1. Leadership Pathway: Rigor in Grades K–5 Winter 2017
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Leadership Pathway:
Rigor in Grades K–5
93 minutes for this session
Handouts packets for Day 2
1 video for this session: Load the video prior to participants’ arrival by opening the link and letting it begin to run. This should have the video ready to view without buffering.
11 min.
Winter 2017

2. The Week at a Glance RIGOR IN GRADES K–5 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
Components of an Effective Literacy Program
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. Objectives and Agenda Objectives:
RIGOR IN GRADES K–5
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?
Find the Rigor
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 K-5.

4. Feedback on Feedback RIGOR IN GRADES K–5 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 GRADES K–5
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 GRADES K–5
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. For the coaching role play. This is a one-way coaching practice: 3 min. to coach and 2 min. 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 GRADES K–5
3. I’m going to make sure I spend at least half my time this year teaching the major work of the grade.
Teachable Moments Activator
1. Counting and Cardinality isn’t relevant in 1st grade, because there is no CC domain in 1st– only Kindergarten. .
2. I decided to skip the 4th grade Geometry 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 4.NF.A.1 so I’m teaching 3.NF.A.I 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. to analyze and role play
4 min. analyze statement for misconceptions
6 min. to role play coaching conversation
3 min. role play
3 min. feedback on effectiveness of coach
5 min. to 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.
Correct Answers
It is relevant as a prerequisite. From our Kindergarten Counting & Cardinality: Unbound Content Guide: Counting & Cardinality standards in Kindergarten provide a significant conceptual basis for almost all later work within the Operations & Algebraic Thinking (OA) and Number & Operations in Base Ten (NBT) domains. Together, these two domains comprise the heart of the mathematics students learn in Kindergarten through Grade 2.
Additional clusters are not to be skipped—doing so would put students behind as they move to the next grades where Geometry is major work.
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 planfully. The Coherence Map 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
2 min.
Speaker’s Notes:
Ask: Can I hear from 1–2 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 GRADES K–5
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. – To read; Say: 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 CCSS. 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 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?
SOURCE:

10. Paired Learning Activator
RIGOR IN GRADES K–5
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: It is important that people stand for this activity so 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 GRADES K–5 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 GRADES K–5
2 min.
Speaker’s Notes:
TIMSS video study in the late 1990s compared 8th-grade math instruction in seven 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 what students need, ... and what we control.
Other TIMSS background:
The TIMSS 1999 Video Study was a study of 8th-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, U.S. 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. U.S. mathematics data collected as part of the TIMSS 1995 Video Study were also re-analyzed.

13. From TIMSS Video Study RIGOR IN GRADES K–5 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 that have large access to technology, the 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 GRADES K–5
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 GRADES K–5
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 GRADES K–5
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. to do all 3 tasks and identify standards
Speaker’s Notes:
Hand out the tasks sheet.
Say: Rigor is baked into the standards. We’ll start to see what Rigor looks like in a task and then how it is embodied in the standards.
Take 10 minutes. For each task, “do the math” and discuss which aspects of Rigor are present.
Determine the grade level standard associated with each one.
After the 10 minutes, we’ll come back together to see if we agree.

17. RIGOR IN GRADES K–5
Task #1
Juanita spent $9 on each of her 6 grandchildren at the fair. How much money did she spend?
Nita bought some games for her grandchildren for $8 each. If she spent a total of $48, how many games did Nita buy?
Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $42, how much did each grandchild get?
1 min.
Speaker’s Notes:
Answers:
a) Juanita spent $54.
b) Nita bought 6 games.
c) Each grandchild gets $6.
The highlighted aspect of Rigor is Application because students must use multiplication and division to solve real-world problems. Note the mix of multiplication and division within the task--students must choose different strategies for each problem.
<Click> to reveal the standard 3.OA.A.3
Source:
3.OA.A.3
Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem).

