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Title: Mathematics Alliance for Teaching Mathematics to Special Education Learners Strengthening Content Knowledge and Collaboration of General and Special Education Teachers


1
Mathematics Alliance for Teaching Mathematics
to Special Education Learners Strengthening
Content Knowledge and Collaboration of General
and Special Education Teachers
  • Milwaukee Public Schools
  • University of Wisconsin-Milwaukee

Judith Winn, jwinn_at_uwm.edu TED
Conference Austin, Texas November 10, 2011
2
  • I believe that development is more dependent on
    instruction than on age or biological maturation
    and that types of instructional experiences can
    foster, or impede, development.
  • Pierre M. van Hiele

3
(No Transcript)
4
van Hiele Levels of Geometric Reasoning
  • Level 0 Visualization Recognize figures as total
    entities, but do not recognize properties.
  • Level 1 Analysis (Description) Identify
    properties of figures and see figures as a class
    of shapes.
  • Level 2 Informal Deduction Formulate
    generalizations about relationships among
    properties of shapes Develop informal
    explanations.

5
van Hiele Levels of Geometric Reasoning
  • Level 3 Deduction Understand the significance of
    deduction as a way of establishing geometric
    theory within an axiom system. See
    interrelationship and role of undefined terms,
    axioms, definitions, theorems and formal proof.
    See possibility of developing a proof in more
    than one way.
  • Level 4 Rigor Compare different axiom systems
    (e.g., non-Euclidean geometry). Geometry is seen
    in the abstract with a high degree of rigor, even
    without concrete examples.

6
How do students progress in developing geometric
reasoning?
  • How would you recognize each of these levels of
    thinking in your students work?
  • Considering the first three levels, where would
    you place the majority of the lessons that you
    teach?

7
Alliance teachers
  • The tricky triangle activity. I had some
    misconceptions about triangles and this
    assignment helped me clear them up. Learning
    about the Van Hiele levels helped me understand
    where I am as a learner of math and what level I
    want to be at. Understanding these levels also
    helped me figure what I need to work on in order
    to get to the next level.
  • It is easier for me to assess students now
    because my expectations have more categories
    vocab--van Hiele levels

8
Project Staff
  • UWM Mathematics Education
  • DeAnn Huinker
  • UWM Mathematics
  • Kevin McLeod Patrick Hopfensperger
  • UWM Special Education
  • Judy Winn Mary Ann Fitzgerald
  • District Teachers and Specialists
  • Chris Guthrie, Special Education Teacher
  • Beth Schefelker, Math Teaching Specialist
  • Melissa Hedges, Math Teaching Specialist
  • Mary Spidell, Special Education Supervisor

9
Milwaukee Public Schools
  • Largest Wisconsin School District (ranks 33rd in
    the US)
  • 81,000 students
  • 184 Schools 118 elementary, 8 middle, 18
    mid/high, 40 high
  • Poverty 77.4 (State 39.3)
  • Disabilities 19.5 (State 13.7)
  • ELL 10.0 (State 5.7)
  • Non-white 85.0 (State 25.6)

10
MPS Students Performance on State Test
11
Vision
  • Improve mathematics performance for students in
    grades 48, particularly for students with
    special needs and for students who struggle in
    mathematics.
  • Support a school culture for collaboration of
    general and special education teachers on
    improving math learning for all students.

12
Goals
  • Strengthen the math content knowledge of general
    and special education teachers
  • Enhance math instruction and assessment, focusing
    on appropriate accommodations and modifications
    for special education and struggling students
  • Increase collaboration on math instruction of
    general and special education teachers.

