Fellows Meeting 4APRIL 21, 2015

ESD 105

Fellows Meeting #4 A candy jar contains 5 Jolly Ranchers (squares) and 13 Jawbreakers (circles). Suppose you had a new candy jar with the same ratio of Jolly Ranchers to Jawbreakers, but it contained 100 Jolly Ranchers. How many Jawbreakers would you have? Explain how you know.

◦ Please try to do this problem in as many ways as you can.◦ If done, share your work with a neighbor.

Road Map of Our Day 8:30-10:00 Principles to Action Book Study

10:00-10:15 Break

10:15-11:30 CSTP- Fellows Groups Together

11:30-12:30 Lunch

12:30-1:30 Discourse and English Language Learners

1:30-1:45 Break

1:45-2:45 SBAC Claims and Depth of Knowledge

2:45-3:30 Next Steps-Evaluations

Best Math Lesson Ever

Turn and Talk What made it so successful? What was the math teacher doing? What were the students doing? What mathematics was being learned?

Teaching Practices that Support Common Core Implementation

• Establish Mathematics Goals to Focus Learning• Implementing Tasks that Promote Reasoning and

Problem Solving• Use and Connect Mathematical Representations• Facilitate Meaningful Mathematical Discourse• Pose Purposeful Questions• Build Procedural Fluency from Conceptual

Understanding• Support Productive Struggle in Learning Mathematics• Elicit and Use Evidence of Student Thinking

Turn and Talk How has the book study around the 8 teaching practices deepened your understanding around your vision of mathematics reform efforts?

How has the study impacted your work with your building/district?

Facilitate Meaningful Mathematical Discourse Purposeful Questioning Math Practices

Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

Review pages 29-41…

What was one thought that resonated with you from either practice?

Share out your thoughts in a small group.

Facilitating Discourse

Simply having students talk does not necessarily advance the mathematical goals of a lesson. oHow can the Five Practices identified on page 30, as

described by Smith and Stein (2011), support and facilitate the purposeful exchange of ideas in the mathematics classroom?oNow consider Mr. Donnelly’s lesson and how he

incorporated the Five Practices to facilitate classroom discussion. (p. 34)

Five Practices to Support Facilitating Discourse

1. Anticipating student response prior to the lesson

2. Monitoring students’ work on and engagement with the tasks

3. Selecting particular students to present their mathematical work

4. Sequencing students’ responses in a specific order for discussion

5. Connecting different students’ responses and connecting the responses to key mathematical ideas

Facilitating Meaningful Discourse

Considering the Levels of Student Discourse:

oWhich of these practices are under utilized in classrooms?

oHow can we help teachers become more intentional incorporating these practices?

Mathematics Teaching PracticePose Purposeful Questions

oGathering Information

oProbing Thinking

oMaking the Mathematics Visible

oEncouraging Reflection and Justification

Pose Purposeful Questions

Consider the math task for your Grade Band from Digging for Dinosaurs1. Review the standards associated with the task you

chose2. Do the math3. Anticipate likely student responses and misconceptions

(see Smith & Stein’s practice 1, p. 30) 4. Create a list of related questions using the framework

in figure 14 (pp. 36–37)5. Create a poster with your questions

Review Levels of Discourse

Review Chart from Principles to Actions (p. 32)

oWhat do you see as next steps to see you move along the continuum?

oHow does this continuum help you think about your work with teachers?

Break-

The Center for Strengthening the Teaching Profession (CSTP)

Module 4 – Case Story Discussion

Objectives Apply your developing understanding of the Teacher Leadership Framework and your skills as a Teacher Leader to Case Stories.

Reflect on your growth as a teacher leader in your role as a Fellow this year.

Pre-flection Review your results from the Teacher Leadership Framework Self-Assessment:◦ Do these results reflect where you are now? Why

or why not?◦ What has gotten more challenging? What has

gotten easier?◦ How do you deal with dilemmas that come up

and still focus on building capacity?

Learning Through Case Stories

Read the Case Story “Overwhelmed and Underappreciated”

As you read, consider what you know from the Teacher Leadership Framework that might connect to the Case Story – either in evidence provided or lack thereof. Annotate your thoughts within the article or on scratch paper.

Learning Through Case Stories

How do you and don’t you see yourself in this dilemma?

Where does this dilemma ‘live’ in terms of the five areas in the Teacher Leadership Framework (could be multiple areas)?

Where do you see evidence of the teacher leader employing specific knowledge, skills and dispositions from the Teacher Leadership Framework?

What from the Teacher Leadership Framework might assist this teacher leader in managing this dilemma?

Set-Up: Circle of Viewpoints

Brainstorm a list of players in this dilemma – in other words, who is part of the system described in the Case Story?

Each person in your group takes on the role of one of the players identified in your brainstorm

Circle of Viewpoints

Use the Circle of Viewpoints Routine to re-examine and discuss the Case Story.

Going one at a time, each group member contributes to the following three prompts:

◦ I am thinking of this Case Story from the point of view of…◦ I think…◦ A question I have is…

Repeat with the next group member until you’ve gone all the way around the whole group.

Reflections & Next Steps

After using the Circle of Viewpoints routine, what new ideas do you have that you didn’t have before?

What implications or realizations did you have for your own work as a fellow in reading this Case Story?

What are your next steps?

I used to think…Now I think…

Fellows 2015-16 Applications are now open..

Returning Fellows

New Fellows

Lunch-- Meet back with your fellows group at 12:30

Math Fellows Next Steps…

Fellows Student Task Data Survey-

Fellows Self-Assessment Pre/Post-

Submit Fellows Plans

Video Questions-

OPSI Clock Hours/Evaluations

Date: April 21, 2015Title: Washington State Math FellowsProfessional Development Hours: 6

The Language of Mathematics for All Children (CCSS to ELP and Beyond)

Helping al l students communicate mathemati cal understanding.

Session Goals… Promote student engagement through

interactive math tasks

Provide strategies and tools to support student discourse

Updates/Assessment Resources

What do you know about English Language Learners in Washington State?

Languages Spoken in Washington State Schools

219 Different Home Languages Most identified language is Spanish, spoken by 67.4% of students

Next were Russian, Vietnamese, Somali, Chinese, Ukrainian, Arabic, Tagalog, Korean, Marshallese, spoken by 19% of Students

ELL’s in Washington State 2013-14

Around 110,000 Bilingual Student a 5.3% increase from the previous year

Comprises 9.7% of the statewide student population - 0.6% points higher than the previous year

Since 2005–06, the number of ELLs served by TBIP in the state has increased by 32.6%

ELL’s in Washington State 2013-14

Twenty-seven districts had an ELL headcount of at least 25% of their total student population.

Thirty districts enrolled more than 1,000 ELLs. These districts collectively served 72% of all ELL’s statewide.

Forty-seven districts enrolled 500 or more ELL students.

Thirteen districts reported an increase of 10–15%.

ELL’s in Washington State 2013-14

Fifty-six districts enrolled fewer than 50 ELL students.

Fifteen districts reported fewer than 10 ELLs. 55.9% served by the TBIP were enrolled in grades K–3.

25% are newly eligible students

ELL’s in Washington State 2013-14

42 districts have more than 20 languages 19 of these districts had more than 50 languages. Of the 219 languages, 103 of these languages have less than 10 students

The largest language increase is in Spanish The greatest decrease is in Korean

Classroom Level Discuss the language supports in your district/classroom….

Focused Mathematical Discourse…

“In linguistically diverse classrooms, unstructured small group and partnering activities continually fail to produce substantive L2 oral language growth. Merely increasing student interaction without explicit, coached language instruction and accountability for application leads to discussions with minimal cognitive or linguistic challenge and negligible academic content.”

Gersten & Baker, 2001

Saunders and Goldenberg, 2010

Preparing ELL’sTo meet both content and language standards

Talk Build on prior knowledge about new ideas

Read Introduce new content

Talk Integrate new content into schema

Write Informally show what you know and ask questions you still have

Talk Refine thinking and deepen learning

“Reading and writing float on a sea of talk.” James Britton

Graphic Organizers…

What do you know about races?

A RaceAmy and Rebecca are running in a road race. The map, drawn to scale, shows the route of the race:

The race consists of four laps of the route and Amy andRebecca run clockwise along the route at a constant speed.

It takes Amy 8 minutes to run a mile.Rebecca takes 12 minutes to run a mile.

Sharing Individual Solutions

P-47

1. Take turns to share your individual work with your partner(s).

2. Share the notes you made on how you might improve your work.

3. Listen carefully to each other, asking questions if you don’t understand.

4. Use the Present an Idea Card and Pose a Question to guide your conversation.

Joint Solution: Making Posters-Talk Through

P-48

1. In your group, agree on the best method for completing the problem.

2. Produce a poster that shows a joint solution to the A Race task, that is better than your individual work.

3. State on your poster any assumptions you have made.

4. Give clear reasons for your choice of method.

Sharing Posters- Talk Through

P-49

1. One person from each group get up and visit a different group.

2. If you are staying with your poster, explain your work to the visitor, giving reasons for your choice of method.

3. If you are the visitor, look carefully at the work, asking clarifying questions to help you to understand the method used.

4. Discuss whether or not the method described on the poster is similar to the visitor’s method.

5. The visitor is to write on a post-it note, suggestions on how the work could be improved.

Sample Responses to Discuss: Sally

P-50

Sample Responses to Discuss

P-51

1. Read each piece of sample student work carefully.

2. Use the E.L. Achieve Discussion Cards (Build on and Idea and Challenge and Idea) to understand what Sally, Diane and George’s mathematical thinking.

