System-wide Change for AllLearners and Educators

Department of Education MSP Meeting Breakout SessionThursday October 20, 2005

Washington D.C.

Terry Millar – SCALE PI, Mathematics Department, UW-Madison

Eunice Krinsky – QED Co-PI, Mathematics Department, CSU Dominguez Hills

Mary Ramberg – Math Masters PI , Director of Teaching and Learning, MMSD

Bruce King – SCALE Researcher, WCER, UW-Madison

Peg Smith – Department of Instruction and Learning, Univ. of Pittsburgh

Brian Sniff – Math Masters Project Director, Teacher, MMSD

LAUSD

PPSD

Univ. of Wisconsin

Univ. of Pittsburgh

MMSD

DPSIFL

Metro State

CSU Dominguez Hills

CSU Northridge

CSU Los Angeles

UCLA

USC

Johnson and Wales University

SCALE

SCALE An NSF Comprehensive MSP

~50 coordinated working groups serving

~1,000,000 students

~40,000 educators

Many institutions

SCALE’s theory of actiondepends on leverage and collaboration

Agenda

SCALE Introduction

Disciplinary Literacy –

Pedagogical Knowledge and Understanding

Middle School Math Teacher Knowledge and Understanding

Explanation Structures – Content Knowledge and Understanding

Warm up – QED pre/post test questions

Example of Partnership Approach – Math Masters Program

Formative Evaluation and Measurement

Professional Development EvaluationExamining the Influence on Teachers’ Content

Knowledge and Classroom Practice

Evaluations were joint efforts between the SCALE research

and evaluation team and district-university partners.

• Successful professional development enhances teachers’ content knowledge and pedagogy.

• Professional development outcomes are regularly assessed.

• Data Sources: Pre & Post-Tests, Content Course evaluations, Inventory on instructional practices, Participant reflections on follow-up activities, Focus group interviews.

• Pre/Post-tests: Jointly developed to assess understanding of specific content covered in each course.

Formative Evaluations

QED Summer Math Institute Study– Examination of how professional development affects teacher

content understanding

QED Follow-up Study/Support– Examination of teacher implementation of curriculum units

developed during the summer institutes

Math Masters Content Course Evaluation– Study of gains in teacher content knowledge

Math Masters Pedagogy Course Evaluation– Qualitative study of teacher implementation of instructional strategies

Enhancing Teacher Content KnowledgePromising results from Math Masters

• Teachers with lower pre-test scores had larger gains.

• Participating teachers had statistically significant gains in all four content courses.

• Effect sizes show positive influence on teacher content learning.

• Education levels and years teaching math were not associated with differences in gains.

Pre-test scores and overall gains

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10

Pre-test scores

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Quality Educator Development (QED)U.S. Department of Education Teacher Quality Enhancement award

In partnership with SCALE

Three week middle school teacher math institutesFoci: Content knowledge Pedagogical content knowledge

ELL strategies Case StudiesPlanned and taught by teams of: Math faculty Math Education faculty LAUSD Master Teachers

Evaluation tools include pre/post exams

Work of two teachers on two problems (The teachers were selected on the basis of large pre/post exam score gains)

Scoring rubric

Quality Educator Development (QED)U.S. Department of Education Teacher Quality Enhancement award

In partnership with SCALE

Scoring Instructions

1. Read the rubric for the problem that you are scoring.

2. Score, according to the rubric, the problem on the pre-test and post-test which has been assigned to your group.

3. Do not write on the test paper.

4. Jot down the score on a separate paper and join your group in discussion.

Quality Educator Development (QED)U.S. Department of Education Teacher Quality Enhancement award

In partnership with SCALE

Discussion Instructions

Consider the following questions:

What evidence did you find in growth of teacher content knowledge?

What evidence did you see that would indicate that the teacher would be able to use that increased knowledge to enhance their instruction?

What next steps for the project would you see as necessary?

Official Scoring Results

Pre-Test Post-Test

6867 #1Total possible = 16

6 13.5

6867 #2Total possible = 15

5.17 12.5

8757 #1 4.33 12.67

8757 #2 5 10.67

Quality Educator Development (QED)

Total Test Results (51 possible)

Pre-Test Post-Test

6867 23.16(45.4%)

41.5(81.4%)

8757 22.83(44.8%)

35.32(69.3%)

Total Group 32.6(63.8%)

37.3(73.2%)

Quality Educator Development (QED)

Math Masters ProgramWisconsin Department of Public Instruction

Title IIb MSP Project

+x

+ 9 other Wisconsin School Districts

2004 -2005 Math Masters Project (MMP) Wisconsin Department of Public Instruction Title IIB Grant

In partnership with SCALE

Four, 20-hour Professional Development Workshops followed by four optional online workshops on implementing quality math instruction using the POL’s

Foci: Content knowledge Pedagogical content knowledge Planned and taught by teams of: UW Math Faculty MMSD Instructional Resource Teachers

Evaluation tools include pre/post exams, and correlation with student achievement data

All courses were repeated in the Summer of 2005

2004-05 School Year Results

Pre-TestAverage

Post-TestAverage

Average Gain

Attendance

Statistics and Probability 55% 72.5% 17.5 39

Algebraic Relationships 66% 80% 14 25

Geometry 55% 71% 16 14

Measurement 46% 61% 15 12

2004-05 Summer Repeat Results

Pre-Test

Average

Post-Test

AverageAverage Gain

Attendance

Measurement 45% 57% 12 10

Algebraic Relationships 72% 83% 11 14

Geometry 45% 68% 23 12

Statistics and Probability Cancelled

2005 -2006 Math Masters Project (MMP) Wisconsin Department of Public Instruction Title IIB Grant

