1. Leadership Pathway: Rigor in High School Winter 2017
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Leadership Pathway:
Rigor in High School
___ minutes for this session
Speaker’s Notes:
Handouts packets for Day 2
Be sure to load 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.
9 min. – Video
Winter 2017

2. The Week at a Glance RIGOR IN HIGH SCHOOL Day Ideas Monday
8:30–5:00
Focus and Coherence
Tuesday
8:30–4:30
Rigor
Observing the Standards and Shifts
Adaptations for Struggling Learners
Wednesday
The Foundation
Text Complexity
Thursday
Building Knowledge and Vocabulary
The Juicy Language of Text
Friday
8:30–2:30
Organizational Systems and Structures
1 min.
Speaker’s Notes:

3. Finding Rigor in the Standards
RIGOR IN HIGH SCHOOL
Objectives and Agenda
Objectives:
Participants will be able to describe the three aspects of Rigor and why Rigor is important.
Participants will be able to evaluate standards, tasks, and lessons for aspects of Rigor.
Participants will be able to observe and coach the Rigor shift in teacher practice.
Agenda:
Opening
Activator
Rigor: What and Why?
Finding Rigor in the Standards
Observing for Rigor
1 min.
Speaker’s Notes:
We’ll start by looking carefully at the shift of Rigor in math, with an emphasis on why it’s important and what it looks like in in the standards Grades 6–8.

4. RIGOR IN HIGH SCHOOL Feedback on Feedback Plus Delta 5 min.
Speaker’s Notes:
Highlight a couple of pluses and a couple of deltas; choose them based on impact on participant learning and/or so they feel heard. Tell how we will respond today or what they can expect. For the pluses or deltas that are about group behavior, encourage the group to keep doing the positive and to monitor or minimize those things that could help the learning environment be improved.

5. Norms That Support Our Learning
RIGOR IN HIGH SCHOOL
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 where it is “safe to not know.”
1 min.
Speaker’s 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).

6. Teachable Moments Activator
RIGOR IN HIGH SCHOOL
Teachable Moments Activator
Step One – Pair
Stand and find a partner. Remain standing.
Step Two – Count
At the facilitator’s direction, count off 1–6.
Step Three – Analyze
Analyze your assigned statement for its misconceptions.
Step Four – Role Play
3 min. – Practice coaching to undo the misconception(s).
3 min. – Provide feedback
3 min. for scenario and protocol
Speaker’s Notes:
Let’s start the day with an activator that serves 3 purposes:
1. It helps you remember what we learned yesterday about Focus and Coherence.
It helps to surface common misconceptions that educators have when they learn about the shifts.
It gives you a chance to practice a coaching conversation to undo a misconception.
Here’s the scenario: Imagine you have just finished a day of PD back at your school. You loved the Institute session on Focus and Coherence so much that you decided to replicate the experience with your teachers (the materials are free after all!). After the session, you check in with individual teachers to hear what they intend to do with their new-found knowledge. Unfortunately, their answers are problematic.
Now here’s the protocol:
<Click > through steps 1 and 2 and have them do them.
<Click> through steps 3 and 4 and explain them. This is a one-way coaching practice: 3 minutes to coach and 2 minutes for the coachee to provide feedback on the effectiveness.
Last Point: Facilitator will monitor time and call out when to switch activities.
IMAGE CREDITS:

