Title: Mathematics Alliance for Teaching Mathematics to Special Education Learners Strengthening Content Knowledge and Collaboration of General and Special Education Teachers
1Mathematics 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)
4van 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.
5van 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.
6How 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?
7Alliance 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
8Project 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
9Milwaukee 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)
10MPS Students Performance on State Test
11Vision
- 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.
12Goals
- 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.
13Timeline
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
14Strands
Year 1 Number, Operations, Algebraic
Reasoning Year 2 Geometry Measurement Year 3
Data Analysis, Statistics, Probability
Differentiated Instruction Interventions
Collaboration
15Participants
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
16Structure
- 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
17Projects/Assignments
18Measures
- 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
21MKT 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
22Content 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
23MKT 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
24Differentiated 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
25Differentiated 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
27Collaboration
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.
28My 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
29Challenges
- 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)
30Addressing 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
31What 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
32What 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
34Thank You!