Accessible Mathematics10 Instructional Shifts

That Raise Student Achievement 

Steven Leinwand

“It’s Instruction, Stupid”

http://www.youtube.com/watch?v=5gWgA4yaFrY

10 Instructional Shifts1. Incorporate ongoing cumulative review into

every day’s lesson.2. Adapt what we know works in our reading

programs and apply it to mathematics instruction.

3. Use multiple representations of mathematical entities.

4. Create language-rich classroom routines.5. Take every available opportunity to support

the development of number sense.

10 Instructional Shifts (cont.)

6. Build from graphs, charts, and tables.7. Tie the math to such questions as: “How

big?” “How much?” “How far?” to increase the natural use of measurement throughout the curriculum.

8. Minimize what is no longer important.9. Embed the mathematics in realistic

problems and real-world contexts.10. Make “Why?” “How do you know?” “Can

you explain?” classroom mantras.

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?

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 ClassroomsJapanese

ClassroomsO The teacher

instructs students in a concept or skill.

O The teacher solves example problems.

O The students practice on their own.

O The teacher poses a complex, thought-provoking problem.

O Students struggle.O Various students

present ideas or solutions.

O Class discusses various solution methods.

O Teacher summarizes class’ conclusions.

O Students practice similar problems.

“Did your previous teacher teach you

anything?”How many of you have asked this question?

Shift 8Minimize 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

“Do I really care whether my children and grandchildren

know and can do this?”

Divide 32,615 by 25

When should we teach certain concepts?

When should students take Algebra 1?

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