Classroom Discussions: Math Discourse in Action What does it look and sound like? How do we guide teachers to provide all students with opportunities to engage in the work of each lesson and exhibit mathematical practices? 90 Minute Session

Hero Sandwich A giant hero sandwich has been created that is 30 feet long. It is to be divided into 4 parts so that each section is one foot longer than the previous section. What will be the lengths of the fours pieces? 10 minutes including the discussion CMC Communicator March 2006 Page 23 Participants share their strategies. Drawings first, to the algebra. Share Tape Diagram strategy if no one share it – four separate equal pieces, add one to the first one, two to the second and three to the first… all equal to 30 (Brace) Model the five steps for orchestrating productive discussions here: Anticipant Solutions (Create a chart with the headers of anticipated solutions, participants and order) The headers for this problem might include: Using a diagram, base ten blocks, number line, hundred chart or manipulative Subtract then add using our traditional algorithm Subtract then add using a non-traditional algorithm Other Monitor Participants (Ask and answer questions, but don’t give away the solution or lead to the solution in any way) No telling! 3. Select Participants (Ask participants to share a particular piece of the work that they’ve done) Sequencing the Participants and having them present Making connections between each of the presentations

Hero Sandwich What are some key aspects of how the hero sandwich problem was delivered? What math standards does the hero sandwich problem involve? How do you know? For the first question, the hope is that they identify the 5 steps for orchestrating productive discussions here: Anticipant Solutions (Create a chart with the headers of anticipated solutions, participants and order) Monitor Participants (Ask and answer questions, but don’t give away the solution or lead to the solution in any way) No telling! 3. Select Participants (Ask participants to share a particular piece of the work that they’ve done) Sequencing the Participants and having them present Making connections between each of the presentations For the second question standards may include: 3.OA.8 - Solve two-step word problems using the four operations. Represent these questions with a letter standing for the four operations. Represent these problems using questions with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4.OA.3 – Solve multistep word problems posed with whole numbers and having-number answer using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. 7.EE.4 – Use variables to represent quantities ni a real-word or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. SMP standards 1-6

Hero Sandwich Focus/Unpacked Standards 3.OA.8 - Solve two-step word problems using the four operations. Represent these questions with a letter standing for the four operations. Represent these problems using questions with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 4.OA.3 – Solve multistep word problems posed with whole numbers and having-number answer using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. 7.EE.4 – Use variables to represent quantities in a real-word or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. SMP Standards 1-6

Objectives As a result of the training, administrators will…. Create a plan for observing academic discourse at your school site. Share your plan with your peers and revise as you receive input. Slide 3- 6: 10 minutes

Agenda What is Classroom Discourse? Student Discourse in Action CCSS Evidence Guide for Planning and Practice in a Single Lesson Planning Time and Next Steps Slide 3- 6: 10 minutes

Academic Discourse Slide 3- 6: 10 minutes Start as a small group first and then as a group brainstorm what Academic Discourse Means Chart Ideas

Academic Discourse What does discourse look like? What does discourse sound like? Other Slide 3- 6: 10 minutes In a large group record ideas from the circle map into the categories listed onto the tree map. Add to the map if needed. Participants will continue to add to this as throughout the session. This is their note taking guide so it may look different for each person.

Classroom Discourse Refers to the written and oral ways of representing, thinking, communicating, agreeing, and disagreeing that teachers and students use to engage in those tasks. - National Council of Teachers of Mathematics Slide 7-15: 15 minutes Add to tree map.

Classroom Discourse Also refers to the ways in which teachers orchestrate and promote discourse and to the interplay of intellectual, social, and physical characteristics that shape the ways of knowing and working that are expected in the classroom. - National Council of Teachers of Mathematics Slide 7-15: 15 minutes

Common Core Shifts in Mathematics Focus: Focus strongly where the standards focus Coherence: Think across grades, and link to major topics within grades Rigor: In major topics pursue conceptual understanding, procedural skill and fluency, and application with equal intensity. Slide 7-15: 15 minutes

Standards for Mathematical Practice 1. Make sense of complex problems and persevere in solving them. 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Slide 7-15: 15 minutes (CCSS, 2010) 12

Five Major Reasons that Talk is Critical to Teaching and Learning Talk can reveal understanding and misunderstanding. Talk supports robust learning by boosting memory. Talk supports deeper reasoning. Talk supports language development. Talk supports development of social skills. Slide 7-15: 15 minutes Page xvii from the book Classroom Discussions: Seeing Math Discourse in Action BY

Implementing Discourse Academic discourse is not something that comes easily to most students; rather, it is something that needs to be taught, modeled and recognized by both teachers and students. With strategic instruction around what academic discourse sounds, looks and feels like, it can be a useful tool that enriches all classroom interactions and facilitates deeper learning and retention. Slide 7-15: 15 minutes http://www.edutopia.org/blog/sammamish-6-academic-discourse-PBL-danielle-lynch Edutopia Blog by Danielle Lynch

Defining the Most Important Components of Academic Discourse 1. Set the expectation that students will present problems and explain how they reached their answer. Slide 7-15: 15 minutes These three components are specific to this highschool but I thought they were worth sharing because they mirror what PUSD focus has been the last few years. Edutopia Blog by Danielle Lynch Sammamish High School, WA

Defining the Most Important Components of Academic Discourse 2. Emphasize the importance of using correct vocabulary. For example, math students often confuse an expression and an equation. Making that distinction is important for students. To retain the difference between the two words, they must practice using those words Slide 7-15: 15 minutes -12=-2x+1 3x + 9 Edutopia Blog by Danielle Lynch Sammamish High School, WA

Defining the Most Important Components of Academic Discourse 3. Make writing in math a norm. Students will be expected to write about the process of how they reached an answer. This serves as another way of seeing how students are processing the material and how they are applying vocabulary words. Slide 7-15: 15 minutes Edutopia Blog by Danielle Lynch Sammamish High School, WA

Elementary Only Solve the problem in small groups and be prepared to share A necklace has 2 red beads for every 3 yellow beads. How many yellow beads are there if the necklace has 6 red beads? Elementary Only- Slide 16 10 min Materials to use: Markers, blank paper, red and yellow color counters America Achieves http://commoncore.americaachieves.org/

Secondary Only - Group Work Work with others in your group to determine whether, for each problem, the solution is correct or incorrect. If it is incorrect, identify the error and write the correct solution. Look at the first page only Secondary Only Slide 17 – 10 min Stop at 5 min on video. http://commoncore.americaachieves.org/

Guidelines for Watching Videos Assume that there are many things you don’t know about the students, the classroom, and the shared history of the teacher and students on the video. Assume good intent and expertise on the part of the teacher. Keep focused on your observations about what students are getting out of the talk and interaction. Keep focused on how the classroom discourse is serving the mathematical goals of the lesson. Slides 18 – 20 20 minutes Classroom Discussion: Seeing Math Discourse in Action

Video Reflection As you view the video add to your tree diagram and answer the following questions: How does the teacher establish a classroom culture in which students explain their thinking? How does the teacher orchestrate conversations in which students talk about each other’s thinking? How does the teacher connect students’ informal language to precise mathematical language? Watch the video Slides 18 – 20 20 minutes To find the videos and materials for the lesson go to http://commoncore.americaachieves.org/ and create an account or log on if you have already have one Go to dashboard and search for math The 5th Grade lesson and videos are called “introduction to ratios” The 9th grade lesson and videos are called “Simplifying Rational Expressions”

Your Turn Determine the most important components of academic discourse needed at your site by starring them on your tree map. Describe why your chose these components for your site. Slides 18 – 20 20 minutes

CCSS Evidence Guides For Planning and Practice These tools provide specific guidance for what the CCSS for ELA/Literacy and math looks like in planning and practice. They are designed as developmental tools for teachers and those who support teachers. Use the Evidence Guides for: Teacher self-reflection Peer-to-peer observation and feedback Instructional coaching Slides 21- 25 – The remainder of the time of at least 15 minutes http://www.achievethecore.org/leadership-tools-common-core/instructional-practice/ Achievethecore.org

The work of the lesson focuses on the Common Core State Standards. CCSS Evidence Guides For Planning and Practice Expectation and Evidence The work of the lesson focuses on the Common Core State Standards. Instructional practices maximize opportunities for all students to master the content of the lesson. The teacher provides all students with opportunities to engage. Slides 21- 25 – The remainder of the time of at least 15 minutes Walk through the entire document fast, but focus more on section 3

3. The teacher provides all students with opportunities to engage A. Uses strategies to keep all students persevering with challenging problems. B. Establishes a classroom culture in which students explain their thinking C. Orchestrates conversations in which students talk about each other’s thinking Slides 21- 25 – The remainder of the time of at least 15 minutes

3. The teacher provides all students with opportunities to engage D. Connects students’ informal language to precise mathematical language appropriate to their grade. E. Established a classroom culture in which students choose and use appropriate tools when solving a problem. F. Asks students to explain and justify work and provides feedback that helps students revise initial work. Slides 21- 25 – The remainder of the time of at least 15 minutes

Your Turn Create a plan for observing academic discourse at your school site. Share your plan with your peers and revise as you receive input. Slides 21- 25 – The remainder of the time of at least 15 minutes