of Public Instruction Competencies

NC Standard Course of Study MAA Call to Change NCTM Curriculum and

Evaluation Standards

MIDDLE MATH: Grounded in StandardsMIDDLE MATH: Grounded in Standards


School mathematicsSchool mathematics Mathematics beyond the Mathematics beyond the

schoolschool NCTM process standardsNCTM process standards Applications from middle Applications from middle

grades mathematicsgrades mathematics Alternate solutionsAlternate solutions TechnologyTechnology

MIDDLE MATH: Program ThemesMIDDLE MATH: Program Themes


Problem Problem solvingsolving

CommunicationCommunication ConnectionsConnections ReasoningReasoning

MIDDLE MATH: Process StandardsMIDDLE MATH: Process Standards


The ECU Mathematics ConcentrationThe ECU Mathematics Concentration

Calculus for Calculus for the Life the Life

Sciences IISciences II


Sciences ISciences I

Algebraic Algebraic Concepts and Concepts and RelationshipsRelationships

Data Data Analysis and Analysis and ProbabilityProbability

Euclidean Euclidean GeometryGeometry

Pre-Calculus Pre-Calculus Concepts and Concepts and RelationshipsRelationships

Discrete Discrete MathematicsMathematics

Applied Applied Mathematics Mathematics via Modelingvia Modeling

Teaching Teaching Mathematics in Mathematics in

the Middle the Middle GradesGrades


Special courses for Special courses for allall middle grades teachersmiddle grades teachers

Mathematics Concentration:Mathematics Concentration:

Algebraic Algebraic Concepts and Concepts and RelationshipsRelationships

Data Data Analysis and Analysis and ProbabilityProbability

Euclidean Euclidean GeometryGeometry


Problem-solving focusConnections to middle

gradesUse of toolsReflection on acquired

knowledgeMultiple representationsDevelopment over time

Algebraic Concepts and RelationshipsAlgebraic Concepts and Relationships

The Middle Grades The Middle Grades MathematicsMathematics Teacher Preparation Teacher Preparation ProgramProgram

Research and Development ModelResearch and Development Model

MIDDLE MATH: A Project to Improve the Undergraduate Mathematics MIDDLE MATH: A Project to Improve the Undergraduate Mathematics Preparation of Middle Grades Teachers (NSF Grant #DUE-9752659)Preparation of Middle Grades Teachers (NSF Grant #DUE-9752659)

Develop Initial Develop Initial Materials (Based on Materials (Based on thought experiments, thought experiments, beliefs, experiences, beliefs, experiences, etc.)etc.)

Conduct Conduct Task-Based Task-Based InterviewsInterviews

Teach Teach Class in Class in Video Video

ClassroomClassroom

Form Form InstructionInstructional Model al Model

and Revise and Revise TasksTasks

Reflect Reflect and and

ReviseRevise

Teach Teach ShadoShado

w w ClassClass

Revise Revise Materials for Materials for Next Next SemesterSemester


Mathematics Concentration: General CoursesMathematics Concentration: General Courses

Courses with other majors Applications


Sciences IISciences II


Sciences ISciences I


Mathematics Concentration: Mathematics Concentration:

Pre-Calculus Pre-Calculus Concepts and Concepts and RelationshipsRelationships

Discrete Discrete MathematicsMathematics

Applied Applied Mathematics Mathematics via Modelingvia Modeling

Teaching Teaching Mathematics in Mathematics in

the Middle the Middle GradesGrades

Special courses Special courses for middle for middle grades grades mathematics mathematics teachersteachers


Capstone course for mathematics Capstone course for mathematics concentrationconcentration

Models and projects tie to Models and projects tie to previous courseworkprevious coursework

Large-scale problems done in Large-scale problems done in teamsteams

Technology appropriate for large-Technology appropriate for large-scale problemsscale problems

Connections to the middle gradesConnections to the middle grades

Applied Mathematics Via ModelingApplied Mathematics Via Modeling


““In-class mini-projects were helpful in seeing others’ In-class mini-projects were helpful in seeing others’ complete thought process to solve the problem instead of complete thought process to solve the problem instead of just the actual solution. You get to discuss the various just the actual solution. You get to discuss the various ways you try to solve the problem before deciding which ways you try to solve the problem before deciding which model to use.”model to use.”

Applied Mathematics Via Modeling: End of Course Survey

Impact: Problem Solving as a ThemeImpact: Problem Solving as a Theme

““MATH 1067 helps you explore problem solving and MATH 1067 helps you explore problem solving and reasoning areas in math.”reasoning areas in math.”

““It is important to be open-minded and accepting to It is important to be open-minded and accepting to alternate solutions of problem solving, another focus alternate solutions of problem solving, another focus of the class.”of the class.”

Algebraic Concepts & Relationships: Describe course for future students


Impact: Problem Solving as a ThemeImpact: Problem Solving as a Theme

What were your What were your expectations expectations for the for the mathematics mathematics concentration concentration and what did and what did you receive?you receive?