3. Take turns explaining your thinking to your partner.

4. Listen carefully and ask clarifying questions. Use the Pose a Question Card to frame your questions.

5. Provide feedback to each of the three responses using the discussion cards.

E.L. Achieve Discussion CardsSupport Your Thinking-Secondary Math

Simple Academic Language•The solution is reasonable because…

•Look at the pattern. I see…

•My method for solving this problem can also work for …

E.L. Achieve Discussion CardsSupport Your Thinking-Secondary Math

Solid Academic LanguageThe solution demonstrates that … because …Based on the data, I see that… My strategy for solving this problem can also be used for ….

E.L. Achieve Discussion CardsSupport Your Thinking-Secondary Math

Sophisticated Academic LanguageAlthough I estimated …., my solution is reasonable because…Based on the rule … I can justify that … because…Because …, I can generalize the that the strategy for solving this problem applies to …

Rich Math Tasks

Rich Math Tasks: Digging for Dinosaurs

Exploration and Extensions…

Having quality Math Task leads to discussion.

How did the use of the E.L. Achieve Cards an other graphic organizers help support critiquing the reasoning of others?

How might you utilize a teaching tool such as the E.L. Achieve Cards and graphic organizers?

Break…

How do we ensure that our student can understand standards?

Smarter Balanced Assessment Consortium Mathematics Content Specifications

Structure of the Smarter Balanced Assessment Consortium Mathematics Content SpecificationsIntroduction and Background

• Claims and Assessment Targets

• Rationale and Evidence for Each Claim

• Cognitive Rigor Matrix / Depth of Knowledge

• General Considerations

4 Claims for Mathematics

“Students can explain and apply mathematical concepts and carry out mathematical procedures with precision and fluency.”

Concepts and Procedures

“Students can frame and solve a range of complex problems in pure and applied mathematics.”

Problem Solving

“Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.”

Communicating Reasoning

“Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.”

Data Analysis and Modeling

(a/o Round 1 – released 8/29/11)

Mathematics Claim #1Concepts and Procedures“This claim addresses procedural skills and the conceptual understanding on which developing skills depend.”

◦ Selected Response◦ Short Constructed Response◦ Highly Scaffolded Tasks◦ Extended Response

Claim #2 Problem Solving

“Assessment items and task focused on this claim include well-posed problems in pure mathematics and problems set in context.”

Single Step/Multistep Problems Balanced types of problems that could include…

◦ Problems in Pure Math◦ Design Problems◦ Planning Problems

Claim #2 Problem SolvingRelevant verbs include:

Understand Solve Apply Describe Illustrate Interpret Analyze

Draw from knowledge and skills within many standards

May draw on knowledge and skills from lower grades

Provide evidence for many assessment targets

Claim #3Communicating Reasoning

“This claim refers to a recurring theme in the CCSSM content and practice standards: the ability to construct and present a clear, logical convincing argument.”

Relevant Verbs Include:

◦ Understand◦ Explain◦ Justify◦ Prove◦ Derive◦ Assess◦ Illustrate◦ Analyze

Claim #4Modeling and Data Analysis “Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decision-making.”

Math Practices in the Claims

Claim 1 – MP 5, 6, 7, 8

Claim 2 – MP 1, 5, 7, 8

Claim 3 – MP 3, 6

Claim 4 – MP 2, 4, 5

SBAC Cognitive Rigor Foundation

The Common Core State Standards require high-level cognitive demand, such as requiring students to demonstrate deeper conceptual understanding through the application of content knowledge and skills to new situations and sustained tasks.

SBAC Cognitive Rigor Foundation

For each Assessment Target in English language arts and mathematics, the depth(s) of knowledge (DOK) that the student needs to bring to the item/task has been identified.

Content Specification Documents

Math Content Specifications, p. 41

Webb’s Depth of Knowledge (DOK)

http://vimeo.com/42788913

In a Nutshell:

Depth of Knowledge measures the degree to which the knowledge elicited from students on an assessment matches the complexity of what students must know and do as part of the standards.

Cognitive Rigor and Depth of Knowledge

The level of complexity of the cognitive demand.

Level 1: Recall and ReproductionRequires eliciting information such as a fact, definition, term,

or a simple procedure, as well as performing a simple algorithm or applying a formula.

Level 2: Basic Skills and ConceptsRequires the engagement of some mental processing beyond

a recall of information. Level 3: Strategic Thinking and ReasoningRequires reasoning, planning, using evidence, and explanations

of thinking. Level 4: Extended ThinkingRequires complex reasoning, planning, developing, and

thinking most likely over an extended period of time.

Hess Cognitive Rigor Matrix

What type of thinking (verbs) is needed to complete a task?

How deeply do you have to understand the content to successfully interact with it?

How complex or abstract is the content?

BLOOM’S WEBB’S

Hess Depth of knowledge…(DOK)

Assessing your understanding of the Mathematical Claims and DOK

Work in Small Groups or Partners• Choose a grade band of Sample Test Items• Decide on a Mathematical Claim for the Sample Item• Decide on the DOK for the Sample Item• Provide evidence for your answers• Check answers with Answer Sheets

Fellows Next Steps… Student Data Survey… Teacher Survey… Turn in Fellows Plans…

Fellows Application… Application Topics for Next Year Meeting Dates