Review of TTLP Insert comments for another assigned group within their Google doc (be certain to include your name) Read the comments made on your TTLP Ask questions of the commenting group if you are uncertain of the meaning Determine any modifications you will make to your TTLP MSC Secondary Math Academy, Year 2

Exploring the Utility of the Protocol: Supporting Students’ Exploration MSC Secondary Math Academy, Year 2

Properties of Parallelograms Activity Draw any large scalene triangle and list as many of its properties as you can. Include relationships between angles, sides, and special segments of the triangle. Visualize how the triangle might be cut to form a parallelogram. Draw a line on the scalene triangle, cut out the shapes, and construct a parallelogram. List as many of the parallelogram's properties as you can. Present your construction to the group and explain your reasoning. Have each partner group draw one triangle so they actually work together. Have select groups share out their thinking. MSC Secondary Math Academy, Year 2

Video of Parallelogram Activity http://www.learner.org/vod/vod_window.html?pid=928 Clip from 3:15 to 10:08 What is the teacher trying to accomplish through her questioning? Show the Annenberg video from the Teaching Math: A Video Library; 9-12 collection. Only show the segment from 3:15 to 10:08. MSC Secondary Math Academy, Year 2

Based on work by Dr. Margaret S. Smith, University of Pittsburgh The Importance of Questions Teachers’ questions are crucial in helping students make connections and learn important mathematics and science concepts. Teachers need to know how students typically think about particular concepts, how to determine what a particular student or group of students thinks about those ideas, and how to help students deepen their understanding. Weiss & Pasley, 2004 Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Based on work by Dr. Margaret S. Smith, University of Pittsburgh The Importance of Questions Teachers provoke students’ reasoning about mathematics through the tasks they provide and the questions they ask (NCTM, 1991). Asking questions that reveal students’ knowledge about mathematics allows teachers to design instruction that responds to and builds on this knowledge (NCTM, 2000). Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Characteristics of Questions that Support Students’ Exploration Assessing Questions Clarify what the student has done and what the student understands about what they have done. Advancing Questions Move students beyond their current thinking by pressing students to extend what they know. The teacher must both unveil students understanding through assessing questions and then use that information to move them toward the mathematical goals through advancing questions. Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Analysis of Questioning Review the questions from the transcript of the Properties of Parallelogram video clip How would you categorize each of the teacher’s questions?

Analysis of Questioning Are there other questions from our facilitation of the task that you would consider advancing? What more could the teacher have asked to advance student thinking?

Based on work by Dr. Margaret S. Smith, University of Pittsburgh Candy Jar Task Solve the task. Share your solution with your group. Based on work by Dr. Margaret S. Smith, University of Pittsburgh

Considering Student Learning What do we want students to learn from engaging in the Candy Jar Task? Chart out their thoughts Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Considering Student Learning Review the clear standards and curriculum framework sections from the SAS portal Identify standards, anchors, and/or competencies that this task addresses Based on work by Dr. Margaret S. Smith, University of Pittsburgh

Standards, Assessment Anchors and Competencies Standard 2.1.7.C Use ratio and proportion to model relationships between quantities Assessment Anchor M7.A.2.2 Represent or solve problems using rates, ratios, proportions and/or percents. Competency – Grade 7 Apply a variety of strategies for proportional reasoning and use them to solve real world problems, including problems dealing with similarity and rates of change. Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Based on work by Dr. Margaret S. Smith, University of Pittsburgh Developing Teachers’ Capacity to Support Students’ Exploration of the Task Imagine that you are walking around the room as your students work on the Candy Jar Task, observing what they are doing. For each piece of student work: Indicate what you think the student understands. What are you unsure about with this student’s understanding? With this activity we are focusing on the second broad category of planning -- Supporting studnets’ expoloration of the Task (backside - top) Here we give teachers a few responses to a task and ask the teachers to develop questions that assess and advance understanding. Pick one of the responses in your packet and think about the questions you might ask. Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Based on work by Dr. Margaret S. Smith, University of Pittsburgh Developing Teachers’ Capacity to Support Students’ Exploration of the Task Consider what you would say to the students in order to assess and advance their thinking. Specifically, for each response indicate: What questions will you ask to assess students’ understanding of key mathematical ideas, problem solving strategies, or the representations? What questions will you ask to advance students’ understanding of the mathematical ideas? With this activity we are focusing on the second broad category of planning -- Supporting students’ exploration of the Task (backside - top) Here we give teachers a few responses to a task and ask the teachers to develop questions that assess and advance understanding. Pick one of the responses in your packet and think about the questions you might ask. Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Based on work by Dr. Margaret S. Smith, University of Pittsburgh Developing Teachers’ Capacity to Support Students’ Exploration of the Task In what ways would assessing and advancing questions help you support students’ engagement with a high-level task? [ question comes in first, then other 2 on click] Need to assess where students are before knowing how to move them toward your goals. Need questions that meet students where they are before being able to move them forward. High-level: asking vs. telling -- keeping the mathematics open for students to explore; ask & walk away Pressing and scaffolding - live, on-the-spot press and scaffolding Based on work by Dr. Margaret S. Smith, University of Pittsburgh MSC Secondary Math Academy, Year 2

Homework Read the Case of Marie Hanson from pages 28 to 39 in the book, Improving Instruction in Rational Numbers and Proportionality: Using Cases to Transform Mathematics Teaching and Learning, Volume 1