1. Leadership Pathway: Coherence in Grades 6–8 February 2016
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Leadership Pathway:
Coherence in Grades 6–8
107 minutes as designed
Materials:
Vertical Articulation Challenge slips
1 video - Be sure to have loaded the video prior to participants’ arrival by opening the link and letting it begin to run. This should then have the video ready to view without buffering.
February 2016

2. COHERENCE IN GRADES 6–8 At a Glance
Day
Ideas
Wednesday
8:30-4:00
The Foundation
Components of a Comprehensive Literacy Program
Thursday
Building Knowledge and Vocabulary
The Juicy Language of Text
Organizational Systems and Structures
Friday
Focus, Coherence and Rigor
Saturday
8:30-2:30
Observing the Standards And Shifts
Adaptations for Struggling Learners
L E A R N I N G C O N T E N T
1 min
Speaker Notes:

3. COHERENCE IN GRADES 6–8 Coherence Session
Objectives:
Participants will be able to describe the coherence shift both as a logical sequencing of content across grades and as important connections between standards, clusters, and domains within the grade
Participants will be able to identify prerequisite standards for grade level standards
Participants will be able to observe and coach the coherence shift in teacher practice
Agenda:
Opening and Activator
Coherence: What and Why
Coherence Across Grades
Coherence Within the Grade
Observing for Coherence
Summary and Reflection
1 min
Speaker Notes:
We’ll start by looking carefully at the shift of coherence in math, with an emphasis on why it’s important and what it looks like in grades6-8.

4. Norms that Support Our Learning
COHERENCE IN GRADES 6–8
Norms that Support Our Learning
Take responsibility for yourself as a learner
Honor timeframes (start, end, activity)
Be an active and hands-on learner
Use technology to enhance learning
Strive for equity of voice
Contribute to a learning environment in which it is “safe to not know”
1 min
Speaker Notes:
Choose to remind them of a norm if you think it has been slipping:
Keep an open mind (esp. about what don't know or thought you knew);
Stay in learning orientation vs. performance orientation—growth mindset;
Be active during video observation by capturing evidence in writing
Appreciate everyone's perspective and journey;
Share ideas and ask questions, one person at a time (airtime);
Be okay with discomfort and focus on growth;
Be present (monitor multi-tasking, technology, honoring timeframes)

5. Coherence: What and Why?
COHERENCE IN GRADES 6–8
Coherence: What and Why?
How would you teach students to graph the proportional relationship between the number of pounds of coffee and the total cost?
Lena paid $18.96 for 3 pounds of coffee.
3 min
Speaker Notes:
Ask participants how they would explain this to an 8th grader who is just beginning to relate proportional reasoning to graphing. (1 min independent reflection)
Share responses include: teaching unit rate, teaching slope, teaching how to construct an appropriately scaled graph (1 minute)
Ask which one would be appropriate to teach first. Explain: unit rate comes in 6th grade, must be a secure foundation before moving on; lines cannot be graphed before students know how to construct an appropriate scale (1 minute)
TAKE AWAY – The study of mathematics rests on the idea of developing ideas from existing ones. Similarly this is how students learn; they learn mathematics based on what they already understand, developing ideas from existing ones.

6. COHERENCE IN GRADES 6–8
What’s the Right Order?
Use ratio and rate reasoning to solve real-world and mathematical problems by making tables of equivalent ratios, finding missing values in tables, and plotting the pairs of values on the coordinate plane.
Graph proportional relationships, interpreting the unit rate as the slope of the graph; compare different proportional relationships in different ways.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Grade 6
Grade 7
3 minutes
Speaker Notes:
Ask participants to try to order these standards sequentially – work individually
Click to share correct answer.:
A = Grade 6
B = Grade 8
C = Grade 7
Emphasize logical progression.
Grade 8

7. Coherence is Key
“A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula. Any approach that continually revisits topics year after year without closure is to be avoided. By the term focused, the Panel means that curriculum must include (and engage with adequate depth) the most important topics underlying success in school algebra. By the term coherent, the Panel means that the curriculum is marked by effective, logical progressions from earlier, less sophisticated topics into later, more sophisticated ones. Improvements like those suggested in this report promise immediate positive results with minimal additional cost.”
1 min
Speaker Notes:
KEY POINT: The idea of logical progressions of learning is an important one. This is what mathematics is: developing new ideas from existing ones.
In the Final Report of the National Mathematics Advisory Panel, this idea was highlighted.
Anticipated Questions: how do we know this is important? Can connect to what lead writers of CCSS heard in testimony, noticed in college students: seeing math as branching out of isolated skills and procedures that get more complicated without seeing underlying principles and how all math is unified by them (McCallum video on coherence);
IMAGE CREDITS:

