1. Amplifying Student Discourse in Math Class
CALLI High School Math Opt-in
Vinci Daro, Jim Malamut, & Phil Daro

2. Essential Questions
1. What does it mean to cultivate academic student discourse in the classroom? 2. How can we create structures that will build the capacity of teachers to cultivate academic student discourse in the classroom? 3. How do we know quality academic student discourse is being cultivated in the classroom?
Will address the first two in this session and end with a look towards the third

3. What does it mean to cultivate academic student discourse in the classroom?
What are we looking for?
What challenges are we facing?
What steps are we already taking?
Looking for cross-district communication structure here. Give everyone post-its to physically post in their own district 3 columns and then do a carousel?
Possible challenges: range of experience with disciplinary language, range of English language proficiency, distinct challenges in generating oral language in pair/group/class discussion vs written language needed for argument/justification/explanation, etc.
Steps we are already taking: We will revisit the steps that Crista is taking later today

4. What does it mean to cultivate academic student discourse in the classroom?
What are we looking for?
What challenges are we facing?
What steps are we already taking?
Evidence of reasoning/critical thinking
Building on others’ ideas/citing evidence
Discuss, debate, explain, argue, justify, describe, clarify
On-task/engagement
Academic language and vocabulary
Students who don’t like to talk
Off-task talk
Students afraid to take risks
Students are used to more traditional pedagogy/not buying in
Teachers are used to more traditional pedagogy/not buying in
Seating
Partners, small groups, whole class
Coaching/release time
Lesson Study
Professional Development
Sentence Starters
Looking for cross-district communication structure here. Give everyone post-its to physically post in their own district 3 columns and then do a carousel?
Possible challenges: range of experience with disciplinary language, range of English language proficiency, distinct challenges in generating oral language in pair/group/class discussion vs written language needed for argument/justification/explanation, etc.
Steps we are already taking: We will revisit the steps that Crista is taking later today

5. How can we create structures that will build the capacity of teachers to cultivate academic student discourse in the classroom?
Pass out Mathemafish Population Hand-out

6. Mathemafish Population https://www. illustrativemathematics
You are a marine biologist working for the Environmental Protection Agency (EPA). You are concerned that the rare coral mathemafish population is being threatened by an invasive species known as the fluted dropout shark. The fluted dropout shark is known for decimating whole schools of fish. Using a catch-tag-release method, you collected the following population data over the last year.

7. Mathemafish Population https://www. illustrativemathematics
Draft a Summary Report.
What to include in your summary report:
Calculate the average rate of change of the mathemafish population over specific intervals. Indicate how and why you chose the intervals you chose.
When was the population decreasing the fastest?
During what month did you notice the largest effects of the plan?
Explain the overall effects of the plan.
Remember to justify all your conclusions using supporting evidence.
Added:
Remember to use full sentences and use multiple forms of evidence (visuals, diagrams, etc.) to justify your claims.

8. Stronger and Clearer Each Time
Find a partner from a different district. You will each have one minute to explain your summary report so that your partner can clearly understand your ideas.
When you are the listening partner, you can ask clarifying questions, especially related to justifying (Why did you do that? Why did you write it that way?). Press your partner to be as specific and clear about their ideas as possible.
After both partners have had a minute to share, we will signal you to find a new partner. Repeat the process.
Purpose: To provide a structured and interactive opportunity for students to revise and refine both their ideas and their verbal and written output. This routine provides a purpose for student conversation as well as fortifies output. The main idea is to have students think or write individually about a response, use a structured pairing strategy to have multiple opportunities to refine and clarify the response through conversation, and then finally revise their original written response. Throughout this process, students should be pressed for details, and encouraged to press each other for details.

9. Stronger and Clearer Each Time
Revise your summary report using ideas that you heard and new insights that you had from meeting with your partners.
What to include in your summary report:
Calculate the average rate of change of the mathemafish population over specific intervals. Indicate how and why you chose the intervals you chose.
When was the population decreasing the fastest?
During what month did you notice the largest effects of the plan?
Explain the overall effects of the plan.
Remember to justify all your conclusions using supporting evidence.
Remember to use full sentences and use multiple forms of evidence (visuals, diagrams, etc.) to justify your claims.

10. Connect and Compare
Take a look at some of the displayed Summary Reports.
What’s similar and what’s different? What correspondences do you see between different representations?
What mathematics worked well in each Summary Report?
What could be improved to make each Summary Report more complete or easier to understand?
What are the common strategies used to justify conclusions across the Summary Reports?
Purpose: To foster students’ meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, and language. Teachers should model thinking out loud (e.g., exploring why we one might do/say it this way, questioning an idea, wondering how an idea compares or connects to other ideas and/or language), and students should be prompted to reflect and respond. This routine supports meta-cognitive and meta-linguistic awareness, and also supports mathematical conversation.

11. How can we create structures that will build the capacity of teachers to cultivate academic student discourse in the classroom?
What were some specific moves that were used to enhance student discourse in the lesson?
We can do deeper on some of these other Math Language Routines in future opt-in sessions based on your interests.

12. Mathemafish Population https://www. illustrativemathematics
You are a marine biologist. You are concerned that the mathemafish population is being eaten by the dropout shark. The dropout shark is known for decimating whole schools of fish. You measured the following population data over the last year.
school of mathemafish
In general we want to amplify rather than simplify language but, in this case, there was a lot of extra unfriendly linguistic information that could have distracted from goals. This is always a hard call.
Ask someone how to say “sea” in Spanish. A marine biologist is a scientist who studies things that live in the sea. (Also potential to break down bio-logy)
Ask everyone to act out decimating.
Ask someone what schools of fish are. Highlight two meanings of the word “school”.
Ask someone what population is.
dropout shark

13. Mathemafish Population https://www. illustrativemathematics
You made a plan to reduce the dropout shark population and slow the decimation of the mathemafish population. Your boss asks you to summarize the effects of your plan in order to get more funding for your plan.
Changed mentions of collecting, measuring, and observing to all be “measuring” for consistency.
All of the supports in the past 2 slides have been in the context of a whole-class sense-making of the directions. There are also strategies for pushing more responsibility/cultivating more agency in students to become more independent in sense-making.

14. Connect and Compare Lead class discussion of Summary Reports.
Select a progression of Reports roughly from most concrete, easy entry to mathematically closest to target mathematics of the unit, including use of target representations and language.
Students present selected reports in turn. Teacher plays dumb, asks productive questions to elicit more explicit reasoning, labeling etc. ask for connections to previous reports.
Summarize mathematics learned today illustrating by connecting and comparing reports.
Purpose: To foster students’ meta-awareness as they identify, compare, and contrast different mathematical approaches, representations, and language. Teachers should model thinking out loud (e.g., exploring why we one might do/say it this way, questioning an idea, wondering how an idea compares or connects to other ideas and/or language), and students should be prompted to reflect and respond. This routine supports meta-cognitive and meta-linguistic awareness, and also supports mathematical conversation.

15. How can we create structures that will build the capacity of teachers to cultivate academic student discourse in the classroom?
Principles for the Design of Mathematics Curricula: Promoting Language and Content Development
We can do deeper on some of these other Math Language Routines in future opt-in sessions based on your interests.

16. Call to Action:
Select an instructional item or task that your district will be using between now and our next session.
Modify/Enhance/Adapt that task using some strategies/moves we discussed.
Collect samples of student thinking (written samples or recorded video/audio) during the task, and bring to our next session.
Do we want them to do this with their district teams or cross-district?

17. Looking forward: How do we know that quality student discourse is being cultivated in a classroom?
What tools are you already using for observation?
How are you monitoring progress?

18. Looking forward: How do we know that quality academic student discourse is being cultivated in a classroom?
Equitable distribution of peers participating in discourse
Articulation of a chain of reasoning rather than one sentence answers
Listening to, referring to, and building on each other’s ideas
Teacher guides students to do most of the talking rather than telling or doing most of the talking themselves