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Mathematics Design Collaborative 2012 and Beyond

Mathematics Design Collaborative 2012 and Beyond. GACIS 2012. Last Year’s Presentation – In Review. The project is working to design and develop well-engineered assessment tools to support US schools in implementing the Common Core State Standards for Mathematics (CCSS).

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Mathematics Design Collaborative 2012 and Beyond

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  1. Mathematics Design Collaborative 2012 and Beyond GACIS 2012

  2. Last Year’s Presentation – In Review • The project is working to design and develop well-engineered assessment tools to support US schools in implementing the Common Core State Standards for Mathematics (CCSS). • Data shows long range retention • The Big Idea of Formative Assessment • Students and Teachers • Using evidence of learning • To adapt teaching and learning • To meet the immediate learning needs • Minute-to-minute and day-by-day

  3. Five Strategies of Formative Assessment • Clarifying and sharing learning intentions and criteria for success • Engineering effective discussion, questions, activities, and tasks that elicit evidence of learning. • Providing feedback that moves students forward • Activating students as instructional resources for one another • Activating students as owners of their own learning

  4. 2011-2012 • School Level – Micah Hoyt, East Hall High School, Hall County • Lessons learned • Collaboration is key • District Level – Dr. Cassie Rape, Houston County Mathematics Supervisor, 6-12 • Scaling district-wide • Vertical and horizontal collaboration • Analysis for Growth (and repair)

  5. MDC Tools and Takeaways • Student Engagement • Depth of Understanding • Collaboration and planning

  6. The Changing Face of Student Engagement Before After Students communicating mathematically with each other Students working together to solve an authentic problem Students activating each other as learning resources Students UNDERSTANDING mathematics • Students working quietly • Students completing a task with a high degree of accuracy • Students asking questions of the teacher • Students DOING mathematics

  7. Student Comments • “I liked the class a lot better than I had been”. (sic) • “I loved the math class today. I actually had fun interacting with everyone and solving the problems.” • “I think that it’s more fun and intriguing than a regular math class because we didn’t just do book work.” • “It felt like I was in science class with the polluted water.”

  8. Teaching for Conceptual Understanding • Phil Daro – “Against Answer Getting” • Moving toward understanding and away from steps. • Stop making it easy!

  9. What is Happening Now? • Promoting MDC Strategies • Recruiting Teachers • Collaboration • Data Driven Instruction

  10. A Vertical Look at Formative Assessment Lessons Why is this any different from regular math “tasks” or “quizzes?”

  11. We don’t learn passively. • People are active participants in their own learning. • We construct bridges between what we are learning now and what we already know • Misconceptions arise naturally as a result. • FOR INSTANCE: A third grader constructs the following “rule” for themselves based on their previous learning: I will get larger number whenever I multiply two numbers together.

  12. There is a BIG difference between a Mistake and a Misconception. MISTAKES • Computational Errors • Lack of Attention • Careless Errors • Misreading Own Handwriting • Observed Occasionally/ Infrequently MISCONCEPTIONS • Wrong applications of Mathematical Rules • Incorrect interpretation of mathematical concepts • Observed consistently

  13. Why is the consideration of misconceptions important? • Children construct meaning internally by accommodating new concepts within their existing mental frameworks. • Thus, unless there is intervention, there is likelihood that the pupil’s conception may deviate from the intended one. • Pupils are known to misapply algorithms and rules in domains where they are inapplicable. • A surprisingly large proportion of pupils share the same misconceptions.

  14. Undiagnosed Misconceptions Become Owned and Embedded Misconceptions

  15. Undiagnosed Misconceptions Become Owned and Embedded Misconceptions

  16. Formative Assessment is Shown to be more successful than direct instruction alone.

  17. PRE-Test ERRORS ANALYSIS PERCENTAGES

  18. POST-Test ERRORS ANALYSIS PERCENTAGES (approximates)

  19. A SIDE-BY-SIDE COMPARISON PRE • A(10%) • B (25%) • C (80%) • D (95%) • E (50%) • F (5%) • G (90%+) • H (5%) • J (10%) POST • A (5%) • B (5%) • C (30%) • D (45%) • E (5%) • F (less than 5%) • G (10%+) • H (30%) • J (5%)

  20. A Horizontal Look at Formative Assessment Lessons CONVINCING TEACHERS OF FAL VALUE ENSURING FIDELITY IN SCALING ACROSS SYSTEM

  21. The Beliefs of Educated Educators…. A Cycle

  22. TRAINING FOR TEACHERS • STRUCTURED FAL STUDY • TEACHERS START AS STUDENTS • DEMONSTRATE PROCESS • NO-PRESSURE OPPORTUNITIES TO RUN TRIALS • USE LESSONS PERTINENT TO THEIR GRADE/SUBJECT

  23. INSPECT WHAT YOU EXPECT • Make the Expectation Clear: “Non-Optional” Formative Assessments • Observe the Lessons • Ask for Student Work Samples • Ask to see Analysis of Student Errors

  24. PROVIDING for TEACHERS • Lessons Provided by DOE • Matched lessons to units • Opportunities to Collaborate • Materials to Implement • Support for the Process • Time to Analyze Student Work

  25. MOTIVATING TEACHERS • THE GAME IS CHANGING: Math is no longer an exercise in choreography, but in true understanding and application • PARCC • SHELL • CCGPS • Standards for Mathematical Practice

  26. OUR PLATES, as MATH TEACHERS Standards for Mathematical Practice FAL Response to Intervention (R.T.I.) CCGPS New Curriculum Flexible Grouping Differentiated Instruction (D.I.) TASKS Lunch Duty

  27. FAL DOCUMENTS PROVIDED PDF is Bookmarked for Easy Access Lesson

  28. MAP(Shell Centre) Formative AssessmentCompared to Instructional Framework

  29. Why does a FAL matter? Through Course Assessments Summary

  30. Summary • Cohort 1: 6 pilot systems, 2011-2012 • Cohort 2: 44 additional systems • RESA involvement • 2013-2014 and beyond; all training and teacher support will be provided by RESA • MDC provides the best practices strategies, tools, formative assessments and lessons. We enact, observe, collaborate, analyze student work, adjust instruction, and have student talking about mathematics.

  31. So what is formative assessment? • It is the biopsy that we take to diagnose current conditions; rather than the autopsy at the end of the unit . . . when it is too late to administer assistance. • When the chef tastes the sauce, this is formative assessment. When the customer tastes the food, this is summative.

  32. Challenges • Less teaching • More questioning • Collaborative planning • Analysis of growth: pre to post • Next steps • Time

  33. Final Comments Questions??? Share vmixon@doe.k12.ga.us Listen more, talk less Students engaged – teacher facilitates

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