Session 2: Strengthening Collaborative Practices

Session 2: Strengthening Collaborative Practices
Welcome to Session 2: Strengthening Collaborative Practices Please sign in. Add your ideas to handout 2.1: Collaboration Warm-Up. It’s in Section 2 of your binder. © 2010, EDC 1

Topic #1: Introduction In this section, we will:
Follow-up on Session 1 Go over today’s agenda © 2010, EDC

Students w/Disabilities and Math Math Accessibility Framework
Looking Back: Session 1 Topics Students w/Disabilities and Math Math Accessibility Framework Looking at Student Work Accessibility Strategies Concrete, Representational, Abstract Approach (CRA) Figure 0 Strategy Your Feedback Positives Suggestions Skipped Read [Slide Guide] Elaborated Confused Added Example Connections [ District Context Participants’ prior comments Personal Story] © 2010, EDC 3

Ground Rules Reminder “Parking Lot” Contribute your ideas
Respect others’ opinions Assume positive intentions Watch your own air time No side conversations Start and end on time Turn off cell phone ringers No texting or ing “Parking Lot” © 2010, EDC

Session 2 Agenda Introduction Assignment Discussions
Access to Patterns, Tables & Rules Collaboration A Co-taught Math Lesson Collaborative Teaching Models Complexities of Collaboration Strengthening Communication Collaborative Planning Wrap-Up Goals Leave with ideas to: make math more accessible to students strengthen collaboration with colleagues  © 2010, EDC 5

Topic #2: Discuss Assignments
In this section, we will: Discuss the article in small groups Talk with partners about our focal students Skipped Read [Slide Guide] Elaborated Confused Added Example Connections [ District Context Participants’ prior comments Personal Story] © 2010, EDC

Completed Reading Reflection
Discuss Article Take out your Reading Reflection for the article, Math Learning Disabilities. Discuss your topic and summary for the article. Answer the questions on pg. 2.2 for your topic. What would you add to the article Summary? Prepare to share with the whole group/ Time: 20 minutes Skipped Read [Slide Guide] Elaborated Confused Added Example Connections [ District Context Participants’ prior comments Personal Story] Completed Reading Reflection 2.2 © 2010, EDC

Whole Group Share-Out Each group shares:
What are two points that stood out in your small group’s discussion of the article? How did your group want to add to or change the summary? Skipped Read [Slide Guide] Elaborated Confused Added Example Connections [ District Context Participants’ prior comments Personal Story] © 2010, EDC

Pair Share on Focal Students
Talk with someone you do not work with. Take turns presenting: 2 strengths and 2 difficulties that your focal student has in math 1 thing you learned from talking with a colleague about your focal student 1 question you have about the student as a math learner Time: 5 minutes each Completed Focal Student Planner © 2010, EDC

Choose 2 strategies that you would like to try with this student
Math Strategies Goal: Use what you have learned about your focal student to identify strategies that build on the student’s strengths and help address difficulties Directions Use one or more resources: Strategy Cards Reference Sheet B & C Accessibility Strategies for Math 10 minutes with slide 10 and 11. Do we need to use this whole group share out? Choose 2 strategies that you would like to try with this student Share at your table: What did you choose? Why? How do you or would you use the strategies? © 2010, EDC

Whole Group Share-Out What’s one thing that you learned about your focal student from completing and discussing the assignment? What’s one strategy that you would like to try with your focal student? Why? If we have time… do the whole group share out…. © 2010, EDC

Topic #3: Access to Patterns, Tables & Rules
In this section, we will Apply the Math Accessibility Framework to a math problem © 2010, EDC 12 12

Consider the Math 1. Work on the problem yourself.
2. Discuss with a partner: How did you interpret the pattern? How did you come up with a rule? Time: 4 min to work on problem min to discuss Try to identify people as we go around during the task… Julia, Jim, & Sharon (Find People ) 2.3 Letter M Problem 2.3A Answers © 2010, EDC

Whole Group Discussion
What approaches did you use? Did you…. Make drawings? Make a table? Use manipulatives? Write numbers under each part of the pattern? Use Figure 0 (from Session 1)? Other? © 2010, EDC 14

Share Approaches Two volunteers present different approaches to the whole group: How did you interpret the pattern? How did you come up with a rule for finding any Step #? Chart paper, white boards, and document camera © 2010, EDC

Identify the Key Math Goals
Write the goals on the top of 2.4. What are the trajectories… we will bring this to next 3 sessions. We need to consider the rigor of the math. Ref. A on Yellow 2.4 © 2010, EDC

Analyze Problem from an Accessibility Lens
What are the task demands for students? Conceptual? Visual/Spatial? Language? Other? What are the potential difficulties for your focal students? Ref. A on Yellow © 2010, EDC

Directions for Examining the Work
Work individually to: Look at the work sample on 2.5. Fill out the first 2 columns on 2.4. In small groups, discuss: What strengths did you notice? What difficulties did you notice? Make sure to give evidence from the work. Time: ~5 min to work individually ~5 min to discuss Sharon, Strengths and difficulties … Evidence from the work. NOTE: Participant print error See “25” in student work on next slide 2.4& 2.5 © 2010, EDC 18 18

Discuss: - Observations of Strengths. - Observations of Difficulties
Discuss: - Observations of Strengths? - Observations of Difficulties? Give evidence from the work. Strengths, difficulties, next steps… Importantly what do we want to learn next. We must know the mathematical trajectories. What question would we like to ask students or provide scaffolding. We are going to use an example of how we might scaffold this task for many students. We will go deeper into this in the next sessions… We have to give you time to unpack this process. © 2010, EDC

Brainstorm Questions & Strategies
What are you wondering about this students’ understanding? What diagnostic questions would you ask this student to find out more about his/her math understanding? What accessibility strategies do you think would be helpful? First, brainstorm ideas with a partner. Then, we’ll discuss ideas as a group. 2.5, Bottom Ref. C on Blue © 2010, EDC

Sample Strategy: Expanded Table
Common difficulty: moving from the recursive (add 4 to the previous) to the functional (4n + 2) A recursive rule is limited because it depends on knowing the prior step. A functional rule allows you to find the number of toothpicks for any step # without having to know the prior step. The Expanded Table strategy can help students move from recursive to functional rules. © 2010, EDC

Demo Let’s analyze the pattern by using the Figure 0 strategy from Session 1. Step 0 shows what stays the same – 2 toothpicks. We’ve circled what is changing. The pattern grows by adding groups of 4 toothpicks. Step Step Step Step 3 2.6 © 2010, EDC

3. Fill out the second column on 2.6.
Demo 2. To help students move from the pattern to a rule, we’re going to expand the T-table format by adding more columns. 3. Fill out the second column on 2.6. Step Number Expanded format How many toothpicks do you add? 2 1 2 + 4 3 4 5 © 2010, EDC 2.6

Demo 4. Let’s rewrite the repeated addition in column 2 by using multiplication. Fill out the third column on 2.6. Step Number Expanded format How many toothpicks do you add? Written using multiplication 2 2 + (4 × 0) 1 2 + 4 2 + (4 × 1) 2 + (4 × 2) 3 4 5 © 2010, EDC

Written using multiplication
Demo 5. What is the relationship between the Step numbers and the expressions in the 3rd column? Step Number Expanded format How many toothpicks do you add? Written using multiplication 2 2 + (4 × 0) 1 2 + 4 2 + (4 × 1) 2 + (4 × 2) 3 2 + (4 × 3) 4 2 + (4 × 4) 5 2 + (4 × 5) © 2010, EDC

Demo 6. The number that you multiply by 4 is the same as the Step number. Step Number Expanded format How many toothpicks do you add? Written using multiplication 2 2 + (4 × 0) 1 2 + 4 2 + (4 × 1) 2 + (4 × 2) 3 2 + (4 × 3) 4 2 + (4 × 4) 5 2 + (4 × 5) © 2010, EDC

Demo 2 + (4x n) or 2 + 4n or 4n + 2 n 2 + 4n or 4n + 2
7. Continue the pattern in the 3rd column to find the expression: 2 + (4x n) or 2 + 4n or 4n + 2 Step Number Expanded format How many toothpicks do you add? Written using multiplication Number of toothpicks 2 2 + (4 × 0) 1 2 + 4 2 + (4 × 1) 6 2 + (4 × 2) 10 3 2 + (4 × 3) 14 4 2 + (4 × 4) 18 5 2 + (4 × 5) 22 n 2 + (4 ×n) 2 + 4n or 4n + 2 © 2010, EDC

Demo 8. Let’s go back to connect the symbolic expression with the original visual pattern. Step 1 Step Step Step n 2 plus 2 plus plus plus 1 group of 4 2 groups of groups of n groups of 4 2 + 4(1) 2 + 4(2) (3) n © 2010, EDC

Try the Expanded Table Strategy
Try the strategy with the Toothpick Houses Pattern. Choose either handout: 2.7A: Open version or 2.7B: Scaffolded version guides you through the process Time: minutes 2.7A: Open Version 2.7B: Scaffolded 2.7C: Answers 29 © 2010, EDC

Discuss the Expanded Table Strategy
The goal of the Expanded Table Strategy is to help those students who are having difficulty moving from recursive to functional rules. Discuss: What was your experience like trying the Expanded Table Strategy? What are your suggestions for using this strategy with students? 30 © 2010, EDC

Topic #4: Collaboration
In this section, we will: Discuss key elements of collaboration and different ways of collaborating © 2010, EDC

We share a common Goal: To make math instruction more accessible for a
IEP 504 Range of Learners to improve student learning Collaboration is key to reaching this goal! © 2010, EDC 32

Discuss Collaboration
Turn and Talk with a Partner What’s the difference between collaboration and cooperation? Whole Group Discussion What key elements are needed to foster collaboration? Common Goals 2.1: Warm-Up © 2010, EDC

Myths about Collaboration
Everyone is collaborating Collaboration comes naturally. Collaboration is about feeling good and liking others. Source: Friend, 2000 © 2010, EDC 34

Different Ways of Collaborating
Co-teach Co-plan Consult Share practices and reflect Coordinate services There is not one best way to collaborate. Different ways fit different situations. For each situation, there are ways to strengthen collaboration. © 2010, EDC 35

What is Co-teaching? Co-teaching is an approach in which general and special educators share responsibility for planning, instruction and evaluation of all students in the class. What is your situation? Co-teaching Working together a few times a week Teaching alone Other Definition Source: Cook, L. & Friend, M. © 2010, EDC 36 36

Different Models Fit Different Situations
We will look at six models for collaborative teaching Some models work well in a variety of situations. Some models are better suited to co-teaching partners. As we go through this section: Look for ideas to apply in your situation (current or future). Share your experiences and suggestions. © 2010, EDC

Two Models Where One Teacher Leads
One Teach, One Support One teacher leads the lesson while the other teacher takes on a supportive role, such as clarifying directions or working one-on-one One Teach, One Observe One teacher leads while the other observes to gather information on students’ math understandings Teachers need to plan in advance on the focus of the observations Poster: What are you learning about today? Why is that important? support/observer What do you do? Ask Questions/write notes/place welcoming… 2.8 © 2010, EDC 38

Station Teaching Teachers work with small groups of students at different stations Students rotate from station to station Example of Using Stations to Review Math Teacher’s station: One way of solving proportions Special educator’s station: A different way of solving proportions Independent station: Students solve practice problems using the method of their choice What are your suggestions for using stations? 2.8 © 2010, EDC 39

Models with Two Groups of Students
Alternative Teaching Teachers divide class into two groups (one larger and one smaller) and provide different kinds of instruction For example, smaller group gets more support while larger group does a review Parallel Teaching Teachers divide class in half and teach the same content For both models, it is important to: Vary the composition of the groups and who teaches them Plan together to ensure that instruction is coordinated 2.8 © 2010, EDC 40

Team Teaching Teachers share the instruction and leadership.
I love it when I explain something and the special educator jumps in and says it in a different way. We have to reach 30 students at a time. I’m saying it one way, but how many of these students am I reaching? Yet when somebody else jumps in and says it a different way, we’re reaching that many more. Math Teacher © 2010, EDC 41

Collaboration Evolves Over Time
It takes time to build trust and develop a strong working relationship. One-teach/one-support is a good starting place. Caution: Pairs may get stuck in this model. A variety of models can be used in one lesson. What are your suggestions? © 2010, EDC 42

Ideas to Take Away 1. Write down ideas that you would like to try.
Collaborative teaching models and/or Accessibility strategies 2. Talk with a colleague that you work with. Time: 5 minutes Ref. E on Green © 2010, EDC

Topic #5: A Co-taught Math Lesson
In this section, we will: Part 1: Solve and analyze a math problem. Part 2: Watch and discuss a video of a lesson. Part 3: Discuss sample strategies. Julia © 2010, EDC 44

Part 1: Get to Know the Math Lesson
The lesson uses balance puzzles A visual model for representing an equivalence relationship. Shows how the two sides of an equation are balanced. Helps to address misconceptions about equal sign. How are balance puzzles taught? Students first use manipulatives -- bags & blocks or cups & chips. Then, students make drawings of balance puzzles and connect the drawings with equations. © 2010, EDC

Intro to Balance Puzzles
1. How many blocks are in each bag? Answer © 2010, EDC

Intro to Balance Puzzles
1. How many blocks are in each bag? Answer: 2 blocks in each bag Next, we will use balance puzzles to represent situations and solve equations. © 2010, EDC

