1. NW4 Numeracy Series Examining Data Cross Panel Collaboration Effective Practice

2. Try this puzzle  4 of these pieces (the non-square ones) can be assembled to form a square  Now add the 5 th piece to form a slightly larger square

3. Try this puzzle  4 of these pieces (the non-square ones) can be assembled to form a square  Now add the 5 th piece to form a slightly larger square Hint #1: Look at what forms the outside edges of the 4-piece square. Since the 5-piece square must be larger, it must have slightly larger edges

4. Try this puzzle  4 of these pieces (the non-square ones) can be assembled to form a square  Now add the 5 th piece to form a slightly larger square Hint #2: One of the outside edges of the 5-piece square is formed by putting these two pieces together as here

5. Try this puzzle  4 of these pieces (the non-square ones) can be assembled to form a square  Now add the 5 th piece to form a slightly larger square Hint #3: This is one of the vertices of the 5-piece square.

6. Where’s the math?  Which pieces have the same length sides?  What are the relative areas of the 4-piece and the 5-piece squares?  What are the relative side lengths of all 3 squares?  How do you know? Even better: challenge your students to ask questions and investigate an answer. Celebrate their solutions. Foster a spirit of inquiry.

7. To improve student achievement through  Examining data (EQAO IIR)  Examine current best practice in math (3-part lesson & formative assessment)  Cross panel collaboration  Co-teaching Series Objectives

8. Similarities & Differences Grades 1-8  Processes & Achievement chart  Open course  Number Sense & Numeration  Measurement  Geometry & Spatial Sense  Patterning & Algebra  Data Management & Probability Grade 9  Processes & Achievement chart  LDCC, Applied, Academic  Number Sense & Algebra  Linear Relations  Measurement & Geometry  Analytic Geometry

9. From the Junior EQAO

10. From the Junior EQAO we know … Number Sense & Numeration - successful with questions involving estimation - difficulties with rate and ratio Measurement - successful with finding the area of a rectangle - difficulty with finding the area of a parallelogram - difficulty with the conversion of metric area units Geometry & Spatial Sense - successful with questions involving transformations and identifying angles - difficulties identifying and describing relationships between shapes Patterning & Algebra - students performed well on questions dealing with growing patterns Data Management & Probability - successful with creating a broken-line graph - difficulties with probability * From Summary of Results and Strategies for Teachers, 2008-2009

11. What we can do … model ways of justifying answers, use a variety of representations for comparing fractions, provide opportunities for students to differentiate between when to apply estimation strategies and when to use calculators provide opportunities to construct and deconstruct parallelograms using triangles, reinforce area relationships, practice converting from square metres to square centimetres using a factor of 100 x 100 provide opportunities for identifying, performing and describing transformations; instruct students to make drawings when problem solving provide opportunities to strengthen proportional reasoning by predicting and representing the probability of an outcome; have students create different graphs with the same data using different scales * From Summary of Results and Strategies for Teachers, 2008-2009

12. Try this question

13. The Item Specific Rubric

14. Use the rubric to code these student exemplars

15. What code is this? Code 20 Annotation: Student demonstrates a partial understanding of the concepts; selects lines A and C, but supporting evidence is unclear as reference to the F-pattern on the diagram does not connect to the justification or support the choice of A and C. Mention of the F-pattern shows some understanding of parallel lines.

16. What code is this? Code 10 Annotation: Student demonstrates a misunderstanding of the concepts; justification provided does not relate to parallel lines and choice of lines A and B is incorrect

17. What code is this? Code 40 Annotation: Student demonstrates a thorough understanding of the concepts; Lines A and C are selected as parallel with justification of angles that add up to 180 o and discussion of angles on opposite sides of a transversal

18. What code is this? Code 30 Annotation: Student demonstrates an understanding of most of the concepts; student shows correct angle measures but does not connect line A to line C.

19. Lets try another one

20. Use the rubric to code these student exemplars

21. What code is this? Code 10 Annotation: Student demonstrates a limited identification of important elements of the problem; graphs Liz's line correctly however, Alex's line is incorrect. The intersection point is incorrect based on their graph, and conclusion is omitted.

22. What code is this? Code 20 Annotation: Student demonstrates some understanding of the relationships between important elements of the problem; both lines are graphed incorrectly however the intersection point closely matches graph and its interpretation is correct.

23. What code is this? Code 30 Annotation: Student demonstrates a considerable understanding of the relationships between the important elements of the problem; Alex's line is graphed incorrectly however the intersection point matches the graph and its interpretation is correct.

