Enhancing Student Mathematical Thinking through Conversation LISET GONZALEZ ACOSTA MANDY BREITENSTEIN

By the end of today, you will be able to…  Define: Academic conversation through oracy  Apply the “placemat of conversation” to a classroom activity  Use strategies that promote conversations in the classroom

Talk to a partner:  What do you gain when you have conversations?

Students need … multiple opportunities – every day - to have “rich” academic conversations. What is a ‘rich conversation’?

What 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.

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

Connecting to Math Practices #3, #6

With a partner  Describe the types of conversations your students have in the classroom.  Do they flow naturally?  Who facilitates them, the teacher or the students?

Solve the following problem 4x5 = Turn and talk Tell your partner your answer. What did you gain from this conversation What did you gain from this conversation? prompt # 1

Solve the following problem 4x5 = Turn and talk Explain how you got your solution(s). What did you gain from this conversation What did you gain from this conversation? prompt # 2

Solve 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 What did you gain from this conversation? prompt # 3

Talk to your table partners Reflect on the three prompts with 4x5. What are the implications for the classroom?

3 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

Skills developed when we have conversations 1 Elaborate and Clarify 2 Support Ideas with Examples 3 Build on and/or Challenge a Partner’s Ideas 4 Paraphrase 5 Synthesize Conversation Points

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

Lets 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.

When Can Conversations Take Place?  Whole group  Small group  Partners  Triads  Table groups  Conferring

What needs to happen in order for your students to have effective conversations?  Modeling and practice  Structures: Body language, active listener, one speaker at a time, etc. (team, partner, whole group)  Simple start  Teaching the vocabulary  Reflection time (Sharing, monitoring)  Anchor charts to support language and content  Models of discourse  Positive reinforcement

Content Language

What 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

Oracy components  Dialogue  Language structures  Vocabulary

is…  Planned by the teachers  Open ended  A give an take conversation  Students talking to students and teacher  Problem solving and reasoning is not…  Haphazard conversation  Unplanned questions and prompts  Based on right or wrong answers  Teachers asking all the questions Dialogue

Language 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. Vocabulary

Putting oracy into practice 1. Standard 2. Content Objective 3. Language Required 4. Oracy Objective Language structures Vocabulary Discourse

Putting oracy into practice – Math There 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.

Putting oracy into practice  Content Objective Students 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 Objective Students will be able to ask and answer questions using sequential words to explain their thinking.

Another problem 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.

Putting 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.

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

Let’s practice!  KG.6 with a sample problem  Write a question based on an activity from the placemat.  Share your activities with the whole group.

Conclusion 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.

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

By the end of today, you will be able to…  Define: Academic conversation through oracy  Apply the “placemat of conversation” to a classroom activity  Use strategies that promote conversations in the classroom What ‘stuck’ with you today?

Enhancing Students Mathematical Thinking through Conversations Bibliography Allington, 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. O’Connell S. & SanGiovanni, J. (2013). Putting the Practice into Action: Inplementing the Common Core Standards for Mathematical Practice k-8. Portsmouth, NH: Heinemann Zwiers, J. & Crawford, M. (2011). Academic conversations: Classroom Talk That Fosters Critical Thinking and Content Understandings. Portland, Maine: Stenhouse Publishers.

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