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Enhancing Student Mathematical Thinking through Conversation LISET GONZALEZ ACOSTA MANDY BREITENSTEIN

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Conversaciones Academicas

Enhancing Student Mathematical Thinking through Conversation

Liset Gonzalez AcostaMandy Breitenstein

1By the end of today, you will be able to

Define: Academic conversation through oracyApply the placemat of conversation to a classroom activityUse strategies that promote conversations in the classroom

2Talk to a partner:

What do you gain when you have conversations?

Exchange an idea with the person sitting next to you, and be prepared to share out

Generate new ideas and expand on existing ones. Learn new strategies. Make connections. Understand and share new perspectives. Analyze and validate other points of view. Gain new understandings. Validate your thinking. Reformulate ideas.

5 minute discussion3Students need

multiple opportunities every day - to have rich academic conversations.What is a rich conversation?

4"Since the dawn of language, conversations have been powerful teachers. They engage, motivate, and challenge. They help us build ideas, solve problems, and communicate our thoughts. They cause ideas to stick and grow in our minds. They teach us how other people see and do life, and they teach other people how we see and do life. Conversations strengthen our comprehension of new ideas."

Jeff Zwiers and Marie Crawford, 2011

In one study, Arreaga-Mayer and Perdomo-Rivera (1996) found that ELLs spent only 4 percent of the school day engaged in school talk and 2 percent of the school day discussing focla content of the lessons. pg. 8What is an academic conversation? Purposeful and sustained conversations about content.Anchored in grade-level texts and tasks.Students work together to co-construct knowledge and negotiate meaning.Students use talk moves, such as asking for clarification, paraphrasing, and building on or disagreeing with a previous idea.

We use language to represent our thinking and, in turn, the act of producing language, through speaking or writing, itself helps us both process and retain information. Given this, it seems natural we would want classrooms to be filled with talking students since we want them to be thinking about the content we are teaching.

Fisher et al. 2008

5Academic conversations build: Academic vocabulary and grammar. Critical thinking skills Literacy skills. Complex and abstract essential understandings in content areas.An academic classroom environment

Academic vocabulary and grammar. Critical thinking skills such as persuasion, interpretation, consideration of multiple perspectives, evaluation, and application. Literacy skills such as questioning, predicting, connecting to prior knowledge, and summarizing. Complex and abstract essential understandings in content areas.An academic classroom environment brimming with respect for others' ideas, equity of voice, engagement, and mutual support.

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Connecting to Math Practices #3, #67With a partnerDescribe the types of conversations your students have in the classroom. Do they flow naturally? Who facilitates them, the teacher or the students?

85 minutes; 2 minutes to talk, 3 to shareSolve the following problem

4x5 =

Turn and talk Tell your partner your answer.What did you gain from this conversation?

prompt # 19Solve the following problem

4x5 =

Turn and talk Explain how you got your solution(s).

What did you gain from this conversation?

prompt # 210Solve the following problem

4x5 = Turn and talk What are other ways are there to arrive at the solution?

What did you gain from this conversation?

prompt # 311

Talk to your table partnersReflect on the three prompts with 4x5.

What are the implications for the classroom?

123 Levels of Conversations

Tell different answers, accountability, similarities, validation, wondering

Talk To understanding, find evidence, more clarification, what if

Share With new solutions, new strategies, multiple ways to find a solution, consensus, explaining rational, sharing, multiple ways of thinking

13Skills developed when we have conversations

1 Elaborate and Clarify2 Support Ideas with Examples3 Build on and/or Challenge a Partners Ideas4 Paraphrase5 Synthesize Conversation Points

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The placemat can be used to create effective guided questions for learning!15Lets practice!

9 pennies or 3 pennies Which is greater?

Use question and answer frames from the placemat to justify your reasoning and clarify the reasoning of others.

? For practice teachers share the solution and what they would want students to saythen identify the QA stems to support talk?

Go to the placemat and choose sentence starters to facilitate conversation16When Can Conversations Take Place?Whole groupSmall groupPartnersTriadsTable groupsConferring

17Whole group: Spiral skills at the beginning of math timeSmall group: Table groups/small group during centers or strategy groups during math workshop

VIDEO linkhttps://www.youtube.com/watch?v=TlHbsZsXY9M&feature=youtube_gdata

What needs to happen in order for your students to have effective conversations?Modeling and practiceStructures: Body language, active listener, one speaker at a time, etc. (team, partner, whole group)Simple startTeaching the vocabularyReflection time (Sharing, monitoring)Anchor charts to support language and content Models of discoursePositive reinforcement18

Content Language

19What is oracy?An aspect of oral language that includes a more specific subset of skills and strategies within oral language that is related to the literacy objective in academic settings.

