Student Success 2011 Summer Program NAME OF YOUR MODULE HERE. PUT TITLE HERE. Student Success Summer 2011 Program Mathematics. Welcome. Summer Institute Goals. Participants will: know why questioning is the focus

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Summer Institute Goals Participants will: • know why questioning is the focus • experience the process of creating effective questions including open questions and parallel tasks • consider classroom dynamics to provide environments for powerful learning • become aware of available resources

Provincial Context: Core Priorities • High Levels of Student Achievement • Reducing the Gaps in Student Achievement • Increased Public Confidence in Our Publicly Funded Schools

Student INSTRUCTIONALTASK Teacher/Students LEARNING: SELF-MONITORING Resource Teacher Tutor or Self Learning Goal Success Criteria Learning Tools IEP INSTRUCTIONALTRAJECTORY Coach Coach Look Fors Classroom Resources Board Lead/Consultant District Lead Supporting the Instructional Core Leading Learning – Leadership

Example Board (BIP) Classroom (planning for teaching and learning) Professional Learning Cycle (collaborative inquiry) Literacy: Writing Literacy: Writing Gr. 9 Tech Ed and Visual Arts, Gr. 10 Computer Studies: Common Assessment area - Expression and Organization of Ideas (Achievement Chart) School (SIP) Literacy: Writing Gr. 9 & 10 Applied/Open

PROGRAMS Specialist High Skills Major Dual Credits Expanded Cooperative Education Ontario Skills Passport Board Specific Programs LEADERSHIP DEVELOPMENT Student Success Leaders Student Success Teachers Student Success School and Cross Panel Teams EFFECTIVE INSTRUCTION Differentiated Instruction Math GAINS Literacy GAINS Professional Learning Cycle Student Voice School Effectiveness Framework INTERVENTIONS Credit Rescue / Recovery Transitions Supports/Taking Stock Children and Youth in Care Re-engagement 12 12+Strategy Supervised Alternative Learning School Support Initiative Student Success Grades 7-12 Key Elements

Pyramid of Preventions andInterventions Re-entry to School Program Change Open Questions& Parallel Tasks ALL SOME FEW In-School Interventions (e.g. Credit Recovery) Gap Closing In-Class Interventions (e.g. Credit Rescue) TIPS CLIPS WINS In-School & In-Class Preventions (e.g. Transitions, Differentiated Instruction)

Math Talk Learning Communities Joan Green in Connections by the Staff Development Council of Ontario Winter 2011 Volume 2 Issue2 Informal and formal verbal interactions help students to build relationships that support new awareness and emerging understandings. Vygotsky’s “zone of proximal development” addresses this idea … that talk with more informed peers can support acquisition of concepts or capacity in ways that are not possible for learners working in isolation, no matter how impressive their individual efforts may be. 12

Purposes of Questions Think/Pair/Share What purposes do effective questions have? ? ? ? ? ?

Questioning That Matters 16 • What is (-3) – (-4)? • Tell how you calculated (-3) – (-4). • Use a diagram or manipulatives to show how to calculate (-3) – (-4) and tell why you do what you do. • Why does it make sense that (-3) – (-4) is more than (-3) – 0? • Choose two integers and subtract them. What is the difference? How do you know?

Different Purposes 17 Do you want students to • be able to get an answer? [What is (-3) – (-4)?] • be able to explain an answer? [Explain how you calculated (-3) – (-4).] • see how a particular aspect of mathematics connects to what they already know? [Use a diagram or manipulatives to show …and tell why …]

Different Purposes 18 Do you want students to • be able to describe why a particular answer makes sense? [Why does it make sense that (-3) – (-4) is more than (-3) – 0? ] • be able to provide an answer? [Choose two integers and subtract them. What is the difference? How do you know?]

It is important that every student: 19 responds to questions with these various purposes makes sense of answers and multiple ways of responding believes, ‘I can do it if I try’

Your answer is….? A graph goes through the point (1,0). What could it be? What makes this an accessible, or inclusive, sort of question? 21

Possible responses 22 y x (1,0) x = 1 y = 0 y = x - 1 y = x2 - 1 y = x3 - 1 y = 3x2 -2x -1

Contrast Open: The area of a rectangle is 400 square units. What could its dimensions be? Not open: The area of a rectangle is 432 square units. The length is 12 units, what is the width? 23

Open Questions An open question provides valuable information about the range of knowledge in your classroom. It should be accessible to all students. Student responses help you know how to proceed with your lesson. 24

How to open questions • Begin with the answer. Ask for the question. For example, the sum of two fractions is 1/2 .What might the fractions be? • Ask for similarities and differences. For example, how are y = 3x and y = 2x alike? How are they different? • Leave certain information out of the problem, e.g. omit numbers. For example, two right triangles are similar. One has two side lengths of 4 and 6. The other has one side length of 12. What lengths could the other three sides be? • Provide several numbers and math words; the student must create a sentence using all the numbers and words. For example, create a sentence that uses the words and numbers 40, 5, ratio, scale. • Use “soft” language. For example, two ratios are “almost but not quite” equivalent. What might they be?

