Coaching for Math GAINS

PDSB Mathematics Co-Teaching

Project

Anchor Session #1October 1, 2010

OVERVIEW OF THE MORNING

► Welcome & Welcome Back► Review Norms► Re-capping our journey► Minds On: Activating Prior Knowledge► Action: Brushing up on our skills► Consolidation: Putting your plan together

Reviewing our Norms• Start and end on time.• Contribute to a safe learning environment

that encourages risk taking; be kind.• Listen actively; speak fearlessly.• Invest in your own learning and the

learning of others.• All electronic communication devices

off except during lunch/break.• Suffering is optional!

Ice Breaker

When you registered this morning you received an index card with three numbers on it. The number on the front is your number. The numbers on the back represent the two people you are going to meet with.

Ice BreakerUse the index card to jot down the following information about the people you meet:1. Name and school/family.2. Grade or courses being taught this year.3. Song, Movie or Book Title that best describes

… your experience with Math GAINS last yearor

… how you feel about participating for the first time.

Highlighting Your FeedbackMy Important Book About Math GAINS

The important thing about Math GAINS is … that it makes me want to be a better teacher

It's like … a gentle push to try something newIt can be … a new beginning or the turn of a cornerIt isn't … that hard, if you let it work its magicIt is … a guiding light, a bright light, lit by the minds of my students But the most important thing about Math GAINS is … that it makes me want to be a better teacher.

Re-capping Our Journey► You were introduced to:

Big Ideas and why they are important. Dr. Small’s 6 Big Ideas for Algebra. How to differentiate instruction through

questioning. What open questions are and how to

develop them. What parallel tasks are and strategies for

creating them. Common questions that can be used to

debrief open & parallel tasks

Re-capping Our Journey … continued

► You engaged in activities and discussions about creating powerful lessons, including:

the importance of using open questions in the Minds On part of the lesson to provide assessment for learning.

how consolidating questions help you know whether your students understood the lesson goal

how rich activities/problems help engage students and promote meaningful math talk in your classroom

Re-capping Our Journey … continued

► In your family of schools team, together with your coach/facilitator you …

incorporated these skills and strategies into effective lesson plans

observed how other teachers used the strategies and what impact they had on student learning

provided feedback for others, and received feedback yourself, to help inform and grow your practice

opened-up your classroom to others

Personal Reflection

Consider the reflection guide on the screen.

Using the coloured dots provided, indicate where you are on each continuum posted on the wall.

How comfortable are you with other teachers watching your students learn?

Please stand along the continuum to indicate

your comfort level from very comfortable to

not very comfortable .

Overview for this YearAreas of focus:

• Continued emphasis on co-planning and co-teaching with a facilitator.

• Questioning, differentiated instruction, problem solving, big ideas, lesson goals, building discussion, manipulatives, technology, or assessment

• Incorporating Transformational Practices• Integrating the Math Gains process into the

PLC or TLCP

Are We Numbed by Numbers?Here’s a skill-testing question: To get a

sweepstakes prize in Canada, why do you need to solve a simple math problem?

Because by law, you cannot win by pure luck.  An element of skill must be involved, like calculating (3 × 8) + (17 × 3).

Adult numeracy in Canada is assessed on a scale from 1 (lowest) to 5 (most advanced).  Level 3 is where people demonstrate the math abilities to function well in society.  In a government survey,

45% of adult Canadians were at level 3 or higher 30% were at level 2, and get this a full quarter of adults were at level 1.

Are We Numbed by Numbers?

Are We Numbed by Numbers?

BETTER NEWS:15-year-old Canadian students do fairly well on math scores when compared to other western countries.

Still, too many young people are low in confidence and high in anxiety when it comes to math.

The Organization for Economic Co-operation and Development (OECD) points out that science, math and technology play a bigger role in everyday life than we might think.

And they’re not talking formulas, here.

Being able to identify proportions and patterns is strongly linked with better opportunities for learning, with advancement at work, and with our ability as a nation to meet the skill demands of the modern economy.

Are We Numbed by Numbers?

How is your sense of quantity?

Most hummingbirdsflap their wingsabout 180 000 or sotimes every hour.

Source: http://www.hummingbirdworld.com/h/behavior.htm

With your elbow partner … turn and talk about what you could do to compare the rate at which the hummingbird flaps its wings to a similar activity that a human could perform.

Time to Experiment

Test your idea and share your analysis with the other people at your table.

That's about 1500 times in a 30-second interval. How well did your partner fare against the hummingbird?

Debrief: The Hummingbird Problem

Debrief … continuedWhat might your lesson goal be?

Debrief … continuedWhat might your lesson goal be?

What other questions might you ask to stimulate discussion?

A Fermi problem is a multi-step problem that can be solved in a variety of ways, and whose solution requires the estimation of key pieces of information.

Linking Assessment, p. 116

What is a Fermi Problem?