Balance Puzzle Demo Problem
Tom and Cindy started out with an equal number of candies. They filled bags, putting the same amount in each bag. Tom filled 2 bags and has 1 extra candy. Cindy filled 1 bag and has 3 extra candies. How many candies are in each bag? We will use a pan balance representation. Bags represent the unknown number of candies in each bag Blocks represent individual units/candy I have used cups and counters instead of bags and candy. © 2010, EDC

Demo Tom and Cindy started out with an equal number of candies. They filled bags, putting the same amount in each bag. Tom filled 2 bags and has 1 extra candy. Cindy filled 1 bag and has 3 extra candies. How many candies are in each bag? Let x be the number of candies in a bag: Tom Cindy 2 bags + 1 extra candy bag + 3 extra candies 2x + 1 x + 3 The goal is to solve for x by getting bags on one side and blocks on the other side. © 2010, EDC

Demo Check to see if the answer makes sense.
Put 2 blocks in each bag to see if the two sides balance. Substitute 2 for x in the equation. 5 5 2 x + 1 = x + 3 2(2) +1= 2 + 3 5 = 5 2.9 © 2010, EDC

Solve and Discuss Math Problem
1. Solve the problem in two ways: Balance puzzle A different way 2. Use color-coding to show the connections between the two methods and the word problem. 3. Discuss with a partner: How did you get started? What was your experience like using the balance puzzle strategy? What other approach did you use? Time: minutes 2.10 2.10A © 2010, EDC

Share Approaches Two volunteers each present one approach
Balance Puzzle strategy Another strategy How did you get started? How did you figure out the number of candies in each bag? © 2010, EDC

What are the Key Math Goals?
Add to the list. Draw a balance puzzle to represent a word problem © 2010, EDC

Analyze the Math Problem
What are the demands on students? Conceptual Language Visual-Spatial What are the potential difficulties for your focal students? Ref. A on Yellow © 2010, EDC

Part 2: Video of a Co-taught Math Lesson
Class 7th grade inclusion class Teachers Math Teacher and Special Educator have been working together for 3 years. Special Educator is in the class every day. They do not have scheduled co-planning time. They have a positive and respectful co-teaching relationship. © 2010, EDC 59 59

Video Reminder This video is an example of what two teachers did on one day. It is presented to show an example to spark ideas and discussion. Our task is to observe the teachers’ practices without judging. Thank you Amy and Lisa!!! © 2010, EDC

Video Focus Questions As you watch, focus on:
A. What instructional roles does each teacher play? B. What strategies do the teachers use to make the mathematics accessible? Write notes on 2.11. “Co-taught Lesson” Sequence Meet the teachers Warm-Up Main Investigation Interview 2.11 © 2010, EDC

After the Video: Summary of Roles
While one teacher…. the other teacher … Presents to whole class Circulates and refocuses students Hands out materials Asks questions and clarifies directions Works individually with students Asks questions to student presenters Asks questions to student presenters © 2010, EDC

Part 3: Strategies Now, we will switch our focus from co-teaching roles to accessibility strategies. Discuss: What strategies did you observe the teachers using to make the math accessible to a range of learners? © 2010, EDC

Some Strategies in Video
Overhead/Large visuals Warm-up Reference Sheet Graphic Organizer: link sheet with problem divided into 4 parts Reformatted problem with space for writing variables above words Questioning techniques Highlighting © 2010, EDC

More Strategies for Geri’s Candy Problem
Goal Provide examples of ways to make the problem more accessible Your Task Look over the strategies on 2.12. Choose one strategy that you think would be particularly helpful for your focal student. Talk with a partner: What did you choose? Why? Time: 5 min 2.12 © 2010, EDC

Topic #6: Complexities of Collaboration
In this section, we will: Discuss scenarios Brainstorm ways to strengthen collaboration © 2010, EDC 66

The biggest problem I’ve faced is when two people have two different ideas of what should be going on inside the classroom and when there’s no communication, really, between the special education teacher and the math teacher. Special Educator © 2010, EDC 67

Scenario Activity Goals Start a discussion about collaboration issues
Brainstorm ways to address common challenges Directions Read the scenarios on 2.13. Choose one scenario that you would like to discuss. 3. We will move into new groups for the discussions. 2.13 Scenarios © 2010, EDC 68

Discussions about Scenarios
Discussion Questions What are the issues for each teacher? What suggestions do you have? How would you begin the conversation? Get Organized Move into new groups to talk about specific scenarios Choose a reporter who will share 2 ideas with the whole group. Time: minutes Note: If you want to share your experiences with similar situations, please keep it general and do not use names. © 2010, EDC

Whole Group Share-Out A reporter from each group shares:
What were the collaboration issues in your scenario? What are one or two suggestions that your group came up with? © 2010, EDC