7. Teachable Moments Activator
RIGOR IN HIGH SCHOOL
3. I’m going to make sure I spend at least half my time this year teaching the major work course emphases.
Teachable Moments Activator
1. Within-grade coherence isn’t relevant in Geometry because everything in the course is about Geometry—it is all one domain.
2. I decided to skip the Circles domain because everything in there is an additional cluster.
6. I’m going to make sure all the problems/tasks that I assign always align to at least two different standards.
4. My kids can’t do G-CO.2 so I’m teaching 8.G.A.1 first.
5. To strengthen connections, I’ll make sure that my students are solving each problem in as many different ways as possible.
15 min.
Speaker’s Notes:
10 min. – Analyze and role play
4 min. – Analyze statement for misconceptions
6 min. – Role play coaching conversation
3 min. – Role play
3 min. – Feedback on effectiveness of coach
5 min. – Answer any misconceptions questions they might still have
Keep this focused on the content of misconceptions about focus and coherence.
If any time left, you can ask what an activity like this does for an adult learner or ask if anyone in the room regularly surfaces misconceptions as a part of their professional development activities.
MAIN POINTS: Help build out some of the nuance and inputs to instructional decision-making here.
Correct Answers
“Geometry” is the conceptual category (unlike the grade level standards that have Geometry as a domain), and there are several domains within the Geometry category: Congruence; Similarity, Right Triangles, and Trigonometry; Circles; Expressing Geometric Properties with Equations; Geometric Measurement and Dimension; and Modeling with Geometry. There are many connections to be made among standards in Geometry, some of which are even essential—like congruence and similarity.
Additional clusters are not to be skipped—doing so would put students behind and rob them of significant knowledge and skill. In Geometry, students began basic right triangle trigonometry. In Algebra II, they extend the domains of the three basic trig functions to the entire unit circle.
Major work should comprise the bulk of the learning for the grade level, not “at least half.” Half is not enough, it should be the bulk (at least ⅔ of the learning). Bigger idea is about depth over breadth. Deep learning over fast learning.
Spending a lesson or two on a prerequisite is fine, but students should very quickly be moving into grade-level content. Another way of tapping into prerequisites is to spend the beginning of each lesson connecting students to previous learning (vs. devoting entire lessons to reteaching). The math team calls this “coherent content in context.”
This is overkill. Math is intended to be efficient. Solving problems in different ways may make sense some of the time—particularly when the idea is new—but it is poor practice to do it all of the time.
Another example of an overcorrection. Having students learn the content demanded by one standard is fine, especially when the standards ask demonstration of deep conceptual understanding, modeling, and/or application. Rich, quality math tasks help make this happen for students. Within-grade coherence is helpful when the connections are made appropriately and are well planned. The PARCC Model Content Frameworks can help map these connections out for you. And good curriculum will do that work for you as well.
Final Point: We should not be turning the math shifts into recipes.

8. Rigor: What and Why?
“Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
From the Common Core State Standards
3 min.
Speaker’s Notes:
Ask: Can I hear from 1 or 2 people: how would you define Rigor?
<Click> for the animation to show the definition.
Say:
A common misconception is that Rigor just means “hard.” It doesn’t. Rigor has a specialized meaning in the context of Common Core math. From CoreStandards.org: “Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”
This morning we talked about what mathematical content is important, and what connections exist between standards.
Rigor has everything to do with how students engage with mathematical content—it implies a balance of conceptual understanding, procedural skill and fluency, and application. But why do we care about these aspects of mathematical understanding?
IMAGE CREDITS:

9. From the CCSS for Mathematics
RIGOR IN HIGH SCHOOL
From the CCSS for Mathematics
“Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like?”
“There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics, and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).”
“Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”
1 min.
Speaker’s Notes:
30 sec. – Read: Take a moment to read this quoted section from the CCSS for Mathematics.
30 sec. – Say: The study of mathematics instruction in this country has identified a number of things we are trying to correct for with the state standards. One of them is our lack of helping children understand math concepts deeply. I’d like you to think of how this may have impacted mathematical learning for you. Think for a moment: Is there a time when you learned a procedure or a mnemonic or a way of doing the math without understanding why or what math you were doing? And what impact did that have on your future learning—if any?

10. Paired Learning Activator
RIGOR IN HIGH SCHOOL
Paired Learning Activator
Is there a time where you learned a procedure or a mnemonic or a way of doing the math without understanding why or what math you were doing?
And what impact did that have on your future learning—if any?
7 min.
Speaker’s Notes:
4 min. – Stand and find someone you have not yet connected deeply with in this Institute. Share your experiences for about 4 minutes
Note: This is happening in late afternoon, so it is important that people stand for this activity so that it also acts as a mini-energizer.
3 min. – Still standing with partner, ask the group to share out their experiences.
IMAGE CREDITS:

11. From “Adding It Up” RIGOR IN HIGH SCHOOL 1 min. Speaker’s Notes:
Researchers in the late 90s identified 5 components (or strands) of mathematical proficiency.
Note particularly these 4: adaptive reasoning, conceptual understanding, procedural fluency, and strategic competence. These form the basis of what we call “Rigor” in the standards. (Adaptive reasoning is also about Rigor. It is the application/modeling portion of it and works hand-in-hand with strategic competence.)
The other strands make up the mathematical practices.
Ask a question: “How well do you think our instruction is currently balanced among these three aspects of Rigor?” 1 answer here because of time.