18. RIGOR IN GRADES K–5
Task #2
The teacher gives the equation 4 × ___ = 12. Charlie finds the answer by writing and solving 12 ÷ 4 = ___.
Explain why Charlie’s method works.
3.OA.B.6
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
1 min.
Speaker’s Notes:
Answer: Participants may come up with a variety of responses including verbal descriptions and drawings that relate division to multiplication.
The aspect of Rigor is conceptual understanding—students must have a deep understanding of the meaning of each equation and the relationship between multiplication and division.
<Click> to reveal the standard 3.OA.B.6.
Source:

19. Task #3 1. Facts for speed and accuracy: 3.OA.C.7
RIGOR IN GRADES K–5
Task #3
1. Facts for speed and accuracy:
a. ___ × 5 = 15
b. 10 ÷ 1 = ___
c. ___ = 6 × 10
d. ___ =20 ÷ 5
e. ___ = 7 × 10
f. 1 × 6 = ___
g. 9 × 2 = ___
h. 0 × 5 = ___
1 min.
Speaker’s Notes:
Answers:
a) 3, b) 10, c) 60, d) 4, e) 70, f) 6, g) 18, h) 0
The highlighted aspect of Rigor 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.
Transition to next slide by pointing out that Fluency is not the only aspect of Rigor required by this standard. Note that many standards may imply more than one aspect of Rigor. 3.OA.C.7 is an example (next slide).
Source:
3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

20. Identifying Rigor in the Standards
RIGOR IN GRADES K–5
Identifying Rigor in the Standards
Procedural Skill and Fluency
Conceptual Understanding
3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
1 min.
Speaker’s Notes:
Point out both aspects of Rigor required by this standard.

21. One Final Point: A Balance of Rigor
RIGOR IN GRADES K–5
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, and 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 CREDITS

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 GRADES K–5
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 Rigor 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: 5.MD.1, 5.NF.3 Prepare
RIGOR IN GRADES K–5
Observing for Rigor
Standard: 5.MD.1, 5.NF.3
Prepare
Look up the standard.
Determine the aspects of Rigor embedded
in the standard.
Capture Evidence of Rigor Aligned
to the Standard
Procedural Skill and Fluency
Conceptual Understanding
Modeling/Application
16 min. (5 min. set-up; 11 min. video)
Speaker’s Notes:
5 min.:
Look up the standard and identify the aspects of Rigor.
5.MD.1: Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real world problems.
5.NF.3: Interpret a fraction as division of the numerator by the denominator. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.
Answers:
5.MD.1:
Procedural Skill and Fluency “Convert among different-sized standard measurement units within a given measurement system”
Application “use these conversions in solving multi-step, real world problems”
5.NF.3:
Conceptual understanding “Interpret a fraction as division of the numerator by the denominator.”
Application “Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.”
11 min.:
Play video:

25. After the Observation Procedural Skill and Fluency Evidence
RIGOR IN GRADES K–5
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 asked “why” and to rationalize their thinking.
Students work with models to process their thinking.
Modeling/Application Evidence
Students work 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 with partner. Make your discussions evidence-based
5 min. – Whole group shares.
MAIN POINTS:
Fluency: No evidence of "on the clock" fluency, but the problems gave the students plenty of practice with procedural skill (no direct teaching of procedural skill).
Conceptual Understanding: Do Now discussion and kids explanation of their math (sub being split among 4 people). The girl in the pink sweater explained a lot—but her thinking is incorrect conceptually. In response to “Are they getting more than or less than a whole sub?”: "Less than because a decimal is less than a whole number.”
Modeling/Application: The sub Do Now activity is a rich math problem. The Do Now seemed to be designed for them to "use math absent of external prompts" because it didn't tell them what math to use to solve it.

26. RIGOR IN GRADES K–5
After the Observation
What questions would you now want to ask Mr. Colon?
2 min.
Speaker’s Notes:
Solicit 1–3 answers (don’t spend much time here). We have a couple to suggest that can help unpack his thinking and provide opportunities for his development.

27. Questions That Develop Rigor
RIGOR IN GRADES K–5
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 the 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 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 GRADES K–5 Slide Source8 9
12–14 17 18 19
24–26

29. Image Credits RIGOR IN GRADES K–5
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Slide 28: