study group 6 - high school math (algebra 1 & 2, geometry)

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© 2013 UNIVERSITY OF PITTSBURGH Study Group 6 - High School Math (Algebra 1 & 2, Geometry) Welcome Back! Let’s spend some quality time discussing what we learned from our Bridge to Practice exercises. 1

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Study Group 6 - High School Math (Algebra 1 & 2, Geometry). Welcome Back! Let’s spend some quality time discussing what we learned from our Bridge to Practice exercises. Accountable Talk Features and Indicators. Accountability to the Learning Community - PowerPoint PPT Presentation

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Page 1: Study Group 6 - High School Math (Algebra 1 & 2, Geometry)

1© 2013 UNIVERSITY OF PITTSBURGH

Study Group 6 - High School Math (Algebra 1 & 2, Geometry)

Welcome Back!Let’s spend some quality time discussing what we learned from our Bridge to Practice exercises.

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2© 2013 UNIVERSITY OF PITTSBURGH

Accountability to the Learning Community• Actively participate in classroom talk.• Listen attentively.• Elaborate and build on each others’ ideas.• Work to clarify or expand a proposition.

Accountability to Knowledge• Specific and accurate knowledge• Appropriate evidence for claims and arguments• Commitment to getting it right

Accountability to Rigorous Thinking• Synthesize several sources of information.• Construct explanations and test understanding of concepts.• Formulate conjectures and hypotheses.• Employ generally accepted standards of reasoning.• Challenge the quality of evidence and reasoning.

Accountable Talk Features and Indicators

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© 2013 UNIVERSITY OF PITTSBURGH

Review of the essential understandings for the tasks:For Algebra 1: • The language of change and rate of change (increasing,

decreasing, constant, relative maximum or minimum) can be used to describe how two quantities vary together over a range of possible values

For Algebra 2: • The product of two or more linear functions is a polynomial

function. The resulting function will have the same x-intercepts as the original functions because the original functions are factors of the polynomial.

For Geometry: • Using coordinates of a midsegment of a triangle justifies

that the midsegment is parallel to the side that it does not intersect because the slope of the segment containing the midpoints is the same as the slope of the segment connecting the endpoints of the third side of the triangle.

3

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Let’s Go Over Bridge to Practice #5: Time to Reflect on Our Learning

• Plan a discussion focusing on one or more pieces of your student work that focus on the underlying mathematics from the BTP #4 task/lesson you did.

For Algebra 1, Use No Place Like Home TaskFor Algebra 2, Use Triple Trouble TaskFor Geometry, Use Midsegment Task

• On a piece of paper, scribe several Accountable Talk moves or questions you will use to facilitate the discussion and anticipate student responses (Remember that telling is not allowed. Plan questions that will move students toward the essential understanding)

• Classify the moves according to the Accountable Talk feature they support and why

(Community, Knowledge, and Rigorous Thinking)4

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5© 2013 UNIVERSITY OF PITTSBURGH

Discuss

• What did you notice about planning questions and anticipating student responses?

• What are some things you said and did to hold students accountable to the learning community, knowledge, and rigorous thinking?

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Step Back: Reflecting on the Benefits

What are the benefits of using Accountable Talk features and indicators as a tool for reflecting on the classroom discussion?

For planning?

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© 2013 UNIVERSITY OF PITTSBURGH

Supporting Rigorous Mathematics Teaching and Learning

Strategies for Scaffolding Student Understanding: Academically Productive Talk and the Use of Representations

Tennessee Department of Education

High School Mathematics

Page 8: Study Group 6 - High School Math (Algebra 1 & 2, Geometry)

Rationale

Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask. (NCTM, 1991) Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge. (NCTM, 2000) Questions are one of the only tools teachers have for finding out what students are thinking. (Michaels, 2005)

Today, by analyzing a classroom discussion, teachers will study and reflect on ways in which Accountable Talk® (AT) moves and the use of representations support student learning and help teachers to maintain the cognitive demand of a task.

Accountable talk® is a registered trademark of the University of Pittsburgh.