12. From TIMSS Video Study RIGOR IN HIGH SCHOOL
2 min.
Speaker’s Notes:
TIMSS video study in the late 1990s compared eighth-grade math instruction in 7 participating countries.
Despite the recognition that a balance of the different strands of mathematical proficiency is necessary (Adding It Up), on average, 75% of “private work time” is spent repeating procedures in the United States.
The point of the slide is not to draw conclusions about what the impact of "repeating procedures" might be, but to show the gap between what's happening in the United States and what research about the Adding It Up research says. 
Note: Repeating procedures in this context means following modeled algorithms/procedures rather than independently applying strategies (without heavy guidance) or time spent demonstrating conceptual understanding by explaining thinking.
QUESTION PARTICIPANT MAY ASK:
Might have a leader talk about how our students/culture is different...need to emphasize what the research says about what students need—and what we control.
Other TIMSS background:
The TIMSS 1999 Video Study was a study of eighth-grade mathematics and science teaching in seven countries. The study involved videotaping and analyzing teaching practices in more than one thousand classrooms. In conjunction with the International Association of the Evaluation of Education Achievement (IEA), the study was conducted by the National Center for Education Statistics, US Department of Education under a contract with LessonLab, Inc., of Los Angeles, California. Although Japan did not participate in the mathematics portion of the study, the Japanese mathematics data collected as part of the TIMSS 1995 Video Study were re-analyzed for the TIMSS 1999 Video Study. US mathematics data collected as part of the TIMSS 1995 Video Study were also re-analyzed.

13. From TIMSS Video Study RIGOR IN HIGH SCHOOL
2 min.
Speaker’s Notes:
Additionally, the kind of non-routine problem solving implied by the application shift does not seem to be happening either.
Compared to some other high-performing nations, we spend a smaller amount of time on problems that take longer than 45 seconds. (Only 61% of problems are solved in longer than 45 seconds.)
QUESTIONS PARTICIPANTS MAY ASK:
I think a lot of times educators talk about how technology prevents students from spending extended focus time on problem solving...this graphic completely debunks that. Looking at developed nations, have large access to technology, so excuse that students don't have stamina isn't valid.
Note about these slides:
While TIMSS is conducted every few years, this "interesting" data (about time spent on different things in classrooms, etc.) comes from the TIMSS Video Study, which has only occurred once, in Otherwise, TIMSS is an assessment system that provides information about what students know and can do around the world. Still interesting, but doesn't give us information about what students and teachers are doing in classrooms.

14. Consider this Contrast
RIGOR IN HIGH SCHOOL
Consider this Contrast
USA
How can I teach my kids to get the answer to this problem?
Japan
How can I use this problem to teach the mathematics of this unit?
1 min.
Speaker’s Notes:
Point to the USA question and ask, ”Is this familiar?”
Point to the second question and say, “What differences would we need to see if we approached mathematics instruction this way?”
From:

15. RIGOR IN HIGH SCHOOL
Three Aspects of Rigor
Procedural Skill and Fluency: The standards call for speed and accuracy in calculation.
Conceptual Understanding: The standards call for conceptual understanding of key concepts, such as place value and ratios. 
Modeling/Application: The standards call for students to use math in situations that require mathematical knowledge.
2 min.
Speaker’s Notes:
The standards name and emphasize three aspects of Rigor that are a direct reflection of this research on mathematical understanding.
Procedural skill and fluency shift refer both to “procedural skill” and “fluency.” In some cases, speed with calculations is particularly emphasized. Fluency should be built after conceptual understanding has been achieved.
What does conceptual understanding look like? One way for teachers to get students to understand key concepts is to ask students to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.
Modeling/Application is not “just doing a bunch of real-world problems” but should genuinely require that students know which ideas to apply when and how to “mathematize” real-world situations.

16. Find the Rigor Protocol: Do the math.
RIGOR IN HIGH SCHOOL
Find the Rigor
Protocol:
Do the math.
For each, what aspects of Rigor are emphasized and how do you know?
What are the grade level standards associated with each one?
10 min.
Speaker’s Notes:
Hand out the tasks sheet. Assign 1 task to each table for them to “do the math.” Ask for show of hands from people who think they know or remember enough of the math for each task. Have them spread out to the assigned tables to help the table “do the math” and look up the standards. OPTION: Model how to do each problem instead.
Say: Rigor is baked into the standards. We’ll start to see what Rigor looks like in a task and then and how it is embodied in the standards.
For each task, “do the math” and discuss which aspects of Rigor are present.
Determine the grade level standard associated with each one.