8. Coherence ACROSS Grades
LEADERSHIP PATHWAY: COHERENCE IN HIGH SCHOOL
Coherence ACROSS Grades
Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. 
Across-Grade Coherence
Learning is carefully
connected across grades
so that students can build new understanding onto foundations built in previous years. 
30 seconds
Speaker Notes:
One of our objectives for you today is to be able to describe BOTH aspects of coherence. Coherence will have a couple of meanings for us, but one important one is about the progression of content ACROSS grades.
IMAGE CREDITS:

9. Vertical Coherence Challenge
COHERENCE IN GRADES 6–8
Vertical Coherence Challenge
In your groups, you have 13 standards on pieces of paper; most come from the Ratio and Proportions domain in grades 6-8.
They are not labeled!
Determine which standards are prerequisites for other standards.
Note: There is more than one vertical strand.
Bonus: Can you determine which standards belong in which grade?
30 min
Speaker Notes:
We just talked the fact there are fundamental truths in mathematics that connect across grade levels. Now you are going to have time to explore the how the standards span across grades.
Can we see the vertical coherence of the standards?
Work in pairs
Let participants know that there is more than one branch.
Tell them they should not use resources, just what they know about skills progression. Read the words and discuss the grades and the transitions and the way the verbs change.
String together standards coherently.
(2 min)
Independent - Take a minute to reflect on how you are feeling about this activity. Share with your table.
Now we are going to let you use resources and to continue this challenge.
Link to standards doc participants will use:

10. COHERENCE IN GRADES 6–8 30 secs Speaker Notes:
Our friends at Student Achievement Partners have created a tool to help us determine Coherence (both across and within grades). In addition to coherence, this tool also identifies whether the standards are major, additional or supporting clusters, and it also includes sample tasks for some of the standards. We’re going to show you how to use the tool now, and then you will check your Vertical Progressions Challenge accuracy using the tool.

11. Coherence Map Go to http://achievethecore.org/coherence-map/ Click on
COHERENCE IN GRADES 6–8
Coherence Map
Go to
Click on
Choose a grade level to map-out the Ratio and Proportions (RP) Domain. Use the map to check the accuracy of your Vertical Progression Challenge.
Revise as needed. Note which standards belong in which grade.
10 min
Speaker Notes:
Do this with your partner

12. COHERENCE IN GRADES 6–8 A Picture of Coherence
Grades 4 and 5
Grade 6
Grade 7
Grade 8
High School E
F-BF.1 D
7.RP.1 C
8.F.2 F
6.RP.2 B
5.NF.3 J
4.MD.2 K
7.RP.2 A
8.EE.6 H
7.G.1 L
6.RP.3a
Speaker’s Notes:
Here is a picture of how these standards are organized by grade, as well as some logical connections between them.
What is something you noticed about the coherence across grades?
Ideas to highlight:
While this exercise was centered in the RP domain, it’s impossible to stay there without tapping into other domains. This is the richness of the standards, and also the difficulty of teaching the standards.
Standards F, K, H, A, C, and E illustrate how proportional reasoning (in grades 6 and 7) opens the door to geometry, expressions/equations, and functions in grades 8 and 9.
Standards G, L, and K show the progression of how work with coordinates develops in Grade 5 and becomes a part of understanding ratios in Grades 6 and 7. I
8.EE.8 G
5.G.2 M
7.RP.3

13. COHERENCE IN GRADES 6–8
Table Talk
What are the implications of coherence for students who are struggling mathematically in your schools?
5 min
Table talk – limited share out
KEY TAKEAWAYS - Stress usefulness as resource for thinking through scaffolding for students struggling with grade level standards - can trace connections backwards to previous grades. Also think we talk about the importance about professional development/conversations with teachers across grade levels. I actually think this part is the leadership development: helping leaders think about how they create systems/routines that are rooted in growing and improving the implementation of the shifts. Speaks to the importance of vertical mapping and teachers to engage in this work together across grade levels.
IMAGE CREDITS:

14. Within-Grade Coherence
Coherence is also built into the standards in how they reinforce a major topic in a grade by utilizing supporting, complementary topics. 
15 sec
Speaker Notes:
You may have seen examples of this in the Coherence Map, and we want to focus on it a bit. Coherence has another meaning-- coherence within the grade.
Instead of a list of unrelated standards, content is connected across domains. Let’s see what it looks like in a student task.
IMAGE CREDITS:

