raleigh, north carolina february 11, 2013 steve leinwand american institutes for research
DESCRIPTION
Strengthening Teaching and Learning of K-12 Mathematics through the Use of High Leverage Instructional Practices. Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research [email protected]. Ready? Set!. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/1.jpg)
1
Strengthening Teaching and Learning of K-12 Mathematics
through the Use of High Leverage Instructional Practices
Raleigh, North CarolinaFebruary 11, 2013
Steve LeinwandAmerican Institutes for Research
![Page 2: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/2.jpg)
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?
![Page 3: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/3.jpg)
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.
3
![Page 4: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/4.jpg)
The 5 Key Elements of Effective Mathematics Teaching
• Classroom management• The content• The pedagogy• The tools and resources• The evidence of learning
4
![Page 5: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/5.jpg)
1. Effective teachers of mathematics respond to most student answers with “why?”, “how do you know that?”, or “can you explain your thinking?”
2. Effective teachers of mathematics conduct daily cumulative review of critical and prerequisite skills and concepts at the beginning of every lesson.
3. 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. 4. 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.
5. Effective teachers of mathematics create language-rich classrooms that emphasize terminology, vocabulary, explanations and solutions.
6. Effective teachers of mathematics take every opportunity to develop number sense by asking for, and justifying, estimates, mental calculations and equivalent forms of numbers.
7. Effective teachers of mathematics embed the mathematical content they are teaching in contexts to connect the mathematics to the real world.
8. 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.
9. 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.
5
![Page 6: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/6.jpg)
And what should it look like in our classrooms?
6
![Page 7: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/7.jpg)
Some data. What do you see?
40 410 230 4
7
![Page 8: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/8.jpg)
Predict some additional data
40 410 230 4
8
![Page 9: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/9.jpg)
How close were you?
40 410 230 420 3
9
![Page 10: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/10.jpg)
All the numbers – so?
45 425 315 240 410 230 420 3
10
![Page 11: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/11.jpg)
A lot more information(where are you?)
Roller Coaster 45 4Ferris Wheel 25 3Bumper Cars 15 2Rocket Ride 40 4Merry-go-Round 10 2Water Slide 30 4Fun House 20 3
11
![Page 12: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/12.jpg)
Fill in the blanks
Ride ??? ???Roller Coaster 45 4Ferris Wheel 25 3Bumper Cars 15 2Rocket Ride 40 4Merry-go-Round 10 2Water Slide 30 4Fun House 20 3
12
![Page 13: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/13.jpg)
At this point, it’s almost anticlimactic!
13
![Page 14: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/14.jpg)
The amusement park
Ride Time Tickets
Roller Coaster 45 4Ferris Wheel 25 3Bumper Cars 15 2Rocket Ride 40 4Merry-go-Round 10 2Water Slide 30 4Fun House 20 3
14
![Page 15: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/15.jpg)
The Amusement ParkThe 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.
15
![Page 16: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/16.jpg)
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.
16
![Page 17: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/17.jpg)
Why do you think I started with these tasks?
- 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!!!
17
![Page 18: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/18.jpg)
Ready, Set…..
5 + (-9)
18
![Page 19: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/19.jpg)
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”
19
![Page 20: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/20.jpg)
Understand Why5 + (-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 x x x x O O O O O O O O O On number line, start at 5 and move 9 to the left
20
![Page 21: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/21.jpg)
Major Theme of the Day
Multiple Representations!
21
![Page 22: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/22.jpg)
So look at what you have:• Visual – the displayed slides• Aural – my voice and passion• Hard copy – the handout
Multiple representations to maximize the opportunity to
learn!22
![Page 23: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/23.jpg)
23
The Ice Cream ConeYou 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?