24. What code is this? Code 40 Annotation: Student demonstrates a thorough understanding of the relationships between all of the important elements of the problem; both lines are graphed fairly accurately, point of intersection matches graph and its interpretation is correct.

25. EQAO

26. EQAO Analysis of Item Information Reports- 9 Applied Mathematics 2009  Using the IIR –student roster report  Examining Provincial Observations and Suggested Strategies for Improvement  Setting a focus

27. What it looks like Multiple Choice  Closed questions  One right answer  Three distractors  Single or multi-step  Designed to be answered in about 1 1/2 minutes Open Response  Questions require explanation or justification  Multiple solution methods (Open-middled)  Usually Multi-step  Designed to be answered in about 5 minutes

28. What we know 38% of students in Ontario performed at or above the provincial standard in applied mathematics Since last year, there has been an increase of 4% for students performing at or above the provincial standard in applied mathematics. Over the past five years, the percentage of students taking applied mathematics who performed at or above the provincial standard has increased by 11%, from 27% to 38%. The Provincial Perspective

29. What we know In 2009 The mathematics results for the 36 529 students in the cohort are as follows: 20% (7326) met the provincial standard in Grade 6 and Grade 9; 21% (7809) did not meet the standard in Grade 6 but met it in Grade 9; 10% (3829) met the standard in Grade 6 but did not meet it in Grade 9 and 48% (17 565) did not meet the standard in Grade 6 or Grade 9. Cohort Tracking from Grade 6 to Grade 9 Applied Mathematics

30. IIR ( Item Information Report) Student Roster Organized by strand The Codes: MC= Multiple Choice OR = Open Response NAV.02= Number Sense and Algebra; Overall Expectation # 2 in Curriculum Document Overall Expectation # 2 in Curriculum Document Strand Number Sense and Algebra Item Number † 12345 Item Type ‡ MC OR Overall Expectation § NAV.01NAV.02 NAV.01 Skill** PSAPKU PS Highest Score Code Possible/ Correct MC Response bdcd40

31. IIR ( Item Information Report) Student Roster KU= Knowledge and Understanding AP= Application PS= Thinking Strand Number Sense and Algebra Item Number † 12345 Item Type ‡ MC OR Overall Expectation § NAV.01NAV.02 NAV.01 Skill** PSAPKU PS Highest Score Code Possible/ Correct MC Response bdcd40

32. IIR (Item Information Report) Student Response and Score Code  MC - multiple choice  + (correct response)  a, b, c, d  B (blank)  M (more than 1 response)  OR - open response  B (blank)  I (illegible)  10  20  30  40 a+d+40 ++++ ++++20 B++c10 aad+20 ++ab40 ++d+20 da+bB dca+40 cc++10 ac++20 d++c40 +++c10 cc++20

33. IIR (Item Information Report) Summary Results MC scores show percentage of students who responded correctly OR scores show the average percentage of total points Summary Results §§ School 486354 39 Board 4737504641 Province: All Students 5139524749 Province: Students at Level 3 or Above6856676570

34. IIR (Item Information Report) Gathering Information from the IIR: Student roster Compare your scores for each item for your school with the Board and the Province (Are there questions that show discrepancies?) Highlight problematic questions for your school

35. EQAO Provincial Observations and Suggested Strategies for Improvement* Number Sense and Algebra Observations  successful with questions requiring algebra skills without a context than on contextualized problems requiring algebra skills * From Summary of Results and Strategies for Teachers, 2008-2009

36. EQAO Provincial Observations and Suggested Strategies for Improvement Number Sense and Algebra Observations  More successful with ratio questions involving “friendly numbers” than with less obvious proportional relationships

37. EQAO Provincial Observations and Suggested Strategies for Improvement Number Sense and Algebra Observations  successful with questions requiring algebra skills without a context than on contextualized problems requiring algebra skills  More successful with ratio questions involving “friendly numbers” than with less obvious proportional relationships Strategies – Strategies – provide students with opportunities to use manipulatives to visualize algebraic concepts, integrate the teaching of algebra across the strands, teach different approaches to solving for unknowns in proportional relationships

38. EQAO Provincial Observations and Suggested Strategies for Improvement Linear Relations Observations  Students continue to perform better overall in this strand than the other strands  Successful with comparing linear and non-linear relations  Difficulties with questions requiring them to determine the equation of a line

39. EQAO Provincial Observations and Suggested Strategies for Improvement Linear Relations Observations  Difficulties with questions requiring them to determine the equation of a line

