Milwaukee Public Schools University of Wisconsin-Milwaukee

1. Math Alliance Project Mathematics Alliance for Teaching Mathematics to Special Education LearnersStrengthening Content Knowledge and Collaboration of General and Special Education Teachers Milwaukee Public Schools University of Wisconsin-Milwaukee Judith Winn, jwinn@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

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. Math Alliance Project 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. Math Alliance Project 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. Math Alliance Project Vision • Improve mathematics performance for students in grades 4–8, 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. Math Alliance Project 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. Math Alliance Project Timeline

14. Math Alliance Project Strands Mathematics Content Year 1: Number, Operations, & Algebraic Reasoning Year 2: Geometry & Measurement Year 3: Data Analysis, Statistics, & Probability Differentiated Instruction Interventions Collaboration

15. Math Alliance Project Participants

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. Math Alliance Project 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. I’ve used this in my class and it offers me opportunities to present more strategies to my students. ---General Education Teacher

20. Math Alliance Project 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. Math Alliance Project MKT: Number & Operations --- Special Education Teachers --- General Education Teachers --- Combined Groups Comparison Teachers Mean = 0.05 (n=86)

22. Math Alliance Project Content Knowledge Area as Covering & Deriving Formulas Meaning of π 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. Math Alliance Project MKT: Geometry & Measurement --- Special Education Teachers --- General Education Teachers --- Combined Groups Comparison Teachers Mean = 0.17 (n=97)

24. Math Alliance Project Differentiated Instruction

25. Math Alliance Project Differentiated Instruction

26. Math Alliance Project 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 It’s not all about getting the right answer. Often it’s 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. Math Alliance Project Collaboration 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. Math Alliance Project My students’ math learning has increased because of my collaboration with the general/special education teacher.

29. Math Alliance Project 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 other’s 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. Math Alliance Project 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. Math Alliance Project What are we learning? Special Education Teachers • Putting moreemphasis on concept-based learning (e.g., visual models, strategies, alternative algorithms, reasoning, problem solving). • Deepening their mathematics content knowledge. • Offering more in collaboration 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

32. Math Alliance Project What am I learning from Math Alliance? What has this made me think about?

33. Math Alliance Project 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!