17. RIGOR IN HIGH SCHOOL
Task #1
Let F assign to each student in your math class his/her biological father. Explain why F is a function.
Describe conditions on the class that would have to be true in order for F to have an inverse.
In a case from part (b) in which F does not have an inverse, can you modify the domain so that it does?
F-IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y=f(x).
1 min.
Speaker’s Notes:
Answers:
F is a function because each student only can have one biological father.
The inverse of F would associate a father with only one child in the classroom that is biologically his; this wouldn’t be true if there were siblings in the classroom.
By modifying the domain to exclude siblings, then F would have an inverse.
The highlighted aspect of Rigor is conceptual understanding because students must know and be able to use the concept of a function—including but not limited to its definition—to reason about a given situation. Functions are a key concept in high school math.
Click to reveal the standard. This is standard F-IF. Part (a) strongly signals standard F-IF.A.1; note that parts (b) and (c) also rely on understandings from F-BF.4 (including some Algebra II concepts and (+) standards not assessed on PARCC).
Source:

18. RIGOR IN HIGH SCHOOL
Task #2
John makes DVDs of his friend’s shows. The cost of producing x DVDs is given by C(x) = x.
John wants to cover his costs. Suppose John made 100 DVDs. What is the cost of producing this many DVDs? How much is this per DVD?
Complete the table showing his costs at different levels of production.
Explain why the average cost per DVD levels off.
Find an equation for the average cost per DVD of producing x DVDs.
Find the domain of the average cost function.
Using the data points from your table above, sketch the graph of the average cost function. How does the graph reflect that the average cost levels off?
5 min.
Speaker’s Notes:
Take a moment to do this task from Illustrative Mathematics (note that participants may not have time to complete the entire table, especially without calculators, but should be able to reason through the other portions fairly quickly).
Answers:
a) $26.25 per DVD; b) see completed table pasted below; c) fixed cost is shared by the total number of DVDs, so it becomes increasingly small; d) ( x)/x; e) all positive integers; f) graph has a horizontal asymptote at 1.25
The highlighted aspect of Rigor is application because students are applying their understanding of functions to model a situation that describes a real context.
F-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*
Source:
F-IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

19. RIGOR IN HIGH SCHOOL
Task #3
F-IF.8.a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
1 min.
Speaker’s Notes:
Answer: D (-4) and H (15) are both zeroes of the function.
The aspect of Rigor is procedural fluency—to solve this problem, students have to be able to rewrite expressions in equivalent forms and more specifically, to factor quadratics and to connect factors to zeroes. This is standard F-IF.8.
The highlighted aspect of Rigor FOR THIS TASK is procedural fluency because students must perform computations quickly and accurately.
It’s important to note that there are standards that emphasize procedures, but may not include the word “fluently.” We may emphasize performing procedures accurately with less emphasis on speed for these standards.
<Click> to reveal the standard.

20. Identifying the Rigor in the Standards
RIGOR IN HIGH SCHOOL
Identifying the Rigor in the Standards
Procedural Skill
F-IF.8.a
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
Application
1 min.
Speaker’s Notes:
Point out all aspects of Rigor required by this standard. For example, within F-IF.8.a, the “use the process” part clearly indicates procedural skill, while “interpreting in terms of a context” implies using the processes in a problem-solving (i.e., application) context.

21. One Final Point: A Balance of Rigor
RIGOR IN HIGH SCHOOL
One Final Point: A Balance of Rigor
The Standards set high expectations for all three components of Rigor in the major work of each grade.
(1) The three aspects of Rigor are not always separate in materials.
(2) Nor are the three aspects of Rigor always together in materials.
1 min.
Speaker’s Notes:
In the teacher sessions, teachers are examining curricular materials for all aspects of Rigor, including how to look for a balance. We do not have time for that exploration in this session, but you should know:
Criteria were developed to help states, districts, schools faithfully implement the common core standards through evaluation of curricular materials. ”Crosswalking” is not good enough, good curricular must be able to speak to the spirit of the standards.
The Publishers’ Criteria makes clear this balance is important.
“Of course, that makes it necessary that we first follow through on the focus in the Standards” (From Publishers’ Criteria). We must have a focused curriculum for teachers to be able to develop fluencies, conceptual understanding, and application (it’s an issue of time, essentially).
Transition: In the time we have left today, let’s summarize what we set out to learn and where we are before heading into our reflection and survey.
IMAGE CREDIT:

22. Observing for Rigor 1 min. Speaker’s Notes:
Let’s see what Rigor looks like. In this video, you will see a pretty strong example in a fifth-grade classroom. First, let’s look at what we might see with each of the aspects of Rigor.

