Professional Learning for Mathematics Leaders and Coaches—Not just a 3-part series Day 3

What’s My Number? Multiply the number of brothers you have by 2 Add 3 Multiply by 5 Add the number of sisters you have Multiply by 10 Add the number of living grandparents Subtract 150 Your number is: ____ ____ ____ # of brothers # of sisters # of grandparents

Inside/Outside Circle Each person from your board go to one of the four corners 1 min discussion Share an interesting aspect from the ‘view & discuss’ or ‘do’ that you participated in. How are the Big Ideas impacting your practice? Which is more comfortable for you: Open or Parallel Task, and why? How are you using the MATCH Template and/or PPQT to help you with lesson planning? Check for wording from the program How could we do this strategy for One from each board

Provincial-level Evidence

Provincial-level Evidence

Board-level Evidence and BIPs Halton DSB’s 2009-10 Math GAINS Transition Project paper Peterborough Victoria Northumberland Clarington CDSB 2-part roving Math GAINS report Greater Essex CDSB roving Math GAINS report

Next Steps – Materials K to Grade 8+ Mathematics Package Grade bands K-1, 2-3, 4-5, 6-7, 7-8, ?-? Focused on Number Sense “not just a workbook” for students and “guide” for learning facilitators Intended for home use, but good for other applications 3-part lessons with 4 parallel questions addressing the same learning goal multiple solutions with scaffolding questions

Next Steps – Professional Learning Sessions January to June 2010 with all expenses paid by the ministry - possible themes: K to Grade 8+ Mathematics Package Classroom Management Package Strategic planning work sessions Access customized provincial-level support through Jeff Irvine, Myrna Ingalls, Demetra Saldaris Regular postings on www.edugains.ca

Addressing Questions from Session 2

Scaffolding Thinking Prompts • We ask an open question. • Nobody responds. • One thing we need to work on are strategies to use in that situation. Let’s try an example. Provide BLM at the end of Scaffolding strategies

Scaffolding Thinking Prompts • Let’s start with one of the open questions from last session.

Scaffolding Thinking Prompts Open Question: Create two linear growing patterns that are really similar. • How are they similar?

Scaffolding Thinking Prompts Open Question: Create two linear growing patterns that are really similar. How are they similar? • Could one of your patterns be 1, 4, 9, 16,…? Explain. To see if students know what linear means

Scaffolding Thinking Prompts Open Question: Create two linear growing patterns that are really similar. How are they similar? • If you were describing your pattern to another student, what information would you give them? Turn and talk

Scaffolding Thinking Prompts Open Question: Create two linear growing patterns that are really similar. How are they similar? • Are 2, 5, 8, 11, 14,… and 5, 10, 15, 20,… really similar? To get them to think about what similar mean Recall this was an open question A reasonable response how do you value In an open question – value and then look at the qualifier

Discuss at your table: How do the three questions help students with scaffolding their thinking to answer the open question? Open Question: Create two linear growing patterns that are really similar. How are they similar?

How does the Big Idea and the Lesson Goal impact the questions you are asking for scaffolding? BLM2 to include Big Idea & Lesson Goal

Another example from last time • Which two graphs do you think are most alike? Why? Y = 3x2 – 2 y = -3x2 – 2 Y = 2x2 + 3 y = 3x2 + 2 Why did you choose those functions for the students to talk about? What are you going for? Could provide for the teachers the graphs so that they can have the discussion, not in the ppt but provided at each table

Scaffolding Thinking Prompts • What would you be looking for to decide if two graphs were alike? Do any of the graphs go through the same points? Do any of the graphs open in the same direction? • Are any of the graphs congruent to other graphs?

Scaffolding Thinking Prompts Which one of the Scaffolding Thinking Prompts do you like? Why?

Algebraic expressions It takes more than 5 English words to describe an algebraic expression that has one term. What could the algebraic and verbal expressions be? Double a number and then triple it

Scaffolding Thinking Prompts • How many English words does it take to describe 2n? • Could the algebraic expression be 2n+3? Why or why not? How many terms would the expression “a number squared” take?

Scaffolding Task: Choose one of the open questions: Decide under what conditions would you use those scaffolding questions.

• Now draw another picture that shows This picture shows that 4x + 2 = 2 (2x + 1). no matter what x is. • Explain why. • Now draw another picture that shows another equation that is true no matter what x is.

