1. Classroom Discussions in Math: A Teachers Guide for using talk moves to support the Common Core and more, Third Edition By Chapin, O’Connor, & Anderson 2013

2. Why Use Math Talk in the Classroom? Think about your own students and their learning strengths and difficulties. Which of the five reasons for using classroom talk and discussion seem most relevant to your current teaching? (Think back to the past year) Is there an example from your experience that might support one of the five claims?

3. Video Clip – Is three-fifths less than three- fourths? In this clip, Mrs. Rowan’s students talk about how they know that three-fifths is less than three-fourths. What is the idea that everyone is trying to repeat? What can you tell about student understandings from watching the students try to repeat it? About Mrs. Rowan’s class: 19 ss; 5 boys & 15 girls; school in Cambridge, MA w/student body 33% Caucasian; 35% African American; 18% Hispanic; 11% Asian. 58% - free or reduced lunch. 26% do not have English as their first language.

4. Successful Academic Discussions Talk about successful academic discussions you have conducted in your own class or have seen elsewhere. What were the characteristics of those discussions? What kind of talk moves do you use? (think, pair, share…) What did the students do? Obstacles to Orchestrating Classroom Discussions Discuss

5. Four Steps Toward Productive Classroom Discussions Let’s compare these 4 steps to the characteristics of successful academic discussions that we brainstormed.

6. Digression to edTPA Academic Language The language needed by students to understand and communicate in the academic disciplines. Teachers need to consider language demands as they plan to support student learning of content. The identified language demands should be essential to understanding the central focus and should be embedded in the learning tasks in which students will be engaged. Demands include: functions, vocabulary, syntax, & discourse

7. Function The purpose or reason for using language in a learning task. What will learners do with language in a learning task? What will learners do with language to understand content? Analyze Argue Categorize Compare/contrast Describe Explain Interpret Justify Model Predict Question Retell Summarize

8. Academic Vocabulary Words and phrases with subject-specific meanings that differ from meanings used in everyday life. Subject-specific words defined for use in the discipline.

9. Academic Vocabulary Example Numerator- top number in a fraction, tells number of parts are talking about Denominator- bottom number, tells number of equal parts in the whole Fraction- Names a part of a whole or set Equal- Same amount, size, number, or value Unequal- Different amount, size, number, or value Halves- Two equal parts Thirds – Three equal parts Fourths- Four equal parts Standard Addressed: CCSS.Math.Content.2.G.A.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, and four fourths. Recognize that equal shares of identical wholes need to have the same shape.

10. Discourse Example : “The students will use discourse during the lessons by communicating with the teacher and one another during small groups. As a class, we will analyze and explain each vocabulary word. Then we will use the vocabulary words to describe unit and non-unit fractions. When I ask for an answer like one-half, students will say the numerator is 1 and the denominator is 2. They will be encouraged to use academic vocabulary when describing a fraction. (halves, thirds, fourths, etc.)” How people who are members of a discipline talk and write. How they create and share knowledge.

11. Syntax The set of conventions for organizing symbols, words, and phrases together into structures. Graphs – proper labels and construction Tables Symbols Units Math notation (fraction bar, etc.)

12. Syntax Example The students will be able to decontextualize a word problem using mathematical symbols. (MP2) - This can be applied to any number of mathematical content areas. Transform words to numbers, symbols, and select an appropriate operation. Start with the problem Mary practices the piano 1/2 hour a day for 6 days. How many total hours does she practice Decontextualize with symbols to 1/2 x 6 = 3. They should be able to refer back to the original problem and determine that the product of 3 refers to hours. Standard Addressed: CCSS.Math.Content.5.N F.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

13. Instructional Supports for Academic Language Teachers need to explicitly plan for instructional supports that develop language use for their learners. What opportunities and supports can you provide for students to use the language function, practice and apply academic vocabulary, and integrate discourse and syntax? Consider how these will be differentiated. Examples: graphic organizers, anchor chart, foldable, chart, model, word wall, and strategies such as think, pair, share, etc.

