system-wide change for all learners and educators department of education msp meeting breakout...
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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
-2
2
6
10
Pre-test scores
Gai
ns
pre
-po
st
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 [email protected]
Eunice Krinsky [email protected]
Mary Ramberg [email protected]
Bruce King [email protected]
Peg Smith [email protected]
Brian Sniff [email protected]
SCALEnet: http//:scalenet.org
SCALE website: http//:www.scalemsp.org