Survey participants: first timers, math coaches, classroom teachers, central office, principals, etc… This will allow us to modify presentation accordingly.
Thumbs up if you agree with these norms. Are there other norms we need to add so that we have the best possible learning experience for all?
Share outcomes
Share objectives
Potential problems in any elementary classroom – focus could be on these versus learning
Potential problems in any secondary classroom – focus could be on these versus learning Then allow time for participants to discuss – traditional classroom issues/problems
Why change?
Think for a minute about your answer to this problem, and what students in 1-6 grade might think the answer is. What goes in the box? What might students say? Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School Carpenter, Franke, & Levi, Heinemann, 2003
Across the top you see the various answers students offered: 7, 12, 17, 12 & 17. How did they get each of these responses?
We can see that 5 percent of 1-2 graders produced the correct answer. However, 58 percent thought the answer was 12. How did they get that?
Now we look at 3-4. 2% more were right. Why do 12 % more students think 17 is correct?
Now 5 th -6 th grades. The good news is that very few still think there are 2 answers. The bad news is that we are down to 2 % getting the right answer. Procedures memorized but not understood are getting in the way. Dr. Drew Polly at UNCC replicated this study for 6 th grade, and none of the students got the correct the answer.
More research from NAEP
More research
Research continued Constance Kamii has done extensive research on how young children learn mathematics. Here is a task frequently used to assess understanding of tens and ones. Students usually are successful, and count our 6 blocks.
Kamii found that essentially no first graders could correctly complete this task.
Many 3-5 graders still do not give the correct answer.
Grayson Wheatly’s research with 5,000 middle-school students were given the following task: Some students gave this answer. Others knew the tens had to be in the middle, so….. Many gave this answer, knowing about decimals, and that you could only have 3 digits if a number was in the hundreds. Around 50% of the middle school students gave the correct answer.
Think about the practices!
What would have happened if ? (wait time, no opinions and value judgments, and not repeating student responses pg. 61) Or use post-it notes to use Formative Assessment type task.
Additional problem if needed
Share slide
Tons or research has told us what students need for success in the future.
Again, these standards tell us “what” students need but not “How” Standard III – Teachers Know the Content They Teach Standard IV – Teachers Facilitate Learning for Their Students
These standards also tell us ‘What” not “how” Students learn language and culture through meaningful use and interaction. Students develop language proficiency in listening, speaking, reading, and writing interdependently. Students’ development of social, instructional, and academic language is the foundation for their success in school. Students’ access to instructional tasks requiring complex thinking is enhanced when linguistic complexity and instructional support match their levels of language proficiency.
UDL - Tells us to make learning accessible to all but not “How” Diversity is the norm within modern classrooms. As educators, it is our responsibility to provide students with an equal opportunity to learn and access education. Every classroom is filled with diverse learners. Every learner is unique and processes information in a different way. As educators, it is our job to take time to get to know our students and understand their individual strengths, needs, and interests
Now focus on the “How” Modeled through a math problem.
Pass out handout - Test time. Participants take test and share with shoulder partner Pass out books while discussing test results!
Look at pages 34-35, talk with your shoulder partner.
Look at pages 37, talk with your shoulder partner. The book includes useful guidance on this topic, you can explore this section at a later time.
Take a look at some student types. How many do you know? DO they look familiar?
Distribute Mathematical Practice Handout
Rectangle Problem Model by asking them to reflect on their thinking… Teacher Strategy #9, p.88
Fraction Problem Model by using multiple entries Teacher Strategy # 5, p.78
Fraction Problem Model by using multiple entries Teacher Strategy # 5, p.78
Fraction Problem Model by using multiple entries Teacher Strategy # 5, p.78
I believe students meet our expectations, expectations they infer from observing us.
Student assessment
These are designed for PLC work during which teachers would observe each other. Students from grades 4 and up could also take turns recording. This really builds a community of learners.
Here is where you can get more information…
This should be included for all instructional content sessions
When the system is first rolled out, teachers will have immediate access to content that has been vetted, tagged, and aligned to Common Core and NC Essential Standards. DPI has a team of people reviewing resources and selecting those that are strictly aligned – this process involves a teacher review to ensure that these are resources that teachers will use. At the end of 2012, over 2300 resources had been reviewed and tagged in Math, ELA, Science, Biology, Math I (some Social Studies). This number increases daily. These are some examples of instructional resources that we know we are going to use. You may already know about and use these, but now we will have them all in one place and only include those things that are aligned to NC SCOS.
