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LMT Sharing Session: LMT Sharing Session: April 2011April 2011
Vicky Kukuruda
Riverside County Office of Education
Patty O'Driscoll
Public Works, Inc.
Susan Tucker
Evaluation & Development Associates LLC
AAGGEENNDDAA• Content of LMT
• Appropriate use and fidelity to research embedded in the LMT project
• Strengths and challenges of using LMT• Overview of options• Project examples
LMT OverviewLMT Overview
• Developed by researchers led by Deborah Ball at the University of Michigan
• Builds off of research begun at the MPDI (Math Professional Development Institutes)
• Supported by NSF since 2002• Focuses on nature of the mathematical
knowledge needed for teaching– Special focus on instructional practice that can
intervene on significant patterns of educational inequality in mathematics education
Design of the LMTDesign of the LMT
• Designed to measure effectiveness of PD and its impact on the mathematical content knowledge that teachers need to teach mathematics well
• LMT Design team develops the test through writing, piloting, and analysis of problems that reflect real math tasks facing teachers
• LMT piloted with the help of over 2000 teachers– Mapping item pool against the NCTM and California standards
• Can be used to study:– content-focused PD– teacher learning from pre-service coursework– curriculum materials and projects exploring contribution of
teacher knowledge to student achievement
What you learn in a trainingWhat you learn in a training• Training at UM and national conferences
– no cost for training or for the measures themselves, but users must cover transportation and accommodation expenses
• To use the LMT in a research project, you must attend an LMT training
• Literature and research framework for the development of the assessment system
• How test design is embedded in mathematics professional development
• How it is different from past efforts to measure effectiveness of PD
• When to use it and when not
Training TopicsTraining Topics• LMT measures & their development• Early statistical work and their measures• Item Response Theory (IRT) basics
– focus on its use in scoring the assessment• Orientation to scales and forms• Using technical reports to understand measures• Terms of use of the LMT• Administration & lessons learned from experience• Teaching Knowledge Assessment System (TKAS)
(new on-line version of LMT)
Content covered in LMT about Content covered in LMT about teacher content knowledgeteacher content knowledge
• Number and operations (K-6, 6-8) • Patterns, functions, and algebra (K-6, 6-8) • Geometry (3-8)• Topic-specific modules (4-8) in:
– Rational number – Proportional reasoning – Geometry– Data, probability, and statistics
Appropriate Use of the LMTAppropriate Use of the LMT
• LMT does NOT offer measures that can be used for hiring, promotion, pay, or tenure
• LMT is NOT designed to make highly accurate statements about individuals' math knowledge
• LMT does NOT participate in study design or data analysis or provide PF to teachers or schools
• LMT is for comparing groups of teachers' mathematical knowledge, or examine how a group of teachers' knowledge develops over time
LMT Assumptions LMT Assumptions
• To make progress in developing theory of knowledge for teaching
• To develop items that measured math that teachers use in teaching, not just what they teach
• To orient items around problems that all teachers might face in teaching math
• To produce useable measures:– With items that are not grade-specific – With items that do not represent any single view of teaching
(e.g., “reform”) – Which can discriminate among teachers’ capability in this
area
Fidelity of Use of the LMTFidelity of Use of the LMT
• Want to measure range of teacher ability reliably– Need easy, medium, difficult items– No evidence that teachers must answer any of these
items to be effective
• Limits conclusions– 50% average ≠ “teachers failing”– No conclusions about individuals’ competency
Using the LMT Making SelectionsUsing the LMT Making Selections
• Choose content domain• Identify forms that match your professional
development content• Consider the ability of your participants
– Consider short AND long term development
• Select forms– match to ability and content of PD– look for high reliability scales
Available Scale MeasuresAvailable Scale Measures
• Elementary number and operations (K-6, 6-8)• Elementary patterns, functions, and algebra (K-6,
6-8)• Geometry (3-8)• Rational number (4-8)• Proportional Reasoning (4-8)• Data, probability, and statistics (4-8)
– Each K-6 item has each been piloted with over 600 elementary teachers,
– Middle school items have each been piloted with over 300 middle school
teacher
Sample Item- ElementarySample Item- Elementary7. Which of the following story problems could be used to illustrate
141 divided by 21? (Mark YES, NO, or I’M NOT SURE for each possibility.)
Yes NoI’m n ot
sure
a) You want to split 141 pies evenly between
two families. How much should eachfamily get? 1 2 3
b) You have $1.25 and may soon doubleyour money. How much money wouldyou end up with? 1 2 3
c) You are making some homemade taffy
and the recipe calls for 141 cups of
butter. How many sticks of butter (each
stick = 21cup) will you need?
1 2 3
Sample Item- ElementarySample Item- Elementary
5. Mrs. Johnson thinks it is important to vary the whole when she teaches fractions. For example, she might use five dollars to be the whole, or ten students, or a single rectangle. On one particular day, she uses as the whole a picture of two pizzas.
What fraction of the two pizzas is she illustrating below?
Mark ONE answera)5/4b) 5/3 c)5/8 d)1/4
Sample Item- ElementarySample Item- Elementary
2. Ms. Chambreaux’s students are working on the following problem:
Is 371 a prime number?
As she walks around the room looking at their papers, she sees many different ways to solve this problem. Which solution method is correct? (Mark ONE answer.)
Sample Item-Middle SchoolSample Item-Middle School
18. Mrs. Smith is looking through her textbook for problems and solution methods thatdraw on the distributive property as their primary justification. Which of these familiarsituations could she use to demonstrate the distributive property of multiplication overaddition [i.e., a (b + c) = ab + ac]? (Mark APPLIES, DOES NOT APPLY, or I’M NOTSURE for each.)
