CPAM Leadership Seminar

Practical Strategies for Providing School Based Leadership for More Powerful Teaching of K-12 Mathematics

Steve Leinwand American Institutes for Research [email protected]

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Let’s Reflect: Mirrors, Changes, Engagement, Interactions

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What a great time to be convening as teachers of math!

• • • •

Common Core State Standards Quality K-8 materials $5 billion with a STEM RttT tie-breaker A president who believes in science and data

• •

The beginning of the end of Algebra II A long overdue understanding that it’s instruction, stupid!

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In other words…..

A critical time for leadership!

Our leadership.

Your leadership.

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Today’s Goals

Engage you in thinking about (and then being willing and able to act on) the issues of filling the leadership void and shifting the culture of professional interaction within our departments and our schools.

• • •

Subgoals: validate your concerns, give you some tools and ideas, empower you to take risks

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My Process Agenda

(modeling good instruction)

• • • •

Inform (lots of ideas and food for thought) Engage (focused individual and group tasks) Stimulate (excite your sense of professionalism) Challenge (urge you to move from words to action)

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Today’s content agenda

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Critical Perspectives Problems Examples Themes A blueprint Some discussion A challenge

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What we know and where we fit

(critical perspective 1) Economic security and social well-being

  

Innovation and productivity

  

Human capital and equity of opportunity

  

High quality education (literacy, MATH, science)

  

Daily classroom math instruction

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Critical perspective 2:

We’re being asked to do what has never been done before: Make math work for nearly ALL kids.

But – no existence proof, no road map, not widely believed to be possible

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Critical perspective 3:

We’re therefore being asked to teach in distinctly different ways: Because there is no other way to serve a much broader proportion of students.

But – again, no existence proof, what does “different” mean, how do we bring to scale?

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Critical perspective 4

As mathematics colonizes diverse fields, it develops dialects that diverge from the “King’s English” of functions, equations, definitions and theorems. These newly important dialects employ the language of search strategies, data structures, confidence intervals and decision trees.

- Steen

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The pipeline perspective:

(critical perspective 5) 1985: 3,800,000 Kindergarten students 1998: 2,810,000 High school graduates 1998: 1,843,000 College freshman 2002: 2002: 2006: 1,292,000 College graduates 150,000 STEM majors 1,200 PhD’s in mathematics

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Critical perspective 6

Evidence from a half-century of reform efforts shows that the mainstream tradition of focusing school mathematics on preparation for a calculus-based post-secondary curriculum is not capable of achieving urgent national goals and that no amount of tinkering in likely to change that in any substantial degree.

- Steen

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ERGO: Houston, we have a problem (or clear indicators of a problem)

• • • • • •

Look around. Our critics are not all wrong.

Mountains of math anxiety Tons of mathematical illiteracy Mediocre test scores HS programs that barely work for half the kids Gobs of remediation A slew of criticism Not a pretty picture and hard to dismiss

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Your turn

But Steve… These are global problems.

In my neck of the woods, the three biggest problems I face as a professional educator are _______________.

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Problems

• •

Math problems Structural problems Hypothesis: Starting with math problems grounds our discussions and opens doors to all of the structural problems.

So let’s do some math and model the process.

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Valid or Invalid?

Convince us.

• • • • • • • •

Grapple Formulate Givens and Goals Estimate Measure Reason Justify Solve

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“The kind of learning that will be required of teachers has been described as transformative (involving sweeping changes in deeply held beliefs, knowledge, and habits of practice) as opposed to additive (involving the addition of new skills to an existing repertoire). Teachers of mathematics cannot successfully develop their students’ reasoning and communication skills in ways called for by the new reforms simply by using manipulatives in their classrooms, by putting four students together at a table, or by asking a few additional open ended questions…..

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Rather, they must thoroughly overhaul their thinking about what it means to know and understand mathematics, the kinds of tasks in which their students should be engaged, and finally, their own role in the classroom.”

NCTM – Practice-Based Professional Development for Teachers of Mathematics 20

People won’t do what they can’t envision.

People can’t do what they don’t understand.

ERGO: Our job as leaders is to help people ENVISION and UNDERSTAND!

So let’s use some EXAMPLES to do this.

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Example 1:

Ready Set

Find the difference: _ 10.00

4.59

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Example 2:

1.59 ) 10 vs.

You have $10.00

Big Macs cost $1.59 each So?

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Example 3:

F = 4 (S – 65) + 10 Find F when S = 81 Vs.

First I saw the blinking lights… then the officer informed me that: The speeding fine here in Vermont is $4 for every mile per hour over the 65 mph limit plus a $10 handling fee.

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Example 4:

Solve for x: 16 x .75

x

< 1 Vs. You ingest 16 mg of a controlled substance at 8 a.m. Your body metabolizes 25% of the substance every hour. Will you pass a 4 p.m. drug test that requires a level of less than 1 mg? At what time could you first pass the test?

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Dear sirs:

“I am in Mrs. Eaves Pre-algebra class at the Burn Middle School. We have been studying the area of shapes such as squares and circles. A girl in my class suggested that we compare the square and round pizzas sold by your store. So on April 16 Mrs. Eaves ordered one round and one square pizza from your store for us to measure, compare and… 26

The search for sense-making/future leaders

“What is the reason for the difference in the price per square inch of these two pizzas? Is it harder to cook a round pizza? Does it take longer to cook? Because if 3.35 cents per square inch is acceptable for the square pizza, then the same price per square inch should be used for the round pizza, making the price $10.31 instead of $10.99.

Thanks for the tasty lesson in pizza values.” Sincerely, Chris Collier 27

Ice Cream Cone!!

You may or may not remember that the formula for the volume of a sphere is 4/3πr 3 cone is 1/3 πr 2 h.

and that the volume of a Consider the Ben and Jerry’s ice cream sugar cone, 8 cm in diameter and 12 cm high, capped with an 8 cm in diameter sphere of deep, luscious, decadent, rich triple chocolate ice cream.

If the ice cream melts completely, will the cone overflow or not? How do you know?

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The Basics ( Acquire ) – an incomplete list

• • • • • • • •

Knowing and Using: +, -, x, x/ ÷ ÷ facts by 10, 100, 1000 10, 100, 1000,…., .1, .01…more/less ordering numbers estimating sums, differences, products, quotients, percents, answers, solutions operations: when and why to +, -, x, ÷ appropriate measure, approximate measurement, everyday conversions fraction/decimal equivalents, pictures, relative size

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The Basics (continued)

• • •

percents – estimates, relative size 2- and 3-dimensional shapes – attributes, transformations read, construct, draw conclusions from tables and graphs

• •

the number line and coordinate plane evaluating formulas

• • •

So that people can: Solve everyday problems Communicate their understanding Represent and use mathematical entities

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Some Big Ideas ( Meaning )

• • • • • • • •

Number uses and representations Equivalent representations Operation meanings and interrelationships Estimation and reasonableness Proportionality Sample Likelihood Recursion and iteration

• • • • • • • • • •

Pattern Variable Function Change as a rate Shape Transformation The coordinate plane Measure – attribute, unit, dimension Scale Central tendency

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Questions that “big ideas” answer: ( Transfer )

• • • • • • • • •

How much? How many?

What size? What shape? How much more or less?

How has it changed?

Is it close? Is it reasonable?

What’s the pattern? What can I predict?

How likely? How reliable?

What’s the relationship?

How do you know? Why is that?

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Themes

• • • • •

Powerful teaching Productivity Collaboration Real solutions A vision of effective teaching and learning

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Powerful Teaching

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Provides students with better access to the mathematics:

– – – –

Context Technology Materials Collaboration Enhances understanding of the mathematics:

– – –

Alternative approaches Multiple representations Effective questioning

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We are more productive when we:

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Change some of WHAT we teach (shifting expectations to more rational and responsive expectations) Change some of HOW we teach (shifting pedagogy to more research-affirmed approaches) Change how we interact and grow

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Most teachers practice their craft behind closed doors, minimally aware of what their colleagues are doing, usually unobserved and under supported. Far too often, teachers’ frames of reference are how they were taught, not how their colleagues are teaching. Common problems are too often solved individually rather than by seeking cooperative and collaborative solutions to shared concerns. - Leinwand – “Sensible Mathematics”

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Real solutions

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Changes in our professional culture Ongoing opportunities for substantive, focused, professional interaction

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Ongoing activities that reduce professional isolation

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A focus on the tasks, the teaching and the student work

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It’s instruction, silly!

Research, classroom observations and common sense provide a great deal of guidance about instructional practices that make significant differences in student achievement. These practices can be found in high-performing classrooms and schools at all levels and all across the country. Effective teachers make the question “Why?” a classroom mantra to support a culture of reasoning and justification. Teachers incorporate daily, cumulative review of skills and concepts into instruction. Lessons are deliberately planned and skillfully employ alternative approaches and multiple representations—including pictures and concrete materials— as part of explanations and answers. Teachers rely on relevant contexts to engage their students’ interest and use questions to stimulate thinking and to create language-rich mathematics classrooms.

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A Vision of Teaching and Learning



“An effective and coherent mathematics program should be guided by a clear set of content standards, but it must be grounded in an equally clear and shared vision of teaching and learning – the two critical reciprocal actions that link teachers and students largely determine educational impact.”