Transcript
1. Summer
Institutes
2013
Changing
Teacher
Practice
Changing
Student
Outcomes
4. Norms
• Listen as an Ally
• Value Differences
• Maintain Professionalism
• Participate Actively
5. Learner Outcome
With the development of thoughtful
classrooms aligned to the Standards for
Mathematical Practice, educators will
understand and promote complex level
thinking in students.
6. Session Objectives
• Provide strategies teachers can utilize to
increase students’ complex level
thinking.
• Connect the Strategies for a Thoughtful
Classroom to the Standards for
Mathematical Practice.
7. Let’s Define
the Problem
8. First Grade
• The Leader
• The Ethics Police
• The “I’m Finished First”
Winners
• The Do-Overs
9. High School
Rows of 5, all eyes on cell phones texting
Wondering what’s for lunch?
Students asleep or praying for a fire drill.
16. Estimate the answer to (12/13) + (7/8)
A. 1
B. 2
C. 19
D. 21
Only 24% of 13 year olds answered correctly.
Equal numbers of students chose the other
answers.
NAEP
17. Students were given this problem:
÷168 20
4th
grade students in reform math classes
solved it with no problem. Sixth graders in
traditional classes responded that they hadn’t
been taught that yet.
Dr. Ben Klein, Mathematics Professor
Davidson College
18. Research
Students are shown this number.
Teacher points to the 6 and says,
“Can you show me this many?”
16
Constance Kamii
19. Research
When the teacher points to the 1 in
the tens place and asks,
“Can you show me this many?”
16
Constance Kamii
20. Research
By third grade nearly half the
students still do not ‘get’ this
concept.
16
Constance Kamii
21. More research - It gets worse!
A number contains 18 tens, 2 hundreds,
and 4 ones.
What is that number?
1824
218.4
2824
384
Grayson Wheatly
22. Lesson Comparison
United States and Japan
The emphasis on skill acquisition is
evident in the steps most common in
U.S. classrooms
The emphasis on understanding is
evident in the steps of a typical Japanese
lesson
•Teacher instructs students in concept or
skill
•Teacher solves example problems with
class
•Students practice on their own while
teacher assists individual students
•Teacher poses a thought provoking
problem
•Students and teachers explore the
problem
•Various students present ideas or
solutions to the class
•Teacher summarizes the class solutions
•Students solve similar problems
23. How are you feeling?
24. Let’s Do Some
Math!
25. The Famous Horse Problem
A farmer buys a horse for $60.
How much money did the farmer make or lose?
Later he sells it for $70.
He buys it back for $80.
Finally, he sells it for $90.
26. Feeling Better?
27. Instruction Must Change
28. We know
“What” Students Need…
21st
Century Skills, critical thinking and
problem solving, collaboration and
leadership, agility and adaptability, oral
and written communication, accessing
and analyzing information.
Tony Wagner, Rigor Redefined
29. Teacher Evaluation
30. WIDA
31. Universal Design for Learning
A universally designed
curriculum is
developed from the
start to be accessible
as well as challenging,
for ALL students.
32. We Know the “What”
But Not “How” to Meet Their Needs
Common Core
Standards for Mathematical Practice
33. Creating Active Thinkers
Do You Value Thinking?
“Teacher Test”
Turn and Talk with your shoulder
partner about your Teacher
Test.
34. How do we meet student needs?
35. The First Step
“Before all else, a classroom
environment that fosters complex
thinking must be predictable and
safe.” Creating Active Thinkers, page 35
How do you know if a classroom is
safe and predictable?
36. Characteristics of a safe and
predictable classroom
• Shared decision making
• Lively exchange of opinions and ideas
• Visual evidence of student thinking
37. The Next Step
“Complex thinking is developed in
students primarily through the careful
planning and teaching of lessons.”
Creating Active Thinkers, page 37
What do you need to keep in mind
when planning a lesson?
38. Jigsaw on Teacher Strategies
39. The Nine Teacher Strategies in
the Thoughtful Classroom gives
us the
40. Nine Teacher Strategies
The teacher will…
1.focus and refocus students on task. (pages 62-67)
2.ask open-ended questions.(pages 67-70)
3.ask extension questions.(pages 70-74)
4.wait for student responses.(pages74-78)
5.accept a variety of student responses.(pages 78-81)
6.encourage student interaction.(pages 81-84)
7.not give opinions or value judgments.(pages 84-86)
8.not repeat student responses.(pages 87-88)
9.ask students to reflect on their thinking.(pages 88-90)
41. Student Responsibilities
“The student takes his or her cues from the
teacher.”
Include your students in the journey.
Meet some of your students…
Creating Active Thinkers, page 97-100
42. Student Behaviors
Read the student behaviors on page 101.
Are these student behaviors familiar?
Surprise!
Standards for Mathematical Practice.