Impact: Preparation to TeachImpact: Preparation to Teach

“But most of all I would tell them to go into this class with a good attitude, and if you REALLY want to become the best teacher you can be, this class will be extremely beneficial.”

“It is indeed an INTENSE class to get your geared up and ready to teach middle grades mathematics.”

Student Reflections from Algebraic Concepts and Relationships


Impact: Changing PerspectivesImpact: Changing Perspectives

“I enjoyed this class very much. The work was very demanding, but doing group projects introduced new perspectives and helped me to explore different ideas.”

(Models class reflection)

“There’s a bunch of different ways to [solve a problem]. And it was frustrating to me because I’m the type of person that I like to have one way to do it and then I’ll remember that way and anytime I see a problem like that I know I am going to get it right. . . . I think that was good because now that I’m in a classroom I don’t do it like I was taught. I want to find out how . . . they did it and why they did it this way. I think that was good. It made me change my expectations of math.” (First-year teacher reflection)


Program Changes:Program Changes: ActualActual and and ConsideredConsidered

Flexibility with pre-requisitesFlexibility with pre-requisites Creation and re-creation of Pre-Creation and re-creation of Pre-

calculuscalculus Experimentation with Euclidean Experimentation with Euclidean

GeometryGeometry

Timing of Algebraic Concepts and Timing of Algebraic Concepts and RelationshipsRelationships

Increased Emphasis on TechnologyIncreased Emphasis on Technology

The The Middle Grades MathematicsMiddle Grades Mathematics Teacher Preparation ProgramTeacher Preparation Program

The Case of Denise Johnston:The Case of Denise Johnston:Illustrating the three strands of:Illustrating the three strands of:

Continuous ImprovementContinuous Improvement

Theory to PracticeTheory to Practice

PartnershipPartnership

The The Middle Grades MathematicsMiddle Grades Mathematics Preparation ProgramPreparation Program

The Case of Denise Johnston: BackgroundThe Case of Denise Johnston: Background

Transfer from community Transfer from community collegecollege

Took six of eight Took six of eight mathematics mathematics concentration courses at concentration courses at ECUECU

Mathematics and science Mathematics and science concentrationsconcentrations

1999 graduate1999 graduate Overall GPA:Overall GPA: 3.6113.611 Math GPA:Math GPA: 2.8332.833 MIDG GPA:MIDG GPA: 3.8883.888

The The Middle Grades MathematicsMiddle Grades Mathematics Preparation ProgramPreparation Program

NTE Math Score: 540 Praxis II PLT Score: 174 Interned at H. J.

McDonald Middle School Received teaching license Teaching at Arapahoe

Charter School

The Case of Denise The Case of Denise Johnston: BackgroundJohnston: Background

The The Middle Grades Middle Grades MathematicsMathematics Teacher Teacher Preparation ProgramPreparation Program

Portfolio content knowledge reflection centered on Calculus II, the only mathematics class in which she did not get an “A” or “B.” Her grade was “D.”

“The two attached tests demonstrate significant improvement that I made in my calculus class. This intellectual development meets INTASC Standard 1 since it proves I have an understanding of the central concepts and structures of the discipline I plan to teach. After all, calculus builds upon the algebraic skills eighth-graders are learning. . . The next grade may look like a mere 76, but to me it is a reflection of countless hours spent in study sessions with my professor and a partner. . .”


The The Middle Grades Middle Grades MathematicsMathematics Teacher Teacher Preparation ProgramPreparation Program

NCCTM conference attendanceRevisions of modeling projects Improved instructional pacingFirst internship evaluation: “A

brisker pace will leave more time to complete assignments.”

Third evaluation: “Instructional time is used for the students’ best advantage.”


The The Middle Grades MathematicsMiddle Grades Mathematics Teacher Preparation Teacher Preparation ProgramProgram

““Since communicating humor in the Since communicating humor in the classroom does not come naturally for classroom does not come naturally for me, I used the media to do it for me. me, I used the media to do it for me.

Theory to PracticeTheory to PracticePortfolio Reflection on Geometry Portfolio Reflection on Geometry UnitUnit

I opened the unit with a comic transparency to show the students that math can be lighthearted. I used another comic to introduce angles.”


Theory to PracticeTheory to PracticeInstructional Competence Instructional Competence Evaluation from University Evaluation from University SupervisorSupervisor““Miss Johnston has a strong command Miss Johnston has a strong command of the content and uses varied of the content and uses varied deliveries to creatively present deliveries to creatively present lessons. Many charts, illustrations, lessons. Many charts, illustrations, relevant examples, and hand-on relevant examples, and hand-on experiences are provided to assist experiences are provided to assist students in the learning process. . . students in the learning process. . . Miss Johnston provides many Miss Johnston provides many opportunities for students to work in opportunities for students to work in cooperative groups. She easily cooperative groups. She easily modifies for exceptional children . . . modifies for exceptional children . . . Her questioning skills are excellent.”Her questioning skills are excellent.”


PartnershipsPartnershipsComments about professional Comments about professional attitudes and relationships from attitudes and relationships from university supervisor during university supervisor during internship:internship: “Her ability to organize

[documentation of misbehavior, educational needs] is valuable when communicating with parents, team members, teacher assistance teams, and administrators.”

“Her cooperative and eager manner has made her a valuable member of the eighth grade team.”


PartnershipsPartnerships

Brought sixth-grade students to ECU campus for a mathematical modeling field trip conducted by the Applied Mathematics Via Modeling class.

Came back to campus to provide feedback on the mathematics concentration.

““Throughout the unit, I not only asked Throughout the unit, I not only asked students for their answers to the students for their answers to the problems (which is what they are problems (which is what they are accustomed to), but I also requested accustomed to), but I also requested the process used to arrive at the the process used to arrive at the answer. The class seemed quite answer. The class seemed quite frustrated initially, but as they frustrated initially, but as they adjusted to verbal and written adjusted to verbal and written explanations, I realized just how much explanations, I realized just how much this method enhanced their learning.”this method enhanced their learning.”


Impact: Communication in Problem Impact: Communication in Problem SolvingSolvingReflection on Geometry Unit in PortfolioReflection on Geometry Unit in Portfolio

““She uses questioning strategies She uses questioning strategies extremely well in clarifying and extremely well in clarifying and redirecting learning. . . Ms. redirecting learning. . . Ms. Johnston diagnoses students’ Johnston diagnoses students’ strengths and weaknesses.”strengths and weaknesses.”


Impact: Strategies and AssessmentImpact: Strategies and Assessment

Comments from university Comments from university supervisor during third supervisor during third internship evaluationinternship evaluation

““We really got into the significance of how a We really got into the significance of how a problem is solved. And because we covered problem is solved. And because we covered that so much and just dug really deep into it, that so much and just dug really deep into it, that’s the way I teach. I try to show the kids that’s the way I teach. I try to show the kids that its not as important that you get a right that its not as important that you get a right answer, but that your process is right. And so answer, but that your process is right. And so I’m teaching them to analyze what they’ve I’m teaching them to analyze what they’ve done. They’re learning to look back and done. They’re learning to look back and check over their work and that’s what check over their work and that’s what learning problem-solving is all about anyway learning problem-solving is all about anyway – to be able to look back at what you’ve done – to be able to look back at what you’ve done and see why you’ve messed up or how to and see why you’ve messed up or how to improve.”improve.”

Comments after Teaching a Half YearComments after Teaching a Half Year


Impact: Problem-Solving ProcessImpact: Problem-Solving Process

Impact: Confidence from InternshipImpact: Confidence from Internship

Comments During First Year of Comments During First Year of TeachingTeaching




Principal scored Ms. Johnston above Principal scored Ms. Johnston above average on all eight teacher evaluation average on all eight teacher evaluation indicators. He noted she is well prepared indicators. He noted she is well prepared and that her plans follow the NCSCS. “ECU and that her plans follow the NCSCS. “ECU has prepared her well.” Concerning EOG has prepared her well.” Concerning EOG testing, Arapahoe made “school of testing, Arapahoe made “school of distinction” this year. In math, the eighth-distinction” this year. In math, the eighth-grade level at 3 or 4 was 92.5%; seventh grade level at 3 or 4 was 92.5%; seventh grade was 97.5%, and sixth grade, which grade was 97.5%, and sixth grade, which Ms. Johnston taught, was 89.5%.Ms. Johnston taught, was 89.5%.


Impact:Impact: Principal Principal Evaluation of 1st-Evaluation of 1st-Year TeachingYear Teaching

GOAL 2: Increase significantly the number of mathematics and science teachers and improve the quality of their preparation.

Action Strategies: What Needs to HappenAction Strategies: What Needs to Happen

To identify successful approaches and To identify successful approaches and expand the pool of exemplary institutions expand the pool of exemplary institutions and well-prepared new teachers, rigorous and well-prepared new teachers, rigorous criteria are needed beyond those already criteria are needed beyond those already used by credentialing and accrediting used by credentialing and accrediting bodies. bodies.

Designation as an Designation as an exemplary program must exemplary program must be highly selective, a mark be highly selective, a mark of prestige; nonetheless, of prestige; nonetheless, there should be no there should be no artificial limit on the artificial limit on the number of institutions number of institutions accorded that status.accorded that status.

The East Carolina University Program for The East Carolina University Program for Effective Teacher Preparation Effective Teacher Preparation in Middle School Mathematicsin Middle School Mathematics

Ann Bullock, Ron Preston, Sid RachlinAnn Bullock, Ron Preston, Sid Rachlin




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The East Carolina University Program for Effective Teacher Preparation in Middle School Mathematics Ann Bullock, Ron Preston, Sid Rachlin East Carolina