Where is your vision of effective teaching and learning of mathematics?

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Elements of a Vision

• • • •

Effective mathematics instruction in thoughtfully planned.

The heart of effective mathematics instruction is an emphasis on problem solving, reasoning and sense making.

Effective mathematics instruction balances and blends conceptual understanding and procedural skills.

Effective mathematics instruction relies on alternative approaches and multiple representations.

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Elements of a Vision (cont.)

• • • • •

Effective mathematics instruction uses contexts and connections to engage students and increase the relevance of what is being learned.

Effective mathematics instruction provides frequent opportunities for students communicate their reasoning and engage in productive discourse.

Effective mathematics instruction incorporates on going cumulative review.

Effective mathematics instruction maximizes time on task.

Effective mathematics instruction employs technology to enhance learning.

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Elements of a Vision (cont.)

• • •

Effective mathematics instruction uses multiple forms of assessment and uses the results of this assessment to adjust instruction. Effective mathematics instruction integrates the characteristics of this vision to ensure student mastery of grade-level standards.

Effective teachers of mathematics reflect on their teaching, individually and collaboratively, and make revisions to enhance student learning.

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Interlude:

Questions

(What’s not clear?)

and Discussion

(What’s disturbing you most?)

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Resulting in:

A Blueprint for Cultural Change

A curriculum, accessible resources, and minimal-cost strategies based on the “work of teaching”

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The Curriculum:

• • • • •

The mathematics we teach The teaching we conduct The technology and materials we use The learning we inculcate The equity we foster

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The Resources:

• • • • • • • • • • •

Curriculum guides, frameworks and standards Textbooks, instructional materials Articles, readings Observations Demonstration classes Video tapes Web sites Student work, lesson artifacts Common finals and grade level CRTs Disaggregated test scores Buddies, colleagues Notice the cost!

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Never forget:

It’s not a PLC, it’s the content of, and follow-up and change that emerges from, the professional sharing and interaction that enhances the day-in-and-day-out opportunities for kids to learn mathematics!

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Strategies for the mathematics 1:

• • • • •

1.

Conduct annual collegial discussions for each grade and each course: What works, what doesn’t work?

What math, what order, what’s skipped, what’s supplemented? What’s expected, not expected?

What’s on the common final/grade level CRT?

What gets recorded in a written action plan

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2. Conduct periodic mathematics strand or topic discussions (algebra, fractions, statistics): What works, what doesn’t work Appropriate/inappropriate course/grade placement and overlaps

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3. Baby/bath water discussions and decisions about specific topics What’s still important, what’s no longer important?

Do I care if my own kids can do this?

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Strategies for the mathematics 2:

• • • •

4. Common readings and focused discussions to truly build communities of learners: 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?

5. Collectively and collaboratively give yourselves permission to adjust the curriculum on the assumption that you own the curriculum to a greater degree than most assume.

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Strategies for strengthening the teaching:

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1. Use classroom visits to broaden perspectives and stimulate discussions Typical and demonstration classes Building a sense of we’re all in this together and face common problems

• • •

2. The “roll the videotape strategy”….

Our own lessons Annenberg tapes (www.learner.org) NCTM Reflections lessons (www.nctm.org/reflections) 3. Collaboratively craft powerful lessons (www.nctm.org/illuminations and www.mathforum.com) 4. Here’s the data, what’s the math and what questions best elicit the math?

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Strategies for increasing the learning:

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1. Analyze student work Look at what my kids did!

What does work like this tell us we ought to do?

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2. Review of common finals/grade level CRTs data 3. What’s on the test? or examining the truism that “what we assess and how we assess communicates what we value” Types of items/tasks/questions Content and processes measured Contexts, complexity, appropriateness, memorization required

• • • •

4. Annual action planning sessions: What are we doing well?

What can we do to expand what is working?

What are we not doing as well?

What can we do to improve what is not working as well?

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Strategies for reaching more students:

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1. “What do the data tell us?” sessions 2. “What do the videotapes tell us” sessions Compare and contrast two higher level classes/courses with two lower level classes/courses

• • • •

3. Policy implication discussions Algebra 1 placement Grouping by reading levels Heterogeneous grouping mandates Pull-out programs

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Strategies to tie it all together: 1. Use faculty, grade-level and department meetings as opportunities to inform, stimulate, challenge and grow by adapting the “faculty seminar” model 2. Implement intensive induction procedures, processes and traditions 3. Cultivate and assign topic resource people 4. Appoint course committees – what, how, how well 5. Conduct annual math nights

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Okay: Your turn again

So, which ones can’t you do?