13
Timeline
  Fall Spring Summer
Year 1 2009-2010 Recruitment Math Number, Operations, Algebraic Reasoning Education Development of Math Knowledge with Differentiation for Struggling Learners Math Number, Operations, Algebraic Reasoning Education Development of Math Knowledge with Differentiation for Struggling Learners
Year 2 2010-2011 Math Geometry Measurement   Education Teaching Math to All Learners Part 1 Math Geometry Measurement   Education Teaching Math to All Learners Part 1 Education Collaboration Planning for Math Differentiation
Year 3 2011-2012 Math Data Analysis, Statistics, Probability Education Teaching Math to All Learners Part 2 Math Data Analysis, Statistics, Probability Education Teaching Math to All Learners Part 2
14
Strands
  • Mathematics Content

Year 1 Number, Operations, Algebraic
Reasoning Year 2 Geometry Measurement Year 3
Data Analysis, Statistics, Probability
Differentiated Instruction Interventions
Collaboration
15
Participants
Year 1 Participants Year 2 Participants Continuing from Year 1
Certification General Ed 13 19 68
Certification Special Ed 22 21 86
Total 35 40
Grade Level Elementary 12 12 83
Grade Level Middle 13 21 76
Grade Level Both 10 7 71
16
Structure
  • Tuesday evenings (dinner and 3-hour classes)
  • Year I (Number and Operations)
  • Math content and Teaching all Learners content
    separate (Your turn, my turn)
  • Developed a planning format that combined the two
  • Math team and special education instructional
    teams
  • Year 2 (Geometry and Measurement)
  • Teaching all Learners content planned to link
    with specific math content
  • Mixed teams
  • Year 3 (Statistics and Probability)
  • Alternating weeks but working to link
  • Mixed teams

17
Projects/Assignments
18
Measures
  • Content Knowledge
  • Mathematical Knowledge for Teachers (MKT)
  • Practice
  • Teacher Surveys
  • Focus Group
  • Informal probes
  • Observations
  • Collaboration
  • Survey
  • Focus Group
  • Student Achievement
  • Wisconsin Knowledge and Concepts Exam (WKCE)
  • Benchmark testing

19
Content Knowledge
Distributive Property and Area Model
  • I have learned how the distributive property
    moves through math from elementary to middle to
    high school. I now know the importance of using
    the area model and being able to use it and the
    distributive property method in multiplying. Ive
    used this in my class and it offers me
    opportunities to present more strategies to my
    students.
  • ---General Education Teacher

20
Content Knowledge
Alternative Algorithms
The biggest impact has been exploring 'how you
get there.' I remember doing a lot of memorizing
as a student. Going through the process from
addition to grouping to multiplication gave me
the words to explain more fully those
connections. The activities for multiplication,
as well as the different methods of getting an
answer have really enhanced my teaching.
---Special Education Teachers
21
MKT Number Operations
--- Special Education Teachers --- General
Education Teachers --- Combined Groups
Gain Effect Size Effect Size
Special Ed 0.55 0.76 large
General Ed 0.34 0.38 small
Combined 0.45 0.57 medium
22
Content Knowledge
Area as Covering Deriving Formulas
Meaning of p
  • I can say that when we discussed area as covering
    I became clearer in my understanding. Before this
    class when asked what is area, I would rattle off
    the formula.
  • ---General Education Teacher
  • I hold a deeper level of understanding of how the
    moving and combining principles can be applied
    for various shapes when determining areas.
  • ---Special Education Teacher

Another ah ha moment was when I found out that
you can measure to find the circumference and
that it would be approximately a little bit more
than 3 times the diameter always wondered why we
use pi to figure area of circles. ---General
Education Teacher
23
MKT Geometry Measurement
--- Special Education Teachers --- General
Education Teachers --- Combined Groups
Gain Effect Size Effect Size
Special Ed 0.39 0.70 large
General Ed 0.28 0.28 small
Combined 0.35 0.47 medium
24
Differentiated Instruction
I am confident that I can Special Ed (n12) Special Ed (n12) General Ed (n9) General Ed (n9)
Baseline Year 2 Baseline Year 2
Differentiate instruction in the general education class so that students who struggle in math can profit from the instruction. 4.50 5.00 4.22 4.78
Provide explicit instruction for students who struggle that supports their conceptual understanding in math. 4.83 5.50 4.56 5.11
Provide separate small group or individual instruction for students who struggle with math that makes effective links to the general math curriculum. 5.00 5.42 4.78 5.22
25
Differentiated Instruction
I am confident that I can Special Ed (n12) Special Ed (n12) General Ed (n9) General Ed (n9)
Baseline Year 2 Baseline Year 2
Differentiate instruction in the general education class so that students who struggle in math can profit from the instruction. 4.50 5.00 4.22 4.78
Provide explicit instruction for students who struggle that supports their conceptual understanding in math. 4.83 5.50 4.56 5.11
Provide separate small group or individual instruction for students who struggle with math that makes effective links to the general math curriculum. 5.00 5.42 4.78 5.22
26
Expectations
Discourse
Concept Focused
  • My expectations have increased. I now expect my
    students to explore different ways of solving
    math problems and I expect them to share their
    thinking on a regular basis with their
    classmates.
  • ---Special Education Teacher
  • Its not all about getting the right answer.
    Often its about the process and how/why. I
    expect my students to be better able to explain
    the process they went through and know multiple
    ways of solving a problem not just memorizing a
    formula.
  • ---Regular Education Teacher

