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Shifting Instruction to Strengthen the Opportunity to Learn Both

Content and English

OELAS ConferenceDecember 14, 2012

Steve LeinwandAmerican Institutes for Research

SLeinwand@air.org

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So…the problem is:

If we continue to do what we’ve always done….

We’ll continue to get what we’ve always gotten.

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Algebra:The intense study of the last

three letters of the alphabet

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So what does that result in?

• Little growth of important content knowledge

• Little growth in English facility• Little preparation for the real world• Little preparation for the world of the

Common Core State Standards for Mathematics “mathematical practices”

And what have we gotten?

• Mountains of math anxiety• Tons of mathematical illiteracy• Mediocre test scores• HS programs that barely work for more than

half of the kids• Gobs of remediation and intervention• A slew of criticism

Not a pretty picture!

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If however…..

What we’ve always done is no longer acceptable, then…

We have no choice but to change some of what we do and some of how we do it.

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So what does different mean?

Some data. What do you see?

40 410 230 4

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Predict some additional data

40 410 230 4

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How close were you?

40 410 230 420 3

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All the numbers – so?

45 425 315 240 410 230 420 3

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A lot more information(where are you?)

Roller Coaster 45 4Ferris Wheel 25 3Bumper Cars 15 2Rocket Ride 40 4Merry-go-Round 10 2Water Slide 30 4Fun House 20 3

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Fill in the blanks

Ride ??? ???Roller Coaster 45 4Ferris Wheel 25 3Bumper Cars 15 2Rocket Ride 40 4Merry-go-Round 10 2Water Slide 30 4Fun House 20 3

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At this point, it’s almost anticlimactic!

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The amusement park

Ride Time TicketsRoller Coaster 45 4Ferris Wheel 25 3Bumper Cars 15 2Rocket Ride 40 4Merry-go-Round 10 2Water Slide 30 4Fun House 20 3

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The Amusement Park

The 4th and 2nd graders in your school are going on a trip to the Amusement Park. Each 4th grader is going to be a buddy to a 2nd grader.

Your buddy for the trip has never been to an amusement park before. Your buddy want to go on as many different rides as possible. However, there may not be enough time to go on every ride and you may not have enough tickets to go on every ride.

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The bus will drop you off at 10:00 a.m. and pick you up at 1:00 p.m. Each student will get 20 tickets for rides.

Use the information in the chart to write a letter to your buddy and create a plan for a fun day at the amusement park for you and your buddy.

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Why do you think I started with this task?

- Standards don’t teach, teachers teach- It’s the translation of the words into tasks

and instruction and assessments that really matter

- Processes are as important as content- We need to give kids (and ourselves) a

reason to care- Difficult, unlikely, to do alone!!! 23

Join me in Teachers’ Room Chat• They forget• They don’t see it my way • They approach it differently• They don’t follow directions • They give ridiculous answers • They don’t remember the vocabulary

THEY THEY THEY BLAME BLAME BLAME

An achievement gap or an INSTRUCTION gap?

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Well…..if…..• They forget – so we need to more deliberately

review;• They see it differently – so we need to

accommodate multiple representations;• They approach it differently – so we need to elicit,

value and celebrate alternative approaches;• They give ridiculous answers – so we need to

focus on number sense and estimation;• They don’t understand the vocabulary – so we

need to build language rich classrooms;• They ask why do we need to know this – so we

need to embed the math in contexts.

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Today’s GoalTo provoke and inform your thinking about the need to shift instructional practices and mindsets in ways that are aligned with the vision of the new Common Core State Standards and that truly meet the needs of all students.

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Today’s Agenda• Three perspectives on our reality• The Common Core context• Some glimpses at powerful instruction• Some challenges to you

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1. What a great time to be worrying about mathematics!

• Common Core State Standards adopted by 45 states• Quality K-8 instructional materials• More access to material and ideas via the web than

ever• A president who believes in science and data• The beginning of the end to Algebra II as the killer• A long overdue understanding that it’s instruction

that really matters• A recognition that the U.S. doesn’t have all the

answers28

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2. Let’s be clear:We’re being asked to do what has never been done before:

Make math work for nearly ALL kids and get nearly ALL kids ready for college.There is no existence proof, no road map, and it’s not widely believed to be possible.

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3. Let’s be even clearer:Ergo, because there is no other way to serve a much broader proportion of students:

We’re therefore being asked to teach in distinctly different ways.Again, there is no existence proof, we don’t agree on what “different” mean, nor how we bring it to scale.(That’s the hope of the CCSSM for Math)

Common Core Promises

These Standards are not intended to be newnames for old ways of doing business. They area call to take the next step. It is time for statesto work together to build on lessons learnedfrom two decades of standards based reforms.It is time to recognize that standards are notjust promises to our children, but promises weintend to keep.

— CCSSM (2010, p.5)

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Some design elements of the CCSSM• Fewer, clearer, higher• Fairer – rational grade placement of procedures• NCTM processes transformed into mathematical practices• Learning trajectories or progressions• Spirals of expanding radius – less repetitiveness and redundancy• A sequence of content that results in all students reaching reasonable algebra in 8th grade • Balance of skills and concepts – what to know and what to understand

8 CCSSM Mathematical Practices

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

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8 CCSSM Mathematical Practices

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

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So how should this be playing out in every Arizona mathematics classroom?

Regular EdELL

Special Ed

Let’s Take a Look

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A Tale of Two Mindsets(and the alternate approaches they

generate)

Remember Howvs.