In partnership with SCALE

Six, 30-hour Professional Development Workshops followed by 10 - hour online workshops on implementing quality math instruction using the POL’s

Foci: Content knowledge Pedagogical content knowledge Planned and taught by teams of: UW Math Faculty MMSD Instructional Resource Teachers UW Math Ed. Graduate Student

Evaluation tools include pre/post exams, and correlation with student achievement data

All courses will be repeated in the Summer of 2006

2005-06 School Year ResultsPre-TestAverage

Post-Test

AverageAverage Gain

Attendance

Statistics and Probability 58 82 24 15

Algebraic Relationships 52 71 19 10

Measurement 52 71 19 15

GeometryProjected 27 Nov-Dec 06

Algebraic Relationships II

Jan – Feb 2006

Proportional Reasoning

April-May 2006

Disciplinary Literacy (DL)In partnership with SCALE

Drawing on work from the NSF-funded COMET, ASTEROID, and ESP Projects

Participants: Coaches (teacher-leaders) from urban school districts

Structure: 3-day institutes 2-3 times per yearDistrict-level support for implementation

Foci: Mathematics Knowledge for Teaching Knowledge for Coaching

Approach: Situate teacher learning in the practice of teaching

Situating Teacher Learning in the Practice of Teaching

Materials that depict the work of teaching (e.g., student work, mathematics instructional tasks, classroom episodes) are used as sites for critique, inquiry, and investigation.

Theories or general principles are seen as emerging from the close examination of practice.

Elements that are often treated separately -- content and processes, thought and feeling, and teaching and learning -- are integrated.

Practice-Based ExperiencesExploring and analyzing mathematical tasks from textbooks and other sources;

Examining illuminations of students’ thinking as represented in written responses to open-ended tasks, explanations given by students during instruction, and oral responses in interview situations ; and

Analyzing episodes of teaching through narrative cases, video, and live observation.

Smith, 2001

Strength of Case Methods

Case methods are a strategy for overcoming many of the most serious deficiencies in the education of teachers. Because they are contextual, local, and situated – as are all narratives – cases integrate what otherwise remains separated. Content and process, thought and feeling, teaching and learning are not addressed theoretically as distinct constructs. They occur simultaneously as they do in real life, posing problems, issues, and challenges for new teachers that their knowledge and experiences can be used to discern.

Shulman, 1986

Case Design

Purposeful design

Make salient key ideas related to: Important mathematical contentPedagogical practices that influence how students

engage in mathematical activity and what they learn through the process

Format:Begin with a description of the teacher, students, and

the schoolDescribe the teacher’s goal for the lesson and the

unfolding of the actual lesson in a fairly detailed way

The Power of a Case

Particulars Generalities

The Power of a Case

Particulars Generalities One’s

Own Practice

Advantages of CasesCreates opportunities to see new versions of teaching and

learning and to understand things differently;Fosters critical analysis and reflection;Provides an opportunity to pursue questions and puzzles

that are deeply rooted in practice, but not their practice;Helps “ground” the discussion of abstract mathematical

and pedagogical ideas;Portrays the complexities and dilemmas of teaching;Connects mathematics content and pedagogy; andProvides a common experience for teachers to discuss,

analyze, and reference. Smith, 2000, p.

36

Explanation StructuresDavid Perkins et al

What is an Explanation Structure?

1. Perkins, D. N., Crismond, D., Simmons, R., & Unger, C. (1995). Inside Understanding.

“It is a rich network of explanatory relationships that are encoded mentally in any of the many ways the mind has available – through words, images, cases in point, anecdotes, formal principles, and so on . . .

Any explanation structure includes a stable substrate and momentary extensions, many of which will be forgotten but others that will get consolidated into the substrate. An explanation structure only counts as an understanding because it is extensible and revisable. If not, it would be just a rigid template.” 1

It is what we have when we have an understanding

A Metaphorical Picture of an Explanation Structure:

The word knowledge plays an important role in the education literature on mathematics. For example:

Content Knowledge

Pedagogical Knowledge

Pedagogical Content Knowledge – as in Shulman

Knowledge of and about Mathematics – as in Ball

Knowledge Packages – as in Ma

According to the Oxford English Dictionary (Unabridged), the following are

in the definition of knowledge:

the fact or condition of knowing

the fact of knowing a thing, state, etc

acquaintance with a fact

intellectual acquaintance with, or perception of, fact or truth

acquaintance with a branch of learning, language or the like.

We would like to suggest that understanding and explanation structuresplay a more central role in the taxonomy used to discuss mathematics learning.

According to the Oxford English Dictionary (unabridged) the following are in the definition of understanding:

power or ability to understand; intellect, intelligence

intelligent, capable of judging with knowledge

the faculty of comprehending and reasoning; the intellect

the intellectual faculty as manifested in a person or set of persons

An explanation structure is what one has when one has an understanding.

Teachers must know mathematics.

Teachers must also understand the mathematics they are to teach.

The hexagon is made up of six equilateral triangles

Thus the radius of the circle is equal to a side of a triangle

Start with a regular hexagon inscribed in a circle

Thus the perimeter of the hexagon is equal to 6 radii, or 3 diameters

It is further around the circle than it is around the hexagon

Thus the circumference of the circle is more than 3 diameters

System-wide Change for All Learners and Educators Contact Us

Terry Millar millar@mail.bascom.wisc.edu

Eunice Krinsky ekrinsky@csudh.edu

Mary Ramberg mramberg@madison.k12.wi.us

Bruce King mbking1@wisc.edu

Peg Smith pegs@pitt.edu

Brian Sniff bsniff@madison.k12.wi.us

SCALEnet: http//:scalenet.org

SCALE website: http//:www.scalemsp.org