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TASKS as they appear in curricular/ instructional materials

TASKS as set up by the teachers

TASKS as implemented by students

Student Learning

The Mathematical Tasks Framework

Stein, Smith, Henningsen, & Silver, 2000

Linking to Research/Literature: The QUASAR Project

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Session Goals

Participants will learn about:

• Accountable Talk moves to support the development of community, knowledge, and rigorous thinking;

• Accountable Talk moves that ensure a productive and coherent discussion and consider why moves in this category are critical; and

• representations as a means of scaffolding student learning.

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Overview of Activities

Participants will:

• analyze and discuss Accountable Talk moves;

• engage in and reflect on a lesson in relationship to the CCSS;

• analyze classroom discourse to determine the Accountable Talk moves used by the teacher and the benefit to student learning;

• design and enact a lesson, making use of the Accountable Talk moves; and

• learn and apply a set of scaffolding strategies that make use of the representations.

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Review theAccountable Talk Features

and Indicators

Learn Moves Associated With the Accountable Talk Features

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The Structure and Routines of a Lesson

The Explore Phase/Private Work TimeGenerate Solutions

The Explore Phase/Small Group Problem Solving

1. Generate and Compare Solutions2. Assess and Advance Student Learning

Share, Discuss, and Analyze Phase of the Lesson1. Share and Model2. Compare Solutions3. Focus the Discussion on Key

Mathematical Ideas 4. Engage in a Quick Write

MONITOR: Teacher selects examples for the Share, Discuss,and Analyze Phase based on:• Different solution paths to the same task• Different representations• Errors • Misconceptions

SHARE: Students explain their methods, repeat others’ ideas, put ideas into their own words, add on to ideas and ask for clarification.REPEAT THE CYCLE FOR EACH

SOLUTION PATHCOMPARE: Students discuss similarities and difference between solution paths.FOCUS: Discuss the meaning of mathematical ideas in each representationREFLECT: Engage students in a Quick Write or a discussion of the process.

Set Up the TaskSet Up of the Task

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Accountable Talk Discussion

• Review the Accountable Talk features and indicators.

• Turn and Talk with your partner about what you recall about each of the Accountable Talk features.

- Accountability to the learning community

- Accountability to accurate, relevant knowledge

- Accountability to discipline-specific standards of rigorous thinking

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Accountable Talk Features and Indicators

Accountability to the Learning Community• Active participation in classroom talk.• Listen attentively.• Elaborate and build on each others’ ideas.• Work to clarify or expand a proposition.

Accountability to Knowledge• Specific and accurate knowledge.• Appropriate evidence for claims and arguments.• Commitment to getting it right.

Accountability to Rigorous Thinking• Synthesize several sources of information.• Construct explanations and test understanding of concepts.• Formulate conjectures and hypotheses.• Employ generally accepted standards of reasoning.• Challenge the quality of evidence and reasoning.

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Accountable Talk Moves

Consider:• In what ways are the Accountable Talk moves

different in each of the categories?− Support Accountability to Community− Support Accountability to Knowledge− Support Accountability to Rigorous Thinking

• There is a fourth category called, “To Ensure Purposeful, Coherent, and Productive Group Discussion.” Why do you think we need the set of moves in this category?

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Talk Move Function Example

To Support Accountability to Community

Keeping the Channels Open

Ensure that students can hear each other, and remind them that they must hear what others have said.

Say that again and louder.Can someone repeat what was just said?

Keeping Everyone Together

Ensure that everyone not only heard, but also understood, what a speaker said.

Can someone add on to what was said?Did everyone hear that?

Linking Contributions

Make explicit the relationship between a new contribution and what has gone before.

Does anyone have a similar idea?Do you agree or disagree with what was said?Your idea sounds similar to his idea.

Verifying and Clarifying

Revoice a student’s contribution, thereby helping both speakers and listeners to engage more profitably in the conversation.

So are you saying...?Can you say more? Who understood what was said?

Accountable Talk Moves (continued)

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Talk Move Function Example

To Support Accountability to Knowledge

Pressing for Accuracy

Hold students accountable for the accuracy, credibility, and clarity of their contributions.

Why does that happen?Someone give me the term for that.

Building on Prior Knowledge

Tie a current contribution back to knowledge accumulated by the class at a previous time.

What have we learned in the past that links with this?

To Support Accountability toRigorous Thinking

Pressing for Reasoning

Elicit evidence to establish what contribution a student’s utterance is intended to make within the group’s larger enterprise.

Say why this works.What does this mean?Who can make a claim and then tell us what their claim means?

Expanding Reasoning

Open up extra time and space in the conversation for student reasoning.

Does the idea work if I change the context? Use bigger numbers?

Accountable Talk Moves (continued)

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Accountable Talk Moves

Talk Move Function Example

To Ensure Purposeful, Coherent, and Productive Group Discussion

Marking Direct attention to the value and importance of a student’s contribution.

It is important to say describe to compare the size of the pieces and then to look at how many pieces of that size.

Challenging Redirect a question back to the students or use students’ contributions as a source for further challenge or query.

Let me challenge you: Is that always true?

Revoicing Align a student’s explanation with content or connect two or more contributions with the goal of advancing the discussion of the content.

You said 3; yes, there are three columns and each column is of the whole.

Recapping Make public in a concise, coherent form the group’s achievement at creating a shared understanding of the phenomenon under discussion.

Let me put these ideas all together.What have we discovered?

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Engage In and Reflect On a Lesson

Bike and Truck Task

Algebra I

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21© 2013 UNIVERSITY OF PITTSBURGH

Bike and Truck Task - Algebra I

A bicycle traveling at a steady rate and a truck are moving along a road in the same direction. The graph below shows their positions as a function of time. Let B(t) represent the bicycle’s distance and K(t) represent the truck’s distance.D

ista

nce

from

sta

rt of

road

(in

feet

)

Time (in seconds)

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22© 2013 UNIVERSITY OF PITTSBURGH

Bike and Truck Task - Algebra I

1. Label the graphs appropriately with B(t) and K(t). Explain how you made your decision.

2. Describe the movement of the truck. Explain how you used the values of B(t) and K(t) to make decisions about your description.

3. Which vehicle was first to reach 300 feet from the start of the road? How can you use the domain and/or range to determine which vehicle was the first to reach 300 feet? Explain your reasoning in words.

4. Jack claims that the average rate of change for both the bicycle and the truck was the same in the first 17 seconds of travel. Explain why you agree or disagree with Jack and why.

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The Cognitive Demand of the TaskAlgebra I

Why is this considered to be a cognitively demanding task?

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24© 2013 UNIVERSITY OF PITTSBURGH

The Mathematical Task Analysis Guide- Algebra I

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000) Implementing standards-based mathematics instruction:A casebook for professional development, p. 16. New York: Teachers College Press.

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Analyzing a Lesson: Lesson ContextAlgebra I

The students and the teacher in this school have been working to make sense of the Common Core State Standards for the past two years.

The teacher is working on using the Accountable Talk moves and making sure she targets the mathematics standards in very deliberate ways during the lesson.

Teacher: Shalunda Shackelford Grade Level: Algebra 1School: Tyner Academy School District: Hamilton County School District

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26© 2013 UNIVERSITY OF PITTSBURGH

Instructional Goals - Algebra I

Shalunda’s instructional goals for the lesson are:

• students will use the language of change and rate of change (increasing, decreasing, constant, relative maximum or minimum) to describe how two quantities vary together over a range of possible values; and

• students will describe how one quantity changes with respect to another.

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27© 2013 UNIVERSITY OF PITTSBURGH

Engage In and Reflect On a Lesson

Building a New Playground Task

- Geometry

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Building a New Playground TaskGeometry

The City Planning Commission is considering building a new playground. They would like the playground to be equidistant from the two elementary schools, represented by points A and B in the coordinate grid that is shown.

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Building a New Playground - GeometryPART A 1. Determine at least three possible locations for the park

that are equidistant from points A and B. Explain how you know that all three possible locations are equidistant from the elementary schools.