23. Key Supervision Questions for Rigor
RIGOR IN HIGH SCHOOL
Key Supervision Questions for Rigor
What to Look For
Opportunities for students:
To become more fluent (efficient and accurate) with procedures
Students practice, many times, with facts and procedures.
Fluency activities build upon conceptual understandings students already have.
To build their conceptual understanding
Students being asked “why” to rationalize their thinking.
Students working with models to process their thinking.
To model/apply their thinking, particularly in real world situations
Students working on rich math problems.
Students use math absent of external prompts (e.g., “use addition to solve this problem”).
1 min.
Speaker’s 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.

24. Observing for Rigor Standard: HSF-IF.B.5 Prepare
RIGOR IN HIGH SCHOOL
Observing for Rigor
Standard: HSF-IF.B.5
Prepare
Look up the standard(s).
Determine the aspects of Rigor embedded
in the standard(s).
Capture Evidence of Rigor Aligned
to the Standard
Procedural skill and fluency
Conceptual understanding
Modeling/application
14 min. (5 min. set-up; 9 min. video)
Speaker’s Notes:
5 min.:
Look up the standard and identify the aspects of Rigor.
HSF-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
MAIN POINTS:
Procedural skill and fluency—N/A
Conceptual understanding—“Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.”
Modeling/application
9 min. – Play video

25. After the Observation Procedural Skill and Fluency Evidence
RIGOR IN HIGH SCHOOL
After the Observation
Procedural Skill and Fluency Evidence
Students practice, many times, with facts and procedures.
Fluency activities build upon conceptual understandings students already have.
Conceptual Understanding Evidence
Students being asked “why” and to rationalize their thinking.
Students working with models to process their thinking.
Modeling/Application Evidence
Students working on rich math problems.
Students use math absent of external prompts.
10 min.
Speaker’s Notes:
5 min. – First, you will deconstruct what you just saw in terms of Rigor. Turn & Talk w/ partner. Make your discussions evidence-based
5 min. – Whole group share
MAIN POINTS:
It shows conceptual understanding and modeling (no real attention to procedure here).  But, the alignment is wrong.  Ms. McAtee is teaching F.IF.B.4- interpreting key features of graphs for functions that model relationships between quantities. The standard tag is wrong! If she had discussed Domain—at all—F.IF.B.5 could have been addressed.
Fluency: N/A
Conceptual understanding
Application

26. RIGOR IN HIGH SCHOOL
After the Observation
What questions would you now want to ask Ms. McAtee?
2 min.
Speaker’s Notes:
Solicit 1–3 answers (don’t spend much time here).
On the next slide, we have a couple of suggestions that can help unpack her thinking and provide opportunities for her development around Rigor.

27. Questions That Develop Rigor
RIGOR IN HIGH SCHOOL
Questions That Develop Rigor
Procedural Skill and Fluency
Conceptual Understanding
Modeling/Application
If fluency opportunities are not present:
Ask where fluency practice is/will be built in upcoming lessons.
If students show fluency as a limiter in their math work:
Ask how students’ lack of fluency will be addressed.
Consider curriculum: fluency activities from high-quality lessons for the area that is limiting students.
If conceptual understanding opportunities are not present:
Ask how more opportunities may be worked into what students are thinking when working with math concepts.
If students show conceptual understanding as a limiter in their math work:
Consider gaps: re-ask questions in coherence activities.
Consider curriculum: study high-quality lessons aligned to the standard of focus.
If application opportunities are not present:
Ask how more application opportunities can be folded into the student math experience.
If students are provided external prompts to complete application problems:
Ask how the teacher can adapt opportunities so students can apply math without the prompting.
Consider curriculum: study high-quality tasks aligned to the standard of focus.
4 min.
Speaker’s Notes:
These sets of questions will provide a window into the planning and decision-making that drove the teacher’s lesson. It also leads the discussion into the “what’s next” for these students.
How are these questions the same as or different than the way you usually debrief classroom observations? How would these questions help develop your teachers?
Transition: We are now going to do one more culminating video observation of a math lesson and then have an opportunity to practice using these questions while coaching for rigor (and the other shifts).

28. References RIGOR IN HIGH SCHOOL Slide Source 8 9
12–14 17 18 19
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29. Image Credits RIGOR IN HIGH SCHOOL
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