![Page 24: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/24.jpg)
24
![Page 25: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/25.jpg)
25
![Page 26: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/26.jpg)
26
![Page 27: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/27.jpg)
27
![Page 28: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/28.jpg)
Ergo: A Vision by Example• Solve• Reason• Model• Explain• Critique
CCSSM Math Practices(Construct viable arguments and critique
the reasoning of others)28
![Page 29: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/29.jpg)
My Goal TodayEngage you in thinking about (and then being
willing and able to act on) the issues of what we teach, how we teach, and how much they learn by:
• validating your concerns, • examining standard operating procedures,• giving you some tools and ideas for making
math more accessible to our students, • empowering you to collectively take risks.
29
![Page 30: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/30.jpg)
My content agenda• Part 1: Putting our work in context• Part 2: It’s instruction, silly• Part 3: Tying things together• Part 4: The Smarter Balanced
opportunities• Part 5: Final thoughts on moving forward
30
![Page 31: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/31.jpg)
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)
31
![Page 32: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/32.jpg)
Part 1
Putting our work in context
(glimpses at the what, why and how of what we do)
32
![Page 33: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/33.jpg)
There is no valid psychological or logical reason to limit students of lesser academic ability or aptitude to practice with paper and pencil procedures.
On the contrary, there is ample evidence to suggest that such an approach is often counter-productive, resulting in little improvement in procedural skills and increasingly negative attitudes.
33
![Page 34: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/34.jpg)
from Everybody CountsVirtually all young children like
mathematics. They do mathematics naturally, discovering patterns and making conjectures based on observation. Natural curiosity is a powerful teacher, especially for mathematics….
34
![Page 35: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/35.jpg)
Unfortunately, as children become socialized by school and society, they begin to view mathematics as a rigid system of externally dictated rules governed by standards of accuracy, speed, and memory. Their view of mathematics shifts gradually from enthusiasm to apprehension, from confidence to fear. Eventually, most students leave mathematics under duress, convinced that only geniuses can learn it.
35
![Page 36: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/36.jpg)
Accuracy, Speed and Memory
Tell the person sitting next to you what is the formula for the volume of a sphere.
V = 4/3 π r3
4/3 ? r? 3? π? 36
![Page 37: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/37.jpg)
Sucking intelligence out…
Late one night a shepherd was guarding his flock of 20 sheep when all of a sudden 4 wolves came over the hill.
Boys and girls, how old was the shepherd?
37
![Page 38: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/38.jpg)
38
“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…..
![Page 39: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/39.jpg)
39
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
![Page 40: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/40.jpg)
Questions?Yeah buts…
40
![Page 41: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/41.jpg)
Not convinced?
41
![Page 42: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/42.jpg)
42
![Page 43: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/43.jpg)
43
![Page 44: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/44.jpg)
Envision the last test you gave your students.
Compare your test with the Subway Employment Test.
44
![Page 45: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/45.jpg)
Let’s see if we can be hired.
45
![Page 46: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/46.jpg)
10.00- 4.59
46
![Page 47: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/47.jpg)
If the customer’s order came to $6.22 and he gave you $20.25, what is the change?
47
![Page 48: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/48.jpg)
A customer complained that he was short changed by you, receiving only 13¢ from his $2.00 instead of 31¢. What would you do?
48
![Page 49: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/49.jpg)
So:Four overarching contextual perspectives that frame our
work and our challenges
49
![Page 50: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/50.jpg)
1. What a great time to be convening as teachers of mathematics!
• Common Core State Standards adopted by 46 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
answers50
![Page 51: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/51.jpg)
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
2. Where we live on the food chain
51
![Page 52: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/52.jpg)
52
3. 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.
![Page 53: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/53.jpg)
53
4. 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.
![Page 54: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/54.jpg)
Yes.A lot to think about.
But if you think everything is hunky-dory, you’re not going
to change.54
![Page 55: Raleigh, North Carolina February 11, 2013 Steve Leinwand American Institutes for Research](https://reader038.vdocuments.mx/reader038/viewer/2022110215/5681678c550346895ddcaec7/html5/thumbnails/55.jpg)
Ready?
55