I think that I now possess higher standards for
my students with disabilities than I did in the
past as a result of seeing first-hand their
ability to demonstrate mastering math on a deeper
level. I want to see all students demonstrate
true mastery of a skill through a conceptual
approach versus simply memorizing and applying
formulas that they often do not even
understand. ---Special Education Teacher
27
Collaboration
Special Ed (n12) Special Ed (n12) General Ed (n9) General Ed (n9)
Baseline Year 2 Baseline Year 2
I bring sufficient content knowledge to collaboration. 5.08 5.42 5.33 5.89
I bring sufficient knowledge of the challenges of students who struggle to collaboration. 5.33 5.50 4.76 5.33
So, Special Education teachers are making gains
in bringing content knowledge to collaboration,
whereas General Education teachers are making
gains in bringing more knowledge of students and
their needs.
28
My students math learning has increased because
of my collaboration with the general/special
education teacher.
n Baseline Year 2 Change Effect Size Effect Size
Special Education 11 5.58 5.58 0.00 0.00 none
General Education 10 4.11 5.11 1.00 1.08 large
29
Challenges
  • Curriculum development
  • Literacy dominates special education, Limited
    guidance in math
  • Understand philosophical differences Inquiry vs
    Explicitness Explore vs Systematic
  • Collaborative planning and teaching
  • Challenges consistent with K-12 teacher
    collaboration literature (e.g., time, teacher
    content pedagogical content knowledge (PCK))
  • Understanding each others roles, potential, and
    shifts in practice
  • Range of participants content knowledge
  • Substantial holes in math knowledge, lack of
    PCK (e.g., tools, models)
  • Being able to put change into practice, harder
    for General Education
  • Meeting needs of both Special and General
    Education Teachers in one project (attrition)

30
Addressing challenges
  • Instructional teams with communication
  • Using some of the RtI guidance (e.g., IES
    Practice Guide)
  • Wrestling with explicit instruction with
    participants
  • Focusing on identifying students developmental
    conceptual understanding while acknowledging more
    assessments are needed
  • Van Hiele levels

31
What are we learning?
  • General Education Teachers
  • Collaborating more with Special Education
    Teachers.
  • Putting more differentiated instruction into
    practice.
  • Increasing their expectations of the capabilities
    of students with special needs.
  • Thinking about when more explicitness is needed
  • Special Education Teachers
  • Putting more emphasis on concept-based learning
    (e.g., visual models, strategies, alternative
    algorithms, reasoning, problem solving).
  • Deepening their mathematics content knowledge.
  • Offering more in collaboration

32
What am I learning from Math Alliance? What has
this made me think about?
Learned Think about
Absolute importance of math content knowledge both for teaching math and collaborating to teach math How do we ensure that special education teachers develop this knowledge in our preparation programs? Can we?
We have so say more than he cant do it because is working on a third grade level in math. How to challenge that kind of thinking along with acknowledging it
Lots to understand about explicit instruction How to provide it without guilt but in a way that supports students who struggle without it.
Role of language (bigger than I thought) What can be taken from reading instruction
33
Expectations for All Students to Get It
  • I really believe that I have high expectations
    for all of my students now. I think when I
    encountered a barrier previously it was easy to
    think that a particular student would just never
    get it. Now I know that I can find at least one
    strategy that will reach all students. My
    students are now more confident themselves. We
    have grown together.
  • ----Special Education Teacher

34
Thank You!
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