43. Let’s do some math using
some of the Strategies for
a Thoughtful Classroom
44. Cube Problem
A block made of small cubes is dropped in
paint. The block has four cubes on each edge
as shown below. How many small cubes
have paint on them?
45. Nine Teacher Strategies
The teacher will…
1.focus and refocus students on task.
2.ask open-ended questions.
3.ask extension questions.
4.wait for student responses.
5.accept a variety of student responses.
6.encourage student interaction.
7.not give opinions or value judgments.
8.not repeat student responses.
9.ask students to reflect on their thinking.
46. Fraction Riddle
Using color tiles and grid paper.
Riddle 1: A rectangle is 1/2 red, 1/5 green,
1/10 blue, and the rest yellow. How much of
the rectangle is yellow? Draw the rectangle
on grid paper and record the fraction that tells
which part is yellow.
47. Fraction Riddle
Using color tiles and grid paper.
Riddle 2: A rectangle is 3/5 red. The rest is
blue and yellow but not in equal amounts.
What could the rectangle look like? Record.
48. Fraction Riddle
Using color tiles and grid paper.
Riddle 3: A rectangle is 1/2 red and 1/3 blue.
Also, it has one green tile and one yellow tile.
What could the rectangle look like? What
fractional part is green? Yellow? Record.
Try to make up your own riddle.
49. Nine Teacher Strategies
The teacher will…
1.focus and refocus students on task.
2.ask open-ended questions.
3.ask extension questions.
4.wait for student responses.
5.accept a variety of student responses.
6.encourage student interaction.
7.not give opinions or value judgments.
8.not repeat student responses.
9.ask students to reflect on their thinking.
50. Self Assessment
Students are amazingly honest when
assessing themselves.
Creating Active Thinkers, page 117 – 121; 136-137
51. Self Assessment Doesn’t Always
Work
The last pages contain Observation
Forms, to help identify what your students
and others observe in you during
instruction.
Creating Active Thinkers, Appendix C
52. What questions do
you have?
53. • Learning Opportunities
• Resources
54. Assessment
Student
Information
and Learner
Profile
Instructional
Design, Practice
& Resources
Data Analysis
and
Reporting
Information
a simpler, better
information
system to
replace NC
WISE
Integrated Instructional Solution
a new standards-aligned tool that
connects instructional content with (e.g.
lesson plans, unit plans) assessment for better
data analysis and decision making
Effectiveness
a simpler, better
online evaluation
system
Information Instruction
Educator Effectiveness:
Educator Evaluation
OpenClass
Collaboration
SchoolnetPowerSch
ool
Truenorthlo
gic
Available for the start of the 2013-14 School
Year
55. Home Base Website and Updates
•Home Base website is
http://www.ncpublicschools.org/homebase/
•To sign up for Home Base Biweekly Newsletter, please go to
http://goo.gl/appdp.
•We will continue to email the biweekly updates, but you can
also find them archived on the Home Base website at
http://www.ncpublicschools.org/homebase/updates/
56. Exploring Instructional
Content
57. Open Education Resources (OER)
Samples
• Home Base NCDPI-Vetted OER
Samples Available at
http://goo.gl/8sbFX
58. Sample Mathematics Resources
Summary: This site comprises
six lesson activities including the
definition of a fraction, equivalent
fractions, addition of fractions,
and multiplication of fractions.
Students may respond online to
get immediate feedback, or they
can work the examples on grid
paper.
Who Wants Pizza? A Fun Way
to Learn About Fractions
Exploring Linear Data
Standards:
•CCSS.Math.Content.8.SP.A.1
•CCSS.Math.Content.8.SP.A.2
•CCSS.Math.Content.8.SP.A.3
•CCSS.Math.Content.HSS-ID.B.6c
Standards:
•CCSS.Math.Content.3.NF.A.3a
•CCSS.Math.Content.3.NF.A.3b
•CCSS.Math.Content.4.NF.B.3a
•CCSS.Math.Content.5.NF.A.1
•CCSS.Math.Content.5.NF.A.2
•CCSS.Math.Content.5.NF.B.4a
Summary: Students model linear
data in a variety of settings that
range from car repair costs to
sports to medicine. Students work
to construct scatterplots, interpret
data points and trends, and
investigate the notion of line of
best fit.
60. Facilitated Team Time Preparation
• To prepare for Facilitated Team Time, complete the
brief reflection to identify the “big ideas” gained from
this session that you will share with your Summer
Institute team.
• To access the reflection document, visit
http://bit.ly/SIreflection or scan the QR code.
• To access the reflection responses during Facilitated
Team Time, visit http://bit.ly/SIresponses.
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