•Graph the 2 lines. The 1st is 3x + 2y = 6 and the 2nd is –x + 3y = 17. A third line lies between them. What might its equation be?

Break

General & specific scaffolds •Most of the scaffolds we just saw were very problem specific. • General scaffolds are also helpful.

Fail Safe Strategies • Where have you seen something like this before? • What patterns do you see? • Have you thought about….?

General & specific scaffolds •A useful source for general scaffolds is available in the mathematical process package in TIPS on the Edugains website. (show a questioning piece)

Your turn to scaffold •Looking at the parallel task, decide what possible scaffolds might be needed.

Looking at Student Work In pairs, pick one of the student’s work. What feedback would you give students to move them forward? Share with another pair.

Lunch

Assessment issues •Open questions and parallel tasks are built for instruction. The focus is not on evaluation, but…

Assessment issues •It makes total sense to use parallel tasks to measure communication and/or thinking and maybe (depending) knowledge or application.

Example 1 Task A: Think of a way to represent the pattern with the general term 3n +1. Is 925 a term in the pattern? How do you know? Task B: Think of a way to represent a pattern where each term value is eight times the term number. Is 925 a term in the pattern? How do you know? Learning goal: Represent the general term of a linear growing pattern

Possible Scoring Scheme This could be marked as a 6-mark question 3 marks for a really good representation of the pattern which means that you are representing the right pattern (which is the most important thing) without errors 1 mark for correctly deciding whether 925 is in the pattern 2 marks for a complete explanation for why 925 is or is not in the pattern

Another Example Task A: Task B: Explain and justify each step you would use in solving the equation without using a calculator. Task B: Explain and justify each step you would use in solving the equation without using a calculator. 1.5 x – 4.2 = 7.3 Not measuring algebraic expressions for general term, but yes for representing linear growing patterns, predicting, etc.

Which of those things could you have predicted without sketching? Why? Example 2 Task A: Sketch graphs of y = 2x and y = 2-x. Tell how the graphs are alike and different. Task B: Sketch graphs of y = x2 and y = -2x2. Tell how the graphs are alike and different. Not measuring algebraic expressions for general term, but yes for representing linear growing patterns, predicting, etc. Which of those things could you have predicted without sketching? Why?

Possible Rubric Learning Goal: Examine the effects of the parameters given two graphs of the same type of function

Assessment issues •It makes sense, even on a “test”, to use open tasks to ensure that students get an opportunity to tell as much as they know in whatever form works for them about an idea they have learned.

Example 3 Choose an equation to solve where the solution is an integer. Solve it in at least three different ways, explaining your thinking for each method. Suppose you had chosen an equation where the solution turned out to be a fraction. Which of your methods would be more likely to help you? Why?

A possible Rubric Learning Goal: Different representations of equations are more useful depending on the situation.

Another Example •Describe a number of examples of measurements or situations that would model direct variation. What is it about them that makes the variation direct? Would you use

Another Example •Give as many reasons as you can to explain why there are many quadratic relations that pass through the points (0,0) and (2,4)

It is important … •to use a previously shared rubric or marking scheme before posing such questions to help students meet success.

Assessment issues •Although assessment of learning should drive what you teach, it should not limit the strategies you use to meet all students’ needs.

Break out Move to one of the following areas of interest: Working with Student Samples (Assessment for Learning) Developing Scaffolding Questions Forming Open & Parallel Questions Creating Consolidating Questions

Summarizing big ideas •Our “big idea” for this PLMLC series is that if you think more broadly about what you are focusing on in instruction, you are more likely to:

Summarizing big ideas •help students make essential connections • ensure that students learn what is really important ensure that a much broader range of students can meet success

Work in Boards Group Talk about moving forward with the ideas we have been working on Facilitators will be happy to join your team if you want a different set of eyes Call on another board to share ideas

Your questions •You are welcome to ask any questions or offer any insights on what we’ve discussed in today’s plenary .

Next Steps – Professional Learning Sessions January to June 2010 with all expenses paid by the ministry - possible themes: K to Grade 8+ Mathematics Package Classroom Management Package Strategic planning work sessions Access customized provincial-level support through Jeff Irvine, Myrna Ingalls, Demetra Saldaris Regular postings on www.edugains.ca