Classroom Discussions to Support Problem Solving Core Mathematics Partnership Building Mathematical Knowledge and High-Leverage Instruction for Student Success Thursday, October 23, 2014 4:30 – 7:30

PRR: Orient Students Thinking to Others Find another person who watched a different video than you watched. Briefly describe the math idea and the talk move in the video that made an impact on student learning. Share one talk move that you have documented on you TM log.

Learning Intentions and Success Criteria Learning Intention We are learning to understand how to classroom discussions assist students at becoming better problem solvers. Success Criteria We will be successful when we can identify how talk moves help students connect multiple solutions to specific mathematical concepts.

MP 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to it’s solution. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. They can understand the approaches of others solving complex problems and identifying correspondences between different approaches. Easier said than done! Pulling out What steps are being taken to make sure all students are working toward this MP?

What is a math problem? Mathematical situations and questions for which there is not an apparent algorithm or immediate solution; these are referred to as problems. (Chapin, O’Conner, & Anderson, p. 152) Adding to our background, read the bottom of page 152. What experiences are the authors suggesting students need in order to truly engage in a math “problem”?

4 Suggestions for Discussions in Problem Solving Use whole-class discussions to understand a problem. Use whole-class discussions to explain one solution method. Use whole-class discussions to extend students’ knowledge of problem-solving strategies. Use whole-class discussions to compare solution methods and generalize.

Providing Equitable Access Novice Problem Solvers Good Problem Solvers Spend little or no time understanding the information provided. Rush to a plan without thinking about the plans effectiveness Spend a lot of time trying to understand a problem and all the relevant relationships. Ask themselves key questions about the given and the unknown information in the problem. Point out the top sentence on page 154. Highlight the sentence that says students don’t understand the mathematical relationships inherent in the words. Talking about the problem helps students recognize the important information and is a form of scaffolding for problem solving.

Introducing The Pencil Problem Read through the Pencil Problem (p. 154) Jot down how you might introduce the problem to students. Read the case on p. 155-157. Consider the following… What were some ways Ms. Dunbar used classroom discussion to help students focus on making sense of the problem?

Suggestion 4: Use Discussion to Compare Solution Methods and Generalize Select one card from the pile. Keep this sentence in mind as you read p. 172 – 175. As a table group… Share your statement and why this statement supports the importance of comparing solution methods through discussions. When you have finished…. What is the role of the teacher and the student in comparing solution methods? 15-20 min. Quick jigsaw Final discussion: What is the role of the teacher and the student in comparing solution methods?

The Newspaper Problem Watch Ms. Fournier use talk moves to discuss different approaches. What is the goal of the lesson? How does she use talk moves to keep the focus on the mathematics? The ratio of boys to girls in a school newspaper club is 1 to 3. There are 5 boys in the newspaper club. How many girls are there? Solve this problem in 2 different ways?

MP 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to it’s solution. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. They can understand the approaches of others solving complex problems and identifying correspondences between different approaches. Easier said than done! What steps are being taken to make sure all students are working toward this MP?

Step 3: Helping Students Deepen Their Own Reasoning Even if students express their thoughts and listen to others’ ideas, the discussion can still fail to be academically productive if it does not include solid sustained reasoning. Some classroom discussions are superficial….therefore, the teacher’s role includes and skillful use of tools that keep the focus on reasoning. Highlight the Why Use it and make a connection to meeting the standards MP and Content.

Learning Intentions and Success Criteria Learning Intention We are learning to understand how to classroom discussions assist students at becoming better problem solvers. Success Criteria We will be successful when we can identify how talk moves help students connect multiple solutions to specific mathematical concepts.

Disclaimer Core Mathematics Partnership Project University of Wisconsin-Milwaukee, 2013-2016   This material was developed for the Core Mathematics Partnership project through the University of Wisconsin-Milwaukee, Center for Mathematics and Science Education Research (CMSER). This material may be used by schools to support learning of teachers and staff provided appropriate attribution and acknowledgement of its source. Other use of this work without prior written permission is prohibited—including reproduction, modification, distribution, or re-publication and use by non-profit organizations and commercial vendors. This project was supported through a grant from the Wisconsin ESEA Title II, Part B, Mathematics and Science Partnerships.