AppliesDoes not
applyI’m not
sure
a) Adding 34+54 1 2 3
)b Solving 2 x – 5 = 8 f or x 1 2 3
)c Combining lik e terms in the expression3x2 + 4y + 2x2 – 6y 1 2 3
)d Adding 34 + 25 using this method:34
+25
59
1 2 3
Other considerations/ExamplesOther considerations/Examples
• Pros and Cons– On-line system
• online using the Teacher Knowledge Assessment System (TKAS) available to those who have previously attended an item training workshop.
• contact Katherine Mikesell at [email protected]
– Computer Adaptive testing– Paper-based assessments
• Examples to Share– Riverside– NSF MSP ACES grant at CSUSB– Downey
• Discussion and Questions
Augmenting the LMT at CSUSBAugmenting the LMT at CSUSB
• NSF MSP ACES grant directed by Dr. Davida Fischman
• Working in Ontario-Montclair School District• Demonstrating certain LMT items with think
aloud protocol• Video taping lesson study
– Adapting MQI protocol to analyze videos– Mathematical Quality of Instruction (MQI)– Online training for MQI: Nina Cohodes at
[email protected] or 617.496.4815.
Example of LMT use in Riverside:Example of LMT use in Riverside:
• 110 Teachers grades 3 - Algebra 1
• 4 small feeder K-8 districts, High School district and County Special Education and Alternative Education teachers
• Objective 1: Teacher Content Knowledge
• 3 year Content Focus:
– Numbers and Expressions
– Proportional Reasoning
– Functions and Equations
Project DELTA Design Diagram
Spring
July
Sept – Nov.
Jan. – Mar.
Feb. – May
June
Kick Off Event
Intensive 8-days/ 2 weeks (M-Th, M-Th)
Site/Grade level based lesson study days
(specific dates TBD by
specific lesson study groups)
Intensive Saturday Sessions
Site/Grade level based lesson study days
(specific dates TBD by
specific lesson study groups)
Culminating Event
Functions & Equations
July 1 6-19 July 2 3-26
Proportional Reasoning
July 1 8-21 July 2 5-28
March 9, 2013
June 15, 2013
Jan. 12, 2013
Jan. 21, 2012
Feb. 5 , 2011
Jan. 22, 2011
Numbers & Expressions July 19-22 July 26-29
May 26 , 2010
60 hrs
6 hrs
6 hrs
6 hrs
6 hrs
6 hrs
6 hrs
2 hrs
Jan. 2010 – June 2011
12 quarter-units MCPT coursework*
* For participants seeking Mathematics Supplemental Authorization or Subject Matter Authorization
March 10 , 2012
60 hrs
6 hrs
6 hrs
6 hrs
6 hrs
6 hrs 6
hrs 6
hrs
12 quarter-units MCPT coursework*
July 2011 – June 2012
60 hrs
6 hrs
6 hrs
6 hrs
6 hrs 6
hrs 6
hrs 6
hrs 2
hrs July
2012 – June 2013
6 hrs
6 hrs
6 hrs
6 hrs
8 quarter-units MCPT coursework*
Cycles of Administration:Cycles of Administration:
• First Administration – Pre A 3 surveys on first day of institute (first hour)
• Second Administration- Post B Saturday before we released them
• Third Administration- Post A 2 hour open session with a series of
afterschool choices/locations
Project DELTA LMT MKT Schedule
Spring
July
Sept – Nov.
Jan. – Mar.
Feb. – May
June
Kick Off
Event
Summer Institute (8-days/ 2 weeks)
Intensive
Saturday Sessions
Culminating
Event
2010 –2011
Year 1
2011 – 2012
Year 2
2012 –2013
Year 3
Numbers and Expressions
Middle School Number Concepts
and Operations CK 2007-B
Elem. Number Concepts/Ops. CK 2008 -A
MS Number Concepts/Ops. CK 2007 -A
MS Patterns/ Functions/ Alg. CK 2005 -A
3 Lesson Study Days
Proportional Reasoning
3 Lesson Study Days
3 Lesson Study Days
3 Lesson Study Days
Functions and Equations
3 Lesson Study Days
3 Lesson Study Days
Middle School Patterns,
Functions a nd Algebra
CK 2005-B
Middle School Patterns,
Functions and Algebra
CK 2005-A
Middle School Number Concepts
and Operations CK 2007-A
Elementary Number Concepts
and Operations CK 2008-B
Elementary Number Concepts
and Operations CK 2008-A
Summer Institute
2011 July 18 -22 July 25 -28
Summer Institute
2012
Objective 1: Teacher Content Knowledge•DELTA teachers increased performance on the LMT MKT from pre to mid (ss)
•DELTA Regular Ed teachers performed better than Alt Ed/SPED (RCOE) teachers on the pre LMT MKT, however, Alt Ed/SPED teachers made greater gains and were performing at the same level by mid year.
Q & A about LMTQ & A about LMT
• What are questions you have about:– Content– Use– Challenges– Ways to leverage with other data sources
Citation for the workCitation for the work
• Copyright © 2006 The Regents of the University of Michigan. For information, questions, or permission requests please contact Merrie Blunk, Learning Mathematics for Teaching, 734-615-7632. Not for reproduction or use without written consent of LMT. Measures development supported by NSF grants REC-9979873, REC- 0207649, EHR-0233456 & EHR 0335411, and by a subcontract to CPRE on Department of Education (DOE), Office of Educational Research and Improvement (OERI) award #R308A960003.
Contacts for more info:Contacts for more info:
• Vicky Kukuruda: – [email protected]
• Patty O'Driscoll: – [email protected]
• Susan Tucker: – [email protected]
