CPAM Leadership SeminarPractical Strategies for Providing School Based Leadership for More Powerful Teaching of K-12 Mathematics Steve Leinwand American Institutes for Research SLeinwand@air.org
Let’s Reflect: Mirrors, Changes, Engagement, Interactions
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!
In other words….. A critical time for leadership! Our leadership. Your leadership.
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
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)
Today’s content agenda • Critical Perspectives • Problems • Examples • Themes • A blueprint • Some discussion • A challenge
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
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
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?
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
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: 1,292,000 College graduates 2002: 150,000 STEM majors 2006: 1,200 PhD’s in mathematics
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
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
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 _______________.
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.
Valid or Invalid?Convince us. • Grapple • Formulate • Givens and Goals • Estimate • Measure • Reason • Justify • Solve
“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…..
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
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.
Example 1: Ready Set Find the difference: _ 10.00 4.59
Example 2: 1.59 ) 10 vs. You have $10.00 Big Macs cost $1.59 each So?
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.
Example 4: Solve for x: 16 x .75x < 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?
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…
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
Ice Cream Cone!! You may or may not remember that the formula for the volume of a sphere is 4/3πr3 and that the volume of a cone is 1/3 πr2h. 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?
The Basics (Acquire) – an incomplete list Knowing and Using: • +, -, x, ÷ facts • x/ ÷ 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
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
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 Some Big Ideas (Meaning)
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?
Themes • Powerful teaching • Productivity • Collaboration • Real solutions • A vision of effective teaching and learning
Powerful Teaching • Provides students with better access to the mathematics: • Context • Technology • Materials • Collaboration • Enhances understanding of the mathematics: • Alternative approaches • Multiple representations • Effective questioning
We are more productive when we: • 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
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”
Real solutions • Changes in our professional culture • Ongoing opportunities for substantive, focused, professional interaction • Ongoing activities that reduce professional isolation • A focus on the tasks, the teaching and the student work
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.
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?
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.
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.
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.
Interlude: Questions (What’s not clear?) and Discussion (What’s disturbing you most?)
Resulting in: A Blueprint for Cultural Change A curriculum, accessible resources, and minimal-cost strategies based on the “work of teaching”
The Curriculum: • The mathematics we teach • The teaching we conduct • The technology and materials we use • The learning we inculcate • The equity we foster
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!