Topic #7: Strengthening Communication
In this section, we will Discuss ways to strengthen communication between math teachers and special educators © 2008, EDC © 2010, EDC 71

Collaboration: Key Elements
Communication Respect Common goals Clear roles and responsibilities Problem solving skills Flexibility © 2010, EDC © 2008, EDC

Communications Carousel
Goals To generate specific topics that need to be communicated between math teachers and special educators To brainstorm ways to strengthen communication Directions Divide into small groups. Each small group will start at a different chart paper. Add your ideas to chart paper. (If the idea is already on the chart,  it.) You will get a signal to move to the next chart paper. We’ll go clockwise. Time: 2-3 minutes per chart paper © 2010, EDC © 2008, EDC

After the Carousel: Gallery Walk
Go around the room to look at the chart papers. Place stickers on the topics that you would most like to spend more time talking about with colleagues. On Reference Sheet E, write down 1-2 follow-up actions that you will take. List topics you would like to discuss. Highlight ideas you would like to keep in mind. Time: ~ 7 minutes Ref. E © 2010, EDC © 2008, EDC

Follow-Up Actions Talk with a colleague who you work with.
What’s one action you will take to strengthen communication and/or collaboration with colleagues (across the disciplines of math and special education)? Time: 5 minutes Ref. E © 2010, EDC

Topic #8: Collaborative Planning
In this section, we will: Collaborate with colleagues to plan strategies for making math lessons more accessible to our focal students © 2010, EDC

Collaborative Planning Activity
Goals Collaborate in planning strategies for a math lesson and focal students Apply ideas from today’s session Leave with strategies that you can use with students Collaborative planning can be helpful whether or not you are co-teaching. Focus on common lessons, assessments, and students. © 2010, EDC

Planning Focus and Tools
A. Work with co-teaching partners Plan a strategy for your focal students and how you will use a co-teaching model. Fill out the or B. Work with grade-level colleagues Plan a strategy to make a lesson more accessible to your focal students. Time: minutes Large White Co-teaching Planner Green Accessible Lesson Planner © 2010, EDC

Get Organized for Planning
Divide into Pairs or Groups Co-teaching partners (who are both in the course) work together Everyone else works in small groups with grade-level colleagues Note: If your group has 4 or more people, have a volunteer facilitator to keep the planning process on track © 2010, EDC

After Planning: Share Ideas
What’s one strategy or co-teaching model that you planned? Why? What’s one thing that stood out for you in the collaborative planning process? © 2010, EDC

Session 2 Summary Topics Access to Patterns, Tables, and Rules
Collaboration Co-teaching Models A Co-taught Lesson Complexities of Collaboration Strengthening Communication Collaborative Planning Accessibility Principle Collaborate with colleagues to share expertise, plan, problem solve, and reflect on experiences © 2010, EDC

Session 2 Summary: Math Standards
Expressions & Equations Apply and extend previous understandings of arithmetic to algebraic expressions Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Practice Standards 2. Reason abstractly and quantitatively. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Source: Common Core State Standards

Assignments #1: Reading #2: Strategy #3: Assessment
Read the article, Thinking Through a Lesson: Successfully Implementing High Level Tasks. Focus on pg and consider pert 2 as it relates to your focal student. #2: Strategy Complete the plans you started today Implement with students Fill out a Strategy Reflection Form Collect a work sample from your focal student #3: Assessment Due Date: Session 3 2.16 © 2010, EDC © 2008, EDC 85

Looking Ahead Session 3 focuses on:
Addressing language difficulties in mathematics Making classroom math assessments more accessible What to bring: A math test from your curriculum that you would like to make more accessible. Talk with co-teaching partner and/or grade-level colleagues to choose a common test to bring. Last Steps Fill out Feedback Form Hand in assignments © 2010, EDC

This session was brought to you by the letter C.
Collaboration Communication Collective Wisdom Connections Coordination Constructive Feedback Collegiality Common Goals © 2010, EDC

Credits The course, Enhancing Instructional Practices in Mathematics was developed at Education Development Center, Inc (EDC). Website: The project was funded by the National Science Foundation, grant # ESI Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. This course is distributed through Michigan’s Integrated Mathematics Initiative (Mi)2 a Mandated Activities Project (MAP) funded under the Individuals with Disabilities Education Act (IDEA) through the Michigan Department of Education, Office of Special Education. (MI)2 assists the state in creating a cohesive and collaborative system of support and professional development among existing mathematics resources. The initiative identifies and promotes factors that facilitate improved outcomes for all students in mathematics. © 2010, EDC

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