Solving a Fermi Problem

Goal(s) for a Specific LessonStudents will work cooperatively to solve a problem in a context requiring estimation. Students will communicate mathematical thinking.

Big Idea(s) Addressed by the ExpectationsNumbers are compared in many ways. Sometimes they are compared to each other; other times, they are compared to benchmark numbers. (BIN4)

Curriculum ExpectationsSolve multi-step problems arising from real life contexts … using a variety of tools and strategies; Use estimation when solving problems … to help judge the reasonableness of a solution

Lesson Title: Grade/Program: 8

Solving a Fermi Problem

Goal(s) for a Specific LessonStudents will work cooperatively to solve a problem in a context requiring estimation. Students will communicate mathematical thinking.

Big Idea(s) Addressed by the ExpectationsNumbers are compared in many ways. Sometimes they are compared to each other; other times, they are compared to benchmark numbers. (BIN4)

Curriculum ExpectationsSolve multi-step problems arising from real life contexts … using a variety of tools and strategies; Use estimation when solving problems … to help judge the reasonableness of a solution

Lesson Title: Grade/Program: 8

Solving a Fermi Problem

Goal(s) for a Specific LessonStudents will work cooperatively to solve a problem in a context requiring estimation. Students will communicate mathematical thinking.

Big Idea(s) Addressed by the ExpectationsNumbers are compared in many ways. Sometimes they are compared to each other; other times, they are compared to benchmark numbers.

Curriculum ExpectationsSolve multi-step problems arising from real life contexts … using a variety of tools and strategies; Use estimation when solving problems … to help judge the reasonableness of a solution

Lesson Title: Grade/Program: 8

Solving a Fermi Problem

How many grains are there in a 5 kg bag of rice?

• Work with your elbow partner to brainstorm some ideas for tackling the problem. (2 minutes)

• Share your ideas at your table.• Decide on the strategies you want to use, and work

as a group to solve the problem.• Write up the solution on the chart paper provided

and post your solution.

Providing Descriptive Feedback

Effective feedback should:• Describe and inform, not judge• Be specific, not general• Be clear to students• Suggest what students should do to improveAdapted from Formative Assessment Strategies for Every Classroom, Susan M. Brookhart, ASCD

Providing Descriptive Feedback

Using the sticky notes on your table, and the prompts on the following screen, provide descriptive feedback on at least two of the solutions posted on the wall.

Feedback prompts• I can see you used…..• You have shown you understand…• I’m not sure how you …….• Using repeat addition is one way ,another

way is …..• Your next step is……• Another strategy is ……• Your next step is to meet with me so …….

Gallery WalkExamine the other posters..

Discuss what you see.

Provide Descriptive Feedback using your sticky notes.

Return to your own chart to digest and discuss the feedback you received.

Break Time!

The Pool ProblemA community is planning to build a new library. The library is being built next to the community pool with 72 metres between them. The builders want to make sure that the library building does not put a shadow over the pool. At the time of the maximum shadow, a flag pole that is 3 metreshigh gives an 8 metre shadow.

What is the maximum height for the library building?

Where Does the Pool Problem Fit?

The Pool Problem Cont’d…• Use the materials on your table to solve the

problem as a Gr. 7, 8, 9, and 10 student.

• Record your solutions on separate chart paper.

• Beneath each solution, record potential student misconceptions or struggles for that grade.

Thinking About Student Misconceptions

Welcome Back!

Effective teaching involves risk taking … by both the teacher and the student.

Overview of the Afternoon

1. Tying Lesson Goals to Expectations and Big Ideas

2. Consolidating Questions3. A Few Words About Logistics4. Planning Time

More about the pool problem …Create lesson goals across grades 7/8/9/10P

More about the pool problem …Create a consolidating question(s) for the lesson.

More about the pool problem …If you invited other teachers into your classroom to observe this lesson, what would you ask them to look-for in the interactions of your students?

Discuss at your table.

What Does a Co-Planning and Co-Teaching Cycle Feel Like?

• Today, you participated in discussions similar to what happens during the co-planning process.

• Except, when you co-plan you focus on your course, your students, their learning needs, as well as your own learning needs.

• The Co-teaching and Debriefing are the other parts to the cycle.

Logistics• Each school has 30 release days for co-

planning and co-teaching with a facilitator.• Share the fun across your school / dept. • Use PAM code 835 for your coverage.• Copy Wendy Telford on all meetings and

requests for coverage.• Keep your principal informed.• More details coming soon about possible

purchases.

Planning Time• Determine the dates and locations of the 1st

set of co-teaching cycles (each school should host at least one cycle by Winter Break).

• Sign up on the appropriate Facilitator’s Calendar (this is your real exit ticket)

• Discuss how you want to structure your planning time.

who will meet? (by grade, cross-grade, cross-panel) goals? meeting rooms and resources to book?

Exit Card

Something I learned ….

Something confirmed ….

A question I have …

Thank You!