1. SW1 FOS Networking Session Dec. 16, 2011 David Hornell Junior School

2. DATA GAN Focus/Inquiry Question How did you take your GAN (Greatest Area of Need) and formulate a focus and/or an inquiry question for your Pathway/Professional Learning Team Focus? How did the data inform this focus? Using EQAO Data, report cards and teacher assessments we determined that our area of greatest need in mathematics was problem solving. We worked with Colleen to formulate an “Assessment of Learning Observation & Interview” summary page for different grade levels that included an independent task to begin the pathway. We then determined the key strategies for problem solving that would be taught at the kindergarten, grade 1-3 and grade 4-5 levels.

3. Rationale for the Focus/Inquiry Question What research, resources or educational experiences helped you to formulate this focus and/or inquiry question? As an OFIP school the focus of our pathways for the last 5 years has been literacy. EQAO Data, report cards and teacher assessments showed that the school should continue to use high yield strategies in literacy, but also focus on mathematics, especially problem solving. Problem solving strategies are flexible and can be applied to all 5 math strands so staff decided to use this as a focus. Some teachers had begun to use Three Part Lessons and other staff wanted to implement this strategy. As we proceeded through the Pathway teachers used the initial task, ongoing assessments, observation, moderated marking, sharing between colleagues and final assessments to modify and change their lessons as necessary. Resources used included Ministry materials such as the Effective Guides and Fosnot Kits.

4. Formative InstructionalImprove Assessment Strategies Understanding How did you use a balance of assessment tools and strategies along the Pathway to monitor and improve student thinking and understanding? A preliminary question was developed for different grade levels and administered before teachers began to teach the unit, based on overall expectation “Read, represent, compare and order whole numbers”. Throughout the pathway the teachers used a combination of observations, anecdotal records and moderated marking as assessment tools. Instructional strategies used included establishing learning goals, student success criteria, anchor charts, rubrics, strategy icons such as “Draw a Picture, Make an Organized List”, providing manipulatives and displaying and discussing student work to demonstrate and reinforce the use of effective problem solving strategies. The examples provided the students opportunities to understand why an answer is level 3 or 4 and how to bump a level 2 answer to level 3.

5. Differentiating for Marker Students How did you provide differentiation (instruction and/or assessment) specifically for your Marker Students at any grade? The teachers used flexible groupings throughout the pathway. The students were able to choose the strategy they found most effective. The teachers focused on the development and use of open ended questions. Teachers also used 1:1 direct instruction, modeling, provision of manipulatives and re-teaching. The students were taught to re-read the question and to high light key phrases and words to help increase their understanding of specific questions. Anchor charts were also available in the room.

6. Reflection How did this Pathway inform your thinking and practice? The teachers began to understand how to develop appropriate questions. They also recognized a need for resources to assist them in developing questions in math, such as Marion Small’s book, Good Questions and Fosnot Kits. This pathway supported moving forward throughout the year to help students apply problem solving techniques in other strands of the mathematics curriculum. It also supported the goals of the School Improvement Plan.

7. Rubric for Grade 1/2 Performance Task Curriculum connections: Overall: -Read, represent, compare, and order whole numbers to 50 Specific: -Demonstrate using concrete materials, the concept of conservation of numbers -Relate numbers to the anchors of 5 and 10 -Compose and decompose numbers up to 20 (10) in a variety of ways, using concrete materials Overall: -Solve problems involving the addition and subtraction of single-digit whole numbers, using a variety of strategies. Specific: -Solve a variety of problems involving the addition and subtraction of single-digit whole numbers to 20 using concrete materials -Solve problems involving the addition and subtraction of single-digit whole numbers using a variety of mental strategies

