Accessible Mathematics 10 Instructional Shifts That Raise Student Achievement   Steven Leinwand This book contains 10 shifts in instruction that will improve student achievement within your math classes. You will find that some of these shifts you are already doing, but some of them you will not. Teaching math now, especially with the Common Core, means a lot of work for you guys: a lot of prep work, a lot of studying, a lot of truly knowing and understanding the math. It will be hard and it will take time, but in the end, it will be very beneficial for your kids. These 10 shifts will help you allow the students to truly understand the math and not just memorize processes and procedures.

“It’s Instruction, Stupid”

10 Instructional Shifts Incorporate ongoing cumulative review into every day’s lesson. Adapt what we know works in our reading programs and apply it to mathematics instruction. Use multiple representations of mathematical entities. Create language-rich classroom routines. Take every available opportunity to support the development of number sense.

10 Instructional Shifts (cont.) Build from graphs, charts, and tables. Tie the math to such questions as: “How big?” “How much?” “How far?” to increase the natural use of measurement throughout the curriculum. Minimize what is no longer important. Embed the mathematics in realistic problems and real-world contexts. Make “Why?” “How do you know?” “Can you explain?” classroom mantras. Which of the 10 shifts are you currently doing?

We’ve Got Most of the Answers A man is riding a bike on a trail in the woods. He rides for 30 minutes. In that time he travels 7 miles. How old is the man? What answer would students give?

Introduction “I’ve seen lessons where it was patently obvious that the teacher had not worked out the well-chosen problems the night before and had no idea what opportunities and stumbling blocks lay in the path to getting the right answer. And I’ve observed many lessons where so much time was essentially wasted going over the correct answers to homework problems that not enough time remained to address the day’s new content effectively.”

Introduction (cont.) “…taking this body of knowledge and skills called mathematics and presenting it in ways that result in all or nearly all students being successful. We know that this goal cannot be met by continuing to do what we have always done.”

2007 TIMSS Data http://nces.ed.gov/timss/table07_1.asp

2009 PISA Data http://nces.ed.gov/pubs2011/2011004.pdf

What does a typical American classroom look like?

Comparison between US and Japanese Classrooms US Classrooms Japanese Classrooms The teacher instructs students in a concept or skill. The teacher solves example problems. The students practice on their own. The teacher poses a complex, thought-provoking problem. Students struggle. Various students present ideas or solutions. Class discusses various solution methods. Teacher summarizes class’ conclusions. Students practice similar problems. Which classroom does a better job of incorporating the 8 mathematical practices?

“Did your previous teacher teach you anything?” How many of you have asked this question? So why do kids not retain what they have learned? Do ELA teachers have to reteach students how to read each year? Algebra 2 example – many students say they have never graphed a linear equation (some of course are just saying that, but for some they actually believe that)

Shift 8 Minimize what is no longer important, and teach what is important when it is appropriate to do so. http://maccss.ncdpi.wikispaces.net/Fall+2012+Regional+K-12+PD So what do we teach and when do we teach it? (Refer to the Major Works Document)

“Do I really care whether my children and grandchildren know and can do this?”

Divide 32,615 by 25 What is wrong with this problem? What if kids know how to solve by graphing, elimination, or matrices? For elementary: Divide 32,615 by 25.

When should we teach certain concepts? When should students take Algebra 1? Some of this is out of our control of course – follow CCSS for math.

What should we see in an effective mathematics classroom? A curriculum of skills, concepts, and applications that are reasonable to expect all students to master, and not those skills, concepts, and applications that have gradually been moved to an earlier grade on the basis of inappropriately raising standards. Implementation of a district and state curriculum that includes essential skills and understandings for a world of calculators and computers, and not what many recognize as too much content to cover at each grade level. A deliberate questioning of the appropriateness of the mathematical content, regardless of what may or may not be on the high-stakes state test, in every grade and course.

Please read Chapters 7, 8, and 10 for next time