Understand Why

Mathematics

• A set of rules to be learned and memorized to find answers to exercises that have limited real world value

OR• A set of competencies and understanding

driven by sense-making and used to get solutions to problems that have real world value

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Number facts8 + 9

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Ready, set,

8 + 9 =17 – know it cold 10 + 7 – decompose the 9 to get to 1018 – 1 – add 10 and adjust16 + 1 – double plus 120 – 3 – round up and adjust

Who’s right? Does it matter?

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Subtracting Whole Numbers

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Find the difference:

1000- 459

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Find the difference:

Who did it the right way??91091010 - 4 5 9

How did you get 541 if you didn’t do it this way?

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Find the difference:

1000- 459

• Counting up (1 is 60, 40 more is 500, …)• Moving from left to right! Subtract 400,

then 50, then 9• Subtracting 1 from each number (999-458)• Eastern European Add-Add algorithm

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Find the difference:

Add 10 Add 10

10010 - 4 56 9

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Find the difference:

Add 100 Add 100

101010 - 45 56 9

5 4 1

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Adding and Subtracting Integers5 + (-9)

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Remember How

5 + (-9)

“To find the difference of two integers, subtract the absolute value of the two integers and then assign the sign of the integer with the greatest absolute value”

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Understand Why

5 + (-9)

- Have $5, lost $9 - Gained 5 yards, lost 9- 5 degrees above zero, gets 9 degrees colder- Decompose 5 + (-5 + -4) - Zero pairs: x x x x x O O O O O O O O O

- On number line, start at 5 and move 9 to the left

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Multiplying Decimals

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Remember How 4.39x 4.2

“We don’t line them up here.” “We count decimals.” “Remember, I told you that you’re not allowed to

that that – like girls can’t go into boys bathrooms.” “Let me say it again: The rule is count the decimal

places.”

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Understand Why

4.2 gallons

$ 4.39

Total

How many gallons? About how many? Max/min cost?

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Understand Why

4.2 gallons

$ 4.39

Total183.38

Context makes ridiculous obvious, and breeds sense-making

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Solving Simple Linear Equations

3x + 7 = 22

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3x + 7 = 22

How do we solve equations:

Subtract 7 3 x + 7 = 22 - 7 - 7 3 x = 15

Divide by 3 3 3

Voila: x = 5

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3x + 7 = 22

1. Tell me what you see: 3 x + 72. Suppose x = 0, 1, 2, 3…..3. Let’s record that:

x 3x + 7 0 7

1 10 2 13

4. How do we get 22?

3x + 7 = 22

Where did we start? What did we do?

x 5 x 3 3x 15 ÷ 3

+ 7 3x + 7 22 - 7

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3x + 7 = 22

X X X IIIIIII IIII IIII IIII IIII II

X X X IIIII IIIII IIIII

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Multiplying Whole Numbers

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Remember How

213 X 4

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Understand Why213 x 4

• 213 + 213 + 213 + 213 = 852

• 4 200 10 3 800 40 12 = 852• 4 ( 200 + 10 + 3) =

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Which leads to:

4 threes4 tens4 two hundreds

213 X 4 12 40 800 852

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Place Value

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Remember How

32,485

What is the value of the 4?What digit is in the thousands place?

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Understand Why

32,485About how many? 30,000

32,00032,50032,490

10 more? 10 less? 100 more? 100 less? 1000 more? 1000 less?

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People won’t do what they can’t envision,People can’t do what they don’t understand,People can’t do well what isn’t practiced,But practice without feedback results in little

change, andWork without collaboration is not sustaining.

Ergo: Our job, as professionals, at its core, is to help people envision, understand, practice, receive feedback and collaborate.

So the key things we know

To collaborate, we need time and structures

• Structured and focused department meetings• Before school breakfast sessions• Common planning time – by grade and by department• Pizza and beer/wine after school sessions • Released time 1 p.m. to 4 p.m. sessions• Hiring substitutes to release teachers for classroom visits• Coach or principal teaching one or more classes to free up

teacher to visit colleagues• After school sessions with teacher who visited, teacher who

was visited and the principal and/or coach to debrief• Summer workshops• Department seminars

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To collaborate, we need strategies 1Potential Strategies for developing professional learning communities:• Classroom visits – one teacher visits a colleague and the they debrief• Demonstration classes by teachers or coaches with follow-up debriefing• Co-teaching opportunities with one class or by joining two classes for a

period• Common readings assigned, with a discussion focus on:

– To what degree are we already addressing the issue or issues raised in this article?

– In what ways are we not addressing all or part of this issue?– What are the reasons that we are not addressing this issue?– What steps can we take to make improvements and narrow the gap

between what we are currently doing and what we should be doing?• Technology demonstrations (graphing calculators, SMART boards,

document readers, etc.)• Collaborative lesson development

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To collaborate, we need strategies 2Potential Strategies for developing professional learning communities:• Video analysis of lessons• Analysis of student work• Development and review of common finals and unit assessments• What’s the data tell us sessions based on state and local assessments• “What’s not working” sessions• Principal expectations for collaboration are clear and tangibly

supported• Policy analysis discussions, e.g. grading, placement, requirements,

promotion, grouping practices, course options, etc.

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So….While we acknowledge the range and depth of

the problems we face,It should be comforting to see the availability

and potential of solutions to these problems….

Now go forth and start shifting YOUR school’s mathematics program to better serve our students, our society and our future.

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Thank you!

SLeinwand@air.org