Instruction that Maximizes Opportunity to Learn 7-12 Math Leona Group Steve Leinwand sleinwand@air.org www.steveleinwand.com

What state and how far? Ready? Set! There are 310 million people in the U.S. There are 13,000 McDonalds in the U.S. There is a point somewhere in the lower 48 that is farther from a McDonalds than any other point. What state and how far?

There are 310 million people in the U. S There are 310 million people in the U.S. There are 13,000 McDonalds in the U.S. McDonalds claims that 12% of all Americans eat at McDonalds each day. VALID? INVALID? SURE? NO WAY? Make the case that this claim is valid or invalid.

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!!!

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.

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.

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?

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.

Which is why we have the Math Checklist for Common Core Transitioning Peer interaction and deliberate participation Common Core Support Practices (high leverage practices) Common Core Mathematics Practices More specifically:

8 CCSSM Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.

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.

High Leverage Practices Effective teachers of mathematics respond to most student answers with “why?”, “how do you know that?”, or “can you explain your thinking?” Effective teachers of mathematics conduct daily cumulative review of critical and prerequisite skills and concepts at the beginning of every lesson.

High Leverage Practices Effective teachers of mathematics elicit, value, and celebrate alternative approaches to solving mathematics problems so that students are taught that mathematics is a sense-making process for understanding why and not memorizing the right procedure to get the one right answer. Effective teachers of mathematics provide multiple representations – for example, models, diagrams, number lines, tables and graphs, as well as symbols – of all mathematical work to support the visualization of skills and concepts.

High Leverage Practices Effective teachers of mathematics create language-rich classrooms that emphasize terminology, vocabulary, explanations and solutions. Effective teachers of mathematics take every opportunity to develop number sense by asking for, and justifying, estimates, mental calculations and equivalent forms of numbers.

High Leverage Practices Effective teachers of mathematics embed the mathematical content they are teaching in contexts to connect the mathematics to the real world. Effective teachers of mathematics devote the last five minutes of every lesson to some form of formative assessments, for example, an exit slip, to assess the degree to which the lesson’s objective was accomplished. Effective teachers of mathematics demonstrate through the coherence of their instruction that their lessons – the tasks, the activities, the questions and the assessments – were carefully planned.

Our task: Convert all these words and ideas into practices we can see, model and replicate. So let’s take a look:

Roll the video Integers and absolute value in grade 7 Patterns and fractions/decimals in grade 5 1) Let’s watch 2) Let’s discuss and identify practices 3) Let’s see what coaching can look like.

My coaching touchstones What worked and was worthy of praise? Was there opportunity for the students to learn? Why and why not? What evidence was there that the mathematics was in fact learned? What didn’t work and why? What opportunities were missed? What growth nugget can I end with or leave with the teacher? How often are these critical questions asked and answered? Why not?

8 CCSSM Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.

Finding tasks Great On-line Math Resources Learn Zillion: www.learnzillion.com Inside Mathematics: www.insidemathematics.org Illustrative Mathematics: www.illustrativemathematics.org Conceptua Math: www.conceptuamath.com NCTM Illuminations: http://illuminations.nctm.org Balanced Assessment: http://balancedassessment.concord.org Mathalicious: http://www.mathalicious.com Dan Meyer’s three act lessons: https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE Thinking blocks: http://www.thinkingblocks.com Decimal squares: http://www.decimalsquares.com Math Assessment Project: http://map.mathshell.org/materials/index.php Yummy Math: www.yummymath.com National Library of Virtual Manipulatives: http://nlvm.usu.edu/en/nav/vlibrary.html

Dan Meyer’s three act lessons: https://docs. google

PARCC http://www.ccsstoolbox.com/parcc_entry.html

Questions? Observations? Next Steps?