2. Make a conjecture about the location of all points that are equidistant from A and B. Prove this conjecture.

PART B3. The City Planning Commission is planning to build a third

elementary school located at (8, -6) on the coordinate grid. Determine a location for the park that is equidistant from all three schools. Explain how you know that all three schools are equidistant from the park.

4. Describe a strategy for determining a point equidistant from any three points.

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30© 2013 UNIVERSITY OF PITTSBURGH

The Cognitive Demand of the Task Geometry

Why is this considered to be a cognitively demanding task?

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31© 2013 UNIVERSITY OF PITTSBURGH

The Mathematical Task Analysis Guide - Geometry

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000) Implementing standards-based mathematics instruction: A casebook for professional development, p. 16. New York: Teachers College Press.

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32© 2013 UNIVERSITY OF PITTSBURGH

Analyzing a Lesson: Lesson ContextGeometry

The students and the teacher in this school have been working to make sense of the Common Core State Standards for the past two years.

The teacher is working on using the Accountable Talk moves and making sure she targets the mathematics standards in very deliberate ways during the lesson.

Teacher: Debbee CampbellGrade Level: GeometrySchool: Tyner Academy School District: Hamilton County School District

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33© 2013 UNIVERSITY OF PITTSBURGH

Instructional Goals - Geometry

Debbee’s instructional goals for the lesson are:

• students will determine a set of points that are equidistant from two points, A and B;

• students will recognize and conjecture that all such points fall on the perpendicular bisector of ; and

• students will prove their conjecture.

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Engage In and Reflect On a Lesson

Missing Function Task

Algebra II

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Missing Function Task – Algebra II

If h(x) = f(x) · g(x), what can you determine about g(x) from the given table and graph? Explain your reasoning.

x f(x)-2 0-1 10 21 32 4

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36© 2013 UNIVERSITY OF PITTSBURGH

The Cognitive Demand of the TaskAlgebra II

Why is this considered to be a cognitively demanding task?

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37© 2013 UNIVERSITY OF PITTSBURGH

The Mathematical Task Analysis Guide – Algebra II

Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2000) Implementing standards-based mathematics instruction:

A casebook for professional development, p. 16. New York: Teachers College Press.

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38© 2013 UNIVERSITY OF PITTSBURGH

Analyzing a Lesson: Lesson ContextAlgebra II

The students and the teacher in this school have been working to make sense of the Common Core State Standards for the past two years.

The teacher is working on using the Accountable Talk moves and making sure she targets the mathematics standards in very deliberate ways during the lesson.

Teacher: Jamie BasshamGrade Level: Algebra 2School: Tyner Academy School District: Hamilton County School District

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39© 2013 UNIVERSITY OF PITTSBURGH

Instructional Goals – Algebra II

Jamie’s instructional goals for the lesson are:

• students will multiply two linear functions using their graphs or tables of values and recognize that, given two functions f(x) and g(x) and a specific x-value, x1, the point (x1, f(x1) ∙ g(x1)) will be on the graph of the product f(x) ∙ g(x); and

• students will recognize that the product of two or more linear functions is a polynomial function having the same x-intercepts as the original functions because the original functions are factors of the polynomial.

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Reflection Question(Small Group Discussion)

As you watch the video segment, consider what students are learning about mathematics.

Name the moves used by the teacher and the purpose that the moves served.

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41© 2013 UNIVERSITY OF PITTSBURGH

Reflecting on the Accountable Talk Discussion(Whole Group Discussion)

• Step back from the discussion. What are some patterns that you notice?

• What mathematical ideas does the teacher want students to discover and discuss?

• How does talk scaffold student learning?

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Reflection: The Use of Accountable Talk Moves and Tools to Scaffold Student Learning

What have you learned?

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Bridge to Practice 6: Accountable Talk: Putting it all together!

• Choose an Instructional Task with your PLC that you will all teach.

• Plan the entire lesson together. Anticipate student responses. Write your assessing and advancing questions

• Facilitate the entire lesson with your classes. Put special attention to your (and the student’s) use of the Accountable Talk questions/moves.

• Bring examples of student work and some of the whole class discussion script.