8. CategoriesLevel 1Level 2Level 3Level 4 Knowledge -knowledge of content, facts, terms, procedural skills, use of tools -understanding of composing numbers to 10 using addition - demonstrates limited knowledge of the composition and decomposition of numbers to 20 (10) and is able to relate them to anchors of 5 and 10 -demonstrates limited knowledge of strategies and tool selection to solve the problem - demonstrates some knowledge of the composition and decomposition of numbers to 20 (10) and is able to relate them to anchors of 5 and 10 -demonstrates some knowledge of strategies and tool selection to solve the problem - demonstrates considerable knowledge of the composition and decomposition of numbers to 20 (10) and is able to relate them to anchors of 5 and 10 -demonstrates considerable knowledge of strategies and tool selection to solve the problem - demonstrates thorough knowledge of the composition and decomposition of numbers to 20 (10) and is able to relate them to anchors of 5 and 10 -demonstrates thorough knowledge of strategies and tool selection to solve the problem Thinking Understanding the Problem Planning and Carrying Out the Plan Reflecting - shows limited understanding of the problem -selects a strategy and attempts to develop a solution -provides limited justification for solution -shows some understanding of the problem -selects a strategy and develops a partial solution -provides some justification for solution -shows considerable understanding of the problem -selects a strategy and provides an accurate solution -provides considerable justification for solution -shows thorough understanding of the problem -selects an efficient strategy or a combination of strategies and provides a complex solution -provides thorough justification for solution

9. CategoriesLevel 1Level 2Level 3Level 4 Communication Expression and Organization of Ideas Communication for Different Audiences Use of Conventions (addition) -communicates strategies with limited effectiveness -provides limited explanation and recordings -demonstrates limited ability to use mathematical terminology appropriately -communicates strategies and reasoning with some effectiveness -provides some explanation and recordings -demonstrates some skills in using mathematical terminology appropriately -communicates strategies and reasoning with considerable effectiveness -provides considerable explanation and representation to demonstrate understanding -demonstrates considerable fluency using mathematical terminology - thoroughly communicates strategies and reasoning with clarity -provides thorough explanation and representations -demonstrates thorough fluency using mathematical terminology Application -applies previous knowledge and understanding of “Bunk Bed and Apple Boxes” unit -transfer of knowledge and skills in reference to “Bunk Bed and Apple Boxes” using the number 10 -applies knowledge of the composition and decomposition of numbers to 10 -With limited effectiveness, applies knowledge, skill and understanding of numbers to 10 using previous experience of “Bunk Bed and Apple Boxes” unit -transfers knowledge and skills to new contexts with limited effectiveness -represents with limited effectiveness the composition and decomposition of the number 10. -With some effectiveness, applies knowledge, skill and understanding of numbers to 10 using previous experience of “Bunk Bed and Apple Boxes” unit -transfers knowledge and skills to new contexts with some effectiveness -represents with some effectiveness the composition and decomposition of the number 10. - With considerable effectiveness applies knowledge, skill and understanding of numbers to 10 using previous experience of “Bunk Bed and Apple Boxes” unit -transfers knowledge and skills to new contexts with considerable effectiveness -represents with considerable effectiveness the composition and decomposition of the number 10. - With a comprehensive understanding applies knowledge, skill and understanding of numbers to 10 using previous experience of “Bunk Bed and Apple Boxes” unit -transfers knowledge and skills to new contexts with thorough effectiveness -represents with thorough effectiveness the composition and decomposition of the number 10 demonstrating a successful systematic strategy.

10. Grade 2, Level 2: Nawang found some of the number sentences. He did not use an organized list.

11. Grade 2, Level 3: Ryan found all the combinations. He sued an organized list and was able to explain his thinking and the strategies he used.

12. Grade 2, Level 4: Naiya found all the possible combinations. She used an organized list and was able to explain her thinking and the strategies she used, in detail.

13. Grade 1, Level 2: Jad began to write an organized list and then got confused at 6 + 6.

14. Grade 1. Level 3: Elijah got almost all/most of the combinations. He was able to get himself back on the correct pattern after an error.

15. Grade 1, Level 4: Ran was able to choose her own number and chose a high number, 14. She found all the combinations and was able to explain how she knew all the combinations. She recognized that there was a pattern of numbers increasing or decreasing by 1.