(A discussion to debunk the inevitable “yeah, buts”)

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The obstacles to change

• • • • • • • •

Fear of change Unwillingness to change Fear of failure Lack of confidence Insufficient time Lack of leadership Lack of support Yeah, but…. (no money, too hard, won’t work, already tried it, kids don’t care, they won’t let us)

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The only antidotes I’ve ever seen work

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Sharing Supporting Risk-taking Your challenge: Administer the antidotes!

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To recapitulate: Share “Practice-based professional interaction”

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Professional development/interaction that is situated in practice and built around “samples of authentic practice.” Professional development/interaction that employs materials taken from real classrooms and provide opportunities for critique, inquiry, and investigation. Professional development/interaction that focuses on the “work of teaching” and is drawn from: - mathematical tasks - episodes of teaching - illuminations of students’ thinking

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To recapitulate: Support

The mindsets upon which to start

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We’re all in this together People can’t do what they can’t envision. People won’t do what they don’t understand. Therefore, colleagues help each other envision and understand.

Can’t know it all – need differentiation and team work Professional sharing is part of my job.

Professional growth (admitting we need to grow) is a core aspect of being a professional

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To recapitulate: Take Risks

It all comes down to taking risks

While “nothing ventured, nothing gained” is an apt aphorism for so much of life, “nothing risked, nothing failed” is a much more apt descriptor of what we do in school.

Follow in the footsteps of the heroes about whom we so proudly teach, and TAKE SOME RISKS

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Thank you.

Now go forth and start shifting YOUR department, school and district culture toward greater collegial interaction and collective growth.

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Bonus Slides

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DiTCoQuA

• • • • •

Dignity Transparency Collaboration Quality Accountability

AKA the Gospel According to Steve

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What’s missing in so many of our schools and departments?

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Dignity – rarely treated as professionals Transparency – Collaboration – Quality – we hide, we’re isolated we rarely share much can be done better Accountability – weak, often minimal, and for the wrong outcomes

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Dignity - yin

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Too often:

It’s top-down; They assume we’re ignorant;

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They really think they know best;

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And the kids are treated even worse!



Envision the magnetometer at a high school.

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Hear the tone of disdain and sarcasm in the middle school corridor

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Dignity - yang Instead:

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When professionals are treated like professionals, it’s simply amazing how they tend to act like professionals!

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When students are treated with respect….

Dignity and respect are essential precursors to trust and a healthy work environment!

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Transparency -yin Too often:

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We hide behind closed doors; We hoard lest other “steal” our ideas;

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We rarely observe what our colleagues are doing;

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We rarely videotape ourselves practicing our craft;

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Transparency - yang

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Instead, consider: Never knowing when a colleague will wander in; Feeling completely welcome in everyone else’s classroom; Collegial reviews of lesson videos; School-wide access to our test results and grades.

Would you really want your surgeon to “operate” in secret?

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Collaboration - yin In 1971:

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I could do it all: 3 textbooks 2 walls of blackboard 1 overhead projector and pull-down screen Lots of chalk and boxes on ditto masters!

Who needed to collaborate?

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Collaboration - yang In 2010:

Textbooks Videos Websites Applets Blogs Document cameras LCD projectors Powerful calculators Even more powerful computers Interactive white boards HeyMath Successmaker PowerPoint Geometer Sketchpad Fathom Etc. No one can do it all or know it all: We must collaborate!

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Quality - yin Too often:

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We punt;

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We settle;

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We cut corners; We don’t polish stones;

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We fail to reflect and revise.

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Quality - yang Instead:

Models of excellence:

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Strong visions of teaching and learning math

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Well developed plans

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Videos of instructional quality

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Exemplars of student work

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Accountability - yin

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Too often, a litany of “yeah, buts” It’s the kids It’s their parents It’s the middle school and those teachers It’s the elementary program and teachers who don’t know math They don’t do their homework They don’t know their facts They just don’t care

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Accountability - yang

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Instead:

I can meet them ¾ of the way I can strive to engage them with interesting tasks I can take affirmative actions to reteach rather than blame I can hold myself accountable for their learning if they just try a little

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Logic Model (part 1) Until and unless we are treated, and we treat each other, with dignity and respect, there will not be enough trust for transparency.

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Logic Model (part 2) Until and unless we have much greater transparency and openness (a mindset that we can learn from each other), there are few incentives to collaborate.

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Logic Model (part 3) Until and unless we collaborate, and remember that learning (our students’ as well as our own) is a socially mediated process, it is unlikely we will significantly improve the overall quality of our work.

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Logic Model (part 4)

And until and unless this foundation is built, there is insufficient support and an inadequate culture for meaningful accountability that ensures that every student who tries has the opportunity to learn. Amen.

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