14. Accountable Talk as a Support Use of Academic language or Math Talks - discourse and syntax can be supported with aspects Accountable Talk Learners hold each other accountable for understanding. Learners link or expand their talk to what others say Learners demonstrate skepticism, holding others accountable for thinking. Use question prompts and sentence stems

15. MPs as evidence of and support for academic language How do you see academic demands - function, vocabulary, discourse, and syntax - emphasized with the mathematical practices? MP1 - Make sense of problems and persevere in solving them MP2 - Reason abstractly and quantitatively (contextualize and decontextualize) MP3 - Construct viable arguments and critique the reasoning of others MP4 - Model with mathematics MP5 - Use appropriate tools strategically (use language as they use tools) MP6 - Attend to precision MP7 - Look for and make use of structure MP8 - Look for and express regularity in repeated reasoning

16. Back to… Classroom Discussions in Math Talk Moves that Help Individual students clarify and share their own thoughts. Turn and Talk Revoicing Say More Which have you used? What have your observations been? Benefits? Challenges?

17. Video Clips – Turn and Talk; 6 th grade How do the interactions you see provide opportunities for formative assessment? For language development? For participation by students who may not speak otherwise? Clip 1: How do we know these are greater than a whole? Clip 2: What do six and nine have to do with three?

18. Talk Moves that Help Students Orient to the Thinking of Others Who Can Repeat? Turn and Talk: “Tell us what your partner said.” Which have you used? What have your observations been? Benefits? Challenges?

19. Who Can Repeat? Example – grade 6 What can you observe about the student who said the original utterance and the students who are repeating? How do the interactions you see provide opportunities for formative assessment? Do you see evidence that these interactions could support language development with English language learners? Do you see evidence that students’ learning of academic language may be served by this type of talk move? Do you see evidence that the classroom interactions support more robust understanding on the part of the students? How did you know that seven- eighths was greater than three-fourths?

20. Talk Moves that help students deepen their reasoning Press for Reasoning: “why do you think that?” Who Can Repeat?: “That was important, but sort of complex. Who can put that into their own words?” Turn and Talk: “Does everyone follow that? Let’s do a quick turn and talk about her reasoning.” Which have you used? What have your observations been? Benefits? Challenges?

21. Talk Moves that Help Students Engage with the Reasoning of Others What do You think about that? Do you Agree or Disagree… and Why? Which have you used? What have your observations been? Benefits? Challenges?

22. What do You Think About that Example – grade 6 Does this example show how teachers can broaden participation and engagement with others’ ideas? What are other outcomes of these moves? Can anyone else give an explanation?

23. Putting the Talk Moves Together Grade 6 – that’s the tricky part. What talk moves do you see, and what do you think the teacher is trying to accomplish by using these talk moves in this combination?

24. Classroom Norms These needs to be in place prior to productive classroom discourse to establish: Respectful Discourse Equitable Participation Rights & Obligations - can you think of any that should be added to these lists? How would you introduce the idea of rights and obligations with your students? Review reproducible 2.1B Discuss No Opt Out Technique from Teach Like a Champion 2.0.

25. No Opt Out – 4 Formats 1.You provide the answer; your student repeats the answer. 2.Another student provides the answer; the initial student repeats the answer. 3.You provide a cue; your student uses it to find the answer. 4.Another student provides a cue; the initial student uses it to find the answer.

26. Classroom Norm Video Clips – Grade 3 & 6 What norms did you see evidence for? Was the focus on equitable participation, respectful discourse, or both? Grade 3: Did the teacher run the discussion? How effective do you think it would be in your classroom? What suggestions do you have for adding or changing elements of the discussion? Grade 6: (able to see behavior that reflects knowledge of and adherence to norms already in place) – How could you envision these norms being established? Introducing respectful behaviors Mary, may you please repeat that again?

27. Talking about Computational Procedures Representing Fractions as Percents What strategies might sixth-grade students use to represent the fraction seven-eighths as a percent? What are the purposes and benefits of talking about computational strategies and procedures such as representing a fraction as a percent in math class? Discussion Questions for first and second viewing (on handout)

28. Talking about Solution Methods and problem-solving strategies Placing Fractions on a Number Line Complete the task individually and then discuss it with a partner. Discussion Questions for first and second viewing on handout.

29. Talking about Ratios The Newspaper Problem: students talk about an important generalization about equivalent ratios; 5C Talking about Ratios: using precise language. 7E If I call on you… gives students guidance on what to do if she calls on them to speak and they aren’t ready to respond. 8B