1. INSPECT WHAT YOU EXPECT Dr. Cassie Rape May 10, 2013 GACIS MDC Training

2. A VERTICAL LOOK AT FORMATIVE ASSESSMENT LESSONS Why is this any different from regular math “tasks” or “quizzes?”

3. 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.

4. 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

5. 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.

6. Undiagnosed Misconceptions Become Owned and Embedded Misconceptions

7. Owned

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

9. PRE-Test ERRORS ANALYSIS PERCENTAGES A(10%)B (25%)C (80%)D (95%)E (50%)F (5%) G (90%+) H (95%)J (10%) Tricked by picture. Student interprets the graph as a picture. Student interprets graph as speed vs. time (acceleration) Student fails to mention specific distance or specific time Student does not calculate speed (incorrect descriptions of speed) Does not know that speed is distance (per) time Student misinterprets scale (either misplacing the x and y axis or interpreting the units in the wrong increments). Student does not explain why the graph is realistic Student does not get all of the graph right. Student does not understand conceptually the relationship between slope and speed

10. POST-Test ERRORS ANALYSIS PERCENTAGES (approximates) A (5%)B (5%) C (30%)D (45%) E (5%) F (less than 5%)G (10%+) H (70%)J (5%) Tricked by picture. Student interprets the graph as a picture. Student interprets graph as speed vs. time (acceleration) Student fails to mention specific distance or specific time Student does not calculate speed (incorrect descriptions of speed) Does not know that speed is distance (per) time Student misinterprets scale (either misplacing the x and y axis or interpreting the units in the wrong increments). Student does not explain why the graph is realistic Student does not get all of the graph right. Student does not understand conceptually the relationship between slope and speed

11. 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%)

12. Some Difficult Discussions

13. GET OUT OF YOUR OWN BRAIN! Recognize…the rest of the world does not think the way a math teacher thinks. …and that’s OK.

14. #mathteacherproblems #mathteacherproblems http://youtu.be/6LSOMiLMvAY HOW WE THINK HOW THE REST OF THE WORLD THINKS

15. Things I Can Let Go…. No Work=No Credit Pencil Only or No Credit Do it How I Told You To Show the Steps…no, not your steps…the ones I taught you “MATH RULES”

16. A HORIZONTAL LOOK AT FORMATIVE ASSESSMENT LESSONS CONVINCING TEACHERS OF FAL VALUE ENSURING FIDELITY IN SCALING ACROSS SYSTEM

17. The Beliefs of Educated Educators…. A Cycle No Personal Proof of Effectiveness Unwillingness to Try Because Potentially Ineffective No Results Generated

18. 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

19. 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

20. 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

21. OUR PLATES, as MATH TEACHERS

23. Standard/Esse ntial Question Opening Mini- Lesson Student Work Session Closing Pre- Assessment (NO HELP from teacher)! Analysis of Student Work and Understandin gs Creation of Leading /Probing/Gui ding Questions Opening Collaborative Session (Utilize Questioning) Student Work Session (Utilize Questioning, Create “Experts”) Plenary (Summarizin g) Discussion Post- Assessment (Students can have their Probing Questions and Pre-Test to use during Post- Assessment) Gates Grant (Shell Centre) Formative Assessment, Compared to Instructional Framework

24. Why does an FAL matter?

25. CHECKING 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

27. Things to Learn from Our Successes and Mistakes Make FAL’s an expectation. Set time aside to train every single teacher Re-Train Teachers Follow up with second time to train every single teacher in ANALYSIS of STUDENT WORK Video!!! Praise works better than force! Provide Materials, Share Materials, House Materials Centrally Teachers provide (someone in leadership) dates of FAL enactment Ask for feedback from teachers! Ask for feedback from students!

28. Questions? Dr. Cassie Rape cassie.rape@hcbe.net @DrCRRape