Begin with the answer 26 The solution to the equation is x = 2. What is the equation? The difference of two fractions is 3/5. What are the fractions? The slope of the line is ¾. What points does the line go through? One side of a right triangle is 13 cm. What are the other side lengths?

Ask for similarities and differences 27 How are quadratic equations like linear ones? How are they different? How is calculating 20% of 60 like calculating the number that 60 is 20% of? How is it different? How is dividing rational numbers like dividing integers? How is it different?

How could you open up these? Add: 3/8 + 2/5. A line goes through (2,6) and has a slope of -3. What is the equation? Graph y = 2(3x - 4)2 + 8. Add the first 40 terms of 3, 7, 11, 15, 19,… 28

When to Use Open Questions • How might open questions be effective for identifying students’ prior knowledge? For providing an opportunity to provide formative feedback? For collecting summative evidence? • Do you see them more as “exposing” or as “evoking” thinking? Discuss with a partner. 29

Getting Stuck Using a model write addition sentences that describe your whole as the sum of parts.

Getting Unstuck - Scaffolding • What is the same about your models and addition sentences? What is different? • What is the smallest number of parts that you can add to make one whole? What is the largest? • What do you notice about the denominator if you are using two identical pieces to cover the whole?...three pieces? ...if you use many of the same pieces to cover the whole? • What would be different about your addition sentence if you used different pieces to cover the whole?

Getting stuck You graph 3 lines. The 1st is 3x + 2y = 6 and the 2nd is –x + 3y = 17. Another line lies between them. What might its slope be? How do you know?

Getting Unstuck -Scaffolding • Do you think the slope will be positive or negative? Why? • Might it help to graph the two lines you are given? Do you have to? • If you graph the new line, how would you calculate the slope? • Would it help to decide its intercept first or it slope first?

Parallel Tasks • Engage students in the same mathematical concept, and give them choice based on readiness with respect to factors such as • Strategy • Numbers that they use to do the math • Allow teachers to ask “Common Questions” • that make explicit the important mathematics in the task • invite students to explain and defend their thinking

Parallel Tasks – Example 1 • Choice A: A number between 20 and 30 is 80% of another number. What could the second number be? • Choice B: A number between 20 and 30 is 150% of another number. What could the second number be?

Common Debriefing Questions • Is the second number greater or less than the first one? How did you decide? • Is there more than one answer? How do you know? How far apart are they? • How else could you compare the two numbers? • What strategy did you use?

Scaffolding Questions • How else can you think of 80%? 150%? • How do you know that the second number can’t be 50? • What picture could you draw to help you? • What’s the least the second number could be? How do you know?

Choice A: A line of slope -3/2 goes through (-4,-1). What is the equation? Choice B: A line of slope 2/3 goes through (-4,-1). What is the equation? Parallel Tasks – Example 2

Common Debrief Questions • Do you know which way your line slants? How do you know? • Could (-4, 3) be on your line? How do you know? Could (-3, 0) be on your line? How do you know? • What do you need to know to write the equation? How can you get that information? • What is your equation? How can you be sure you’re right?

Choice A: Use algebra tiles to model two polynomials that add to 6x2 +8x+2. Choice B: Use algebra tiles to model two polynomials that multiply to 6x2 +8x+2. Parallel Tasks – Example 3

Common Debrief Questions • What algebra tiles show 6x2 +8x+2? • Is there any other way to model that polynomial? • How did you arrange your tiles? • How did you figure out how to start? • Is there any other way you could have arranged the tiles?

Parallel Tasks – Example 4 • Task A: One electrician charges an automatic fee of $35 and an hourly fee of $45. Another electrician charges no automatic fee but an hourly fee of $85. What would each electrician charge for a 40 minute service call? • Task B: An electrician charges no automatic fee but an hourly fee of $75. How much would she charge for a 40 minute service call? 43

Common Debriefing Questions • How do you know the charge would be more than $40? • How did you figure out the fee?

Steps for Creating Parallel Questions • Select the initial task. • Anticipate student difficulties or what makes the task too simple for some students. • Create the parallel task, ensuring that the big idea is not compromised. • Create at least three or four common questions that are pertinent to both tasks. You might use Mathematical Processes and Big Ideas to help here. These should provide insight into the solution and not just extend the original tasks. • Ensure that students from both groups are called upon to respond. Proportional Reasoning Package Pg. 23

Common & Scaffolding Practice Choice A: Linear Growing Patterns Choice B: Linear Relations Choice C: Quadratic Relations Choice D: Trigonometric Functions • Choose parallel tasks A, B, C, or D. • Create common questions for the tasks. • Create scaffolding questions for the tasks. • Share with another pair.

Common Debrief Questions • What did you find the most difficult? • What strategies did you use? • How did your questions look the same & different from another group? • What was the same & different between your questions and those from another task?