Shifting Instruction to Strengthen the Opportunity to Learn Both Content and English OELAS Conference December 14, 2012 Steve Leinwand American Institutes for Research SLeinwand@air.org
So…the problem is: If we continue to do what we’ve always done…. We’ll continue to get what we’ve always gotten.
Algebra: The intense study of the last three letters of the alphabet
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!
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.
At this point, it’s almost anticlimactic!
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.
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.
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!!!
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 THEYTHEY BLAME BLAMEBLAME 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.
Today’s Goal To 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.
Today’s Agenda • Three perspectives on our reality • The Common Core context • Some glimpses at powerful instruction • Some challenges to you
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 answers
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.
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 new names for old ways of doing business. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep. — CCSSM (2010, p.5)
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 • 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.
So how should this be playing out in every Arizona mathematics classroom? Regular Ed ELL Special Ed Let’s Take a Look
A Tale of Two Mindsets(and the alternate approaches they generate) Remember How vs. 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
Number facts 8 + 9
Ready, set, 8 + 9 = 17 – know it cold 10 + 7 – decompose the 9 to get to 10 18 – 1 – add 10 and adjust 16 + 1 – double plus 1 20 – 3 – round up and adjust Who’s right? Does it matter?
Find the difference: 1000 - 459
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?
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
Find the difference: Add 10 Add 10 10010 • 456 9 1
Find the difference: Add 100 Add 100 101010 • 45 56 9 5 4 1
Adding and Subtracting Integers 5 + (-9)
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”
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 xxxx O OOOOOOOO - On number line, start at 5 and move 9 to the left
Remember How 4.39 x 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.”