Escamilla et al., 2014

20Oracy components DialogueLanguage structures Vocabulary

21 isPlanned by the teachersOpen endedA give an take conversation Students talking to students and teacherProblem solving and reasoning

is notHaphazard conversationUnplanned questions and promptsBased on right or wrong answers Teachers asking all the questions

Dialogue22Language structures Help the students expand and practice academic language.Help students connect oral language to written language.

Vocabulary supports the mathematical language.Vocabulary supports the final product that the students are expected to achieve. Vocabulary needs to be meaningful, comprehensive and contextualized.

Vocabulary23Putting oracy into practice 1. Standard2. Content Objective3. Language Required4. Oracy Objective Language structures Vocabulary Discourse

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Putting oracy into practice MathThere are 12 eggs in the carton. Two kids share the box of eggs.

How many eggs could each child have?How many ways did you find? Explain your strategy.

25Putting oracy into practice

Content ObjectiveStudents will be able to decompose a number into two groups and explain their thinking to others.

Language Required Ask/answer questions, use sequential words, provide examples.

Oracy ObjectiveStudents will be able to ask and answer questions using sequential words to explain their thinking.

Language structures: Each child could have _____ eggs. My strategy was ________. What was your strategy? Vocabulary: Strategy, decompose, explain, carton Discourse26Another problem10 + 2 Is it the only way to make 12?

Explain the strategy you used and support your thinking with examples.Ask your partner questions to clarify.

27Putting oracy into practice

Content Objective

Students will be able to add two numbers within 20, decompose a number into two groups, and explain their thinking to others.

Language Required

Ask/answer questions, use sequential words

Oracy Objective

Students will be able to ask clarifying questions and explain their reasoning with examples.

Language structures: The strategy I used was _______. For example ______. What was your strategy? Can you show me?

Vocabulary: Strategy, decompose, explain, clarifying questions Discourse

28Talk with your table partners What routines do you currently use to facilitate conversations? What works well and what challenges do you face? Based on todays learning, what will you try in your classroom?

29There will be an opportunity in the afternoon breakout to look at daily oral practice routinesLets practice!

KG.6 with a sample problemWrite a question based on an activity from the placemat.Share your activities with the whole group.

Refer to DOK.

How do you insure its a deeper conversation rather than a yes/no question. 30Conclusion Academic conversations enrich students mathematical thinking by :Promoting the use of precise vocabulary and more complex sentence structures. Enhancing students production of language in purposeful ways. Deepening students critical thinking . Developing students oral and writing abilities. Promoting an environment of cooperation, respect, equity of participation and mutual support.

31When we talk to each other, we put our brains together and we become one big smart!- student

32By the end of today, you will be able to

Define: Academic conversation through oracyApply the placemat of conversation to a classroom activityUse strategies that promote conversations in the classroom

What stuck with you today?

33Enhancing Students Mathematical Thinking through ConversationsBibliographyAllington, Richard L. (2006). Comprehension Through Conversations. Portsmouth, NH: Heinemann.Escamilla, K. et al. (2014). Biliteracy from the Start Literacy Squared in Action. New York, New York: Caslon Publishers.OConnell S. & SanGiovanni, J. (2013). Putting the Practice into Action: Inplementing the Common Core Standards for Mathematical Practice k-8. Portsmouth, NH: HeinemannZwiers, J. & Crawford, M. (2011). Academic conversations: Classroom Talk That Fosters Critical Thinking and Content Understandings. Portland, Maine: Stenhouse Publishers.

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Debrief our morning

Wrap up the morning with an oral routine Lines of CommunicationTake your notes on What stuck with you (leave all your things at tables for now)We will put two table groups together, form two lines (by table group) facing each other. This is a SILENT activity lets see how quickly you can do this without conversing. When you are in your lines, You will be given a prompt.When you have shared ONE idea, one person from one group moves to the opposite end of their line. Share with your new partner. Repeat as time permits.

Table 1 go to Table 11Table 2 go to Table 12Table 3 go to Table 13 etc.

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full day.36