40. EQAO Provincial Observations and Suggested Strategies for Improvement Linear Relations Observations  Students continue to perform better overall in this strand than the other strands  Successful with comparing linear and non-linear relations  Difficulties with questions requiring them to determine the equation of a line Strategies – Strategies – provide opportunities for students to create and interpret graphs, include scales that do not have one-to-one correspondence, have students make connections among different representations of linear relationships

41. EQAO Provincial Observations and Suggested Strategies for Improvement Measurement and Geometry Observations  students performed well on questions requiring specific knowledge about the Pythagorean theorem, angles, and angle relationships  Not as successful on multi-step questions of both types  Lack of attention to detail when answering open-response questions (e.g. diameter versus radius)  Students who were successful on open-response questions provided justification for each step of their solution process

42. EQAO Provincial Observations and Suggested Strategies for Improvement Measurement and Geometry Observations  Lack of attention to detail when answering open-response questions (e.g. diameter versus radius)

43. EQAO Provincial Observations and Suggested Strategies for Improvement Measurement and Geometry Observations  students performed well on questions requiring specific knowledge about the Pythagorean theorem, angles, and angle relationships  Not as successful on multi-step questions of both types  Lack of attention to detail when answering open-response questions (e.g. diameter versus radius)  Students who were successful on open-response questions provided justification for each step of their solution process Strategies – Strategies – require students to provide complete justifications, model working backward with the answer as a strategy, teach students how to choose important words from the questions and how to make a plan, provide sufficient instructional time for the strand

44. EQAO Provincial Observations and Suggested Strategies for Improvement General Observations  Students had difficulty solving multi-step problems  Students continue to misinterpret important details in questions in all strands Strategies Strategies – continue to provide students with multi-step problems in various contexts in all strands, model problem solving processes, provide students with opportunities to demonstrate and discuss problem solving strategies, require students to verify their answers, model working backward to verify a solution, continue to support students by using Universal design for learning

45. Connecting to the Mathematical Processes  Problem solving  Relationships  Contexts  Verifying  Problem solving  Justifying  Explaining  Comparing  Interpreting  Problem Solving  Reasoning and Proving  Reflecting  Selecting Tools & Computational Strategies  Connecting  Representing  Communicating EQAO Themes Seven Processes

46. Connecting It Back To Your School Taking a Closer Look at EQAO Data:  Identify areas of focus  Make a plan based on collected information

47. Next time Middle School Teachers  Fairbank MS  Using diagnostic assessment  Plan & Co-Teach a grade 8 lesson High School Teachers  Location – TBD  Using TIPS4RM materials  Plan & Co-Teach a grade 9 Applied lesson November 12 – Full Day

48. “Co-teaching is an informal professional learning arrangement in which teachers with different knowledge, skills and talents have share responsibility for designing, implementing, monitoring and/or assessing a curriculum program for a class of students on a regular basis (e.g., biweekly, monthly, or per term). The purpose of co-teaching is to enable groups of teachers to improve their instruction and their understanding of students’ thinking and learning through shared observation, and analysis of student work. Co-teaching makes it possible for teachers to engage in teaching as collaborative problem-solving.” What is co-teaching?

49. A group of teachers gather to plan a math lesson A classroom teacher teaches the lesson to his/her own students, along with one or two co-teachers The teacher researchers watch and listen to students as they engage in the mathematics After the lesson, all teachers de-brief to share, discuss, question, plan next steps The Framework

50. It is grounded in inquiry and reflection, participant- driven, and focused on improving planning and instruction. It is collaborative, involving the sharing of knowledge and focusing on communities of practice rather than on individual teachers. It is connected to and derived from teachers’ work with students –teaching, assessing, observing and reflecting on the processes of learning and development. It promotes reflective practice and results in having teachers working smarter, not harder. Why co-teaching?

51. It addresses teacher isolation by providing opportunities for shared teacher inquiry, study and classroom-based research. It motivates teachers to act on issues related to curriculum programming, instruction, assessment, and student learning. Overall, this job-embedded professional learning builds capacity for instructional improvement and leadership …improved student achievement. Why co-teaching?

52. See you on Nov. 12 Bonnie Macdonald Instructional Leader Mathematics/Numeracy Grades K – 8 Northwest Quadrant Freda Liu NW4 K – 8 Numeracy Coach Anthony Meli Instructional Leader Mathematics/Numeracy Grades 7 – 12 West Region Janine Small S4P 9 – 12 Numeracy Coach