15. Do the Math - Grade 7 7.EE.B.3 7.EE.B.4 7.RP.A.3
COHERENCE IN GRADES 6–8
Do the Math - Grade 7
6 min
Speaker Notes:
4 min
Take a look at the following task.
(a) do the math and (b) explain which two domains are evident in the task.
What standards and/or clusters are evident in the task?
2 min
This problem can be solved with a ratio table or by finding a unit rate, or by using expressions and /or equations.
This problem fosters proportional thinking and lends itself to a discussion of algebraic reasoning, especially if the numbers are substituted for “less clean” ones.
The problem highlights using expressions and equations (7.EE.B.3 and 7.EE.B.4) as well as proportional reasoning (7.RP.A.3).
KEY POINT - [Discussion of standard/cluster alignment.] There can be more than one domain/cluster within a grade level for any give tasks. During our first session, we discussed major work of the grade. This is an example of how supporting work connects to the major work and helps build links.
7.EE.B.3
7.EE.B.4
7.RP.A.3

16. Observing for Coherence
1 min
Speaker Notes:
Transition - We will now apply what we have learned to the classroom setting. We want to be proficient at identifying the grade level standards, determining whether the standards being taught are the major work of the grade, and know the questions to ask that will deepen teachers’ understanding of the math coherence. We’re going to observe another math lesson – this time for Coherence (across and within grade), the math knowledge and skills required, and the math above and below the grade level.

17. Key Supervision Questions for Coherence
COHERENCE IN GRADES 6–8
Key Supervision Questions for Coherence
Across Grade Coherence
Does the instruction carefully connect learning across grades so that students can build new understanding onto foundations built in previous years?
Within Grade Coherence
Is the instruction leveraging how the standards within a grade were built to reinforce a major topic by utilizing supporting, complementary topics?
1 min
Speaker Notes:
These are the key questions leaders and coaches ask when engaging classroom observations from a coherence lens. These questions will help you collect the right evidence while in the classroom; they are terrific guiding questions around teacher development as well.

18. Observing for Coherence
COHERENCE IN GRADES 6–8
Observing for Coherence
Leader Tasks
Across Grade Coherence
Within Grade Coherence
Preparation
Determine domain of focus. Review standards, progressions document.
Use standards app and Coherence Map tools.
Look-for
Are the students who get it making connections to previous learning?
For students who are are not getting it, is the teacher leading students to make connections to previous learning?
Are the non-major work standard(s) being taught supporting priority content?
Post-observation
Ask: what prerequisite knowledge is a student lacking to be able to make those connections?
Consider: share time studying the wiring diagram, studying linking standards, with next steps digging into curriculum for additional lessons on knowledge gaps.
If supporting standards are not linking to major work of the grade:
What do the standards say?
Same question as before: How can this chosen standard authentically lead students back to working with math content to be emphasized in this grade?
4 min
Speaker Notes:
Before you observe for Coherence, prepare by knowing what you are walking in to see. If you can, get the information ahead of time. If you cannot, figure out the the domain of focus and the intended standard(s). Use your app!
During your time in the classroom, keep looking for student learning, the teacher’s role in providing connections to prior learning, the teacher’s response to struggling learners, etc.
Post-observation If you haven’t done it before the observation, use the progressions documents and/or the Coherence Map to prepare for the discussion with the teacher. Even better if you use them during the discussion. Use these questions to discuss what you saw, develop the teacher’s knowledge and skill around coherence and math.

19. Observing for Coherence
COHERENCE IN GRADES 6–8
Observing for Coherence
Standard: 7.RP.A.2
Prepare:
Determine the domain of focus for the
unit or module
Look up the standard
Preview the corresponding progressions
document or Coherence Map
Capture Evidence:
Are the students who get it making connections to previous learning?
For students who are are not getting it, is the teacher leading students to make connections to previous learning?
Are the non-major work standard(s) being taught supporting priority content?
14 min (3 min set-up; 11 min video)
Speaker Notes:
3 min: Look up the standard. Use the Coherence Map to check out the prerequisites for this standard and any within grade connections.
Play video

20. After the Observation Is this part of the major work of that grade?
COHERENCE IN GRADES 6–8
After the Observation
Is this part of the major work of that grade?
Are the students who get it making connections to previous learning?
For students who are are not getting it, is the teacher leading students to make connections to previous learning?
Are the non-major work standard(s) being taught supporting priority content?
8 min
Speaker Notes:
5 min – First, you will deconstruct what you just saw in terms of COHERENCE. Turn & Talk w/ partner
3 min – Whole group share:
MAIN POINT:
This is major work.

21. COHERENCE IN GRADES 6–8
After the Observation
What questions would you now want to ask Ms. Doden?
2 min
Speaker Notes:
Solicit 1-3 answers (don’t spend much time here). We have a couple to suggest that can help unpack her thinking and provide opportunities for her development.

22. Questions that Develop
COHERENCE IN GRADES 6–8
Questions that Develop
Leading the Conversation
Are the students who get it making connections to previous learning?
For students who are are not getting it, is the teacher leading students to make connections to previous learning?
Are the non-major work standard(s) being taught supporting priority content?
If students are still not making connections:
Ask: what prerequisite knowledge is a student lacking to be able to make those connections?
Consider: share time studying the wiring diagram, studying linking standards, with next steps being digging into curriculum for additional lessons on knowledge gaps.
If supporting standards are not linking to major work of the grade:
What do the standards say?
Same question as before: How can this chosen standard authentically lead students back to working with math content that is to emphasized in this grade?
2 min
Speaker Notes:
As we did with the video observation of Focus, we’d like to offer these additional post-observation questions that can help develop a teacher’s knowledge and skill around Coherence. We’ve already spent time with this first set of questions in grey. This second set of questions will provide a window into the teacher’s knowledge and skill with what children need to learn the mathematics and demonstrate this standard. It also leads the discussion into the “what’s next” for these students.
How are these questions the same or different than the way you usually debrief classroom observations? How would these questions help develop your teachers?

23. Reflection: Coherence
COHERENCE IN GRADES 6–8
Reflection: Coherence
Think about Common Core implementation in your school:
What is the state of curriculum, planning and professional development around Coherence in your building?
What are some preliminary steps that are needed to improve the state of Coherence in your building?
What systems can you access, adjust or initiate?
Professional development
Planning
Observation and supervision
5 min
Speaker Notes:
1 min set-up; 4 min silent write
Restate session objectives: this session was designed for you to be able to describe the coherence shift both as a logical sequencing of content across grades and as important connections between standards, clusters, and domains within the grade. We also want you to be able to observe and coach the coherence shift in teacher practice.
In whatever format you are using to track your reflections and action steps, take a few minutes to individually, or in district/school teams, reflect on how COHERENCE is currently going in our context and what next steps for improvement you could take.
Anticipated Questions
A leader or two might suggest that the district has aligned the curriculum to the standards. And it has a scope and sequence in place. Might want to highlight the work that the teachers are doing around aligning teaching to curriculum. Emphasize Engage as an aligned curriculum that takes some of this pressure off teachers to ensure that the curriculum is both focused and coherent. Allow teachers and leaders to focus on implementation during instruction. Charter vs district - less control over curriculum. How is coherence relevant to me? If you're stuck with something it's still your responsibility. Work with what you have but ensure shifts and standards are being taught. Moral obligation to speak to decision-makers about curriculum and show why not aligned?

24. Take a break… IMAGE CREDITS:

25. References COHERENCE IN GRADES 6–8 Slide Source 7 10 15
19-21
5 min
Speaker Notes:
1 min set-up; 4 min silent write
Restate session objectives: this session was designed for you to be able to describe the coherence shift both as a logical sequencing of content across grades and as important connections between standards, clusters, and domains within the grade. We also want you to be able to observe and coach the coherence shift in teacher practice.
In whatever format you are using to track your reflections and action steps, take a few minutes to individually, or in district/school teams, reflect on how COHERENCE is currently going in our context and what next steps for improvement you could take.
Anticipated Questions
A leader or two might suggest that the district has aligned the curriculum to the standards. And it has a scope and sequence in place. Might want to highlight the work that the teachers are doing around aligning teaching to curriculum. Emphasize Engage as an aligned curriculum that takes some of this pressure off teachers to ensure that the curriculum is both focused and coherent. Allow teachers and leaders to focus on implementation during instruction. Charter vs district - less control over curriculum. How is coherence relevant to me? If you're stuck with something it's still your responsibility. Work with what you have but ensure shifts and standards are being taught. Moral obligation to speak to decision-makers about curriculum and show why not aligned?

26. Image Credits COHERENCE IN GRADES 6–8
Slide 7:
Slide 8, 13:
Slide 14:
Slide 24: