Classroom Sneak Peek # 1 - Make Sense of Problems and Persevere in Solving Them

The common core standards are here and it's time we start reflecting about the necessary changes that will be needed to meet these standards in the classroom.  This blog is designed to first look at the mathematical practice and then to put into what the classroom should look like, feel like, and sound like.  Teacher questioning will be critical to the success of the CCSS vision, so we will also explore this.  If you are interested in this process to facilitate this discussion with your staff, read What Do the Common Core Standards Look Like in the Classroom.

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 its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. 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. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

So what does this really look like?  The chart below is a work in progress.  I've designed this with the expertise of many classroom teachers.  If you have other ideas, please don't hesitate to email me and share your expertise as well. 

Mathematical Practice: #1 Make sense of problems and persevere in solving them.

Student Actions:	Teacher Actions:	Open-Ended Questions:
Feel like a detective or mathematician, look for clues and evidence on how to solve the problem Believe they are a mathematician and can solve the problem and understand that mistakes are the way we learn. Talk to other students about how they might solve the problem. (Partner, small group, or whole group discussion) Think about and tries several ways to solve the problem Use a variety of mathematical tools to solve the problem Reflect about what the problem is asking Write about how they solved the problem Listen to other students and may change their own strategy based upon the thinking of others Understand other student strategies Share their thinking and solution.	Create a classroom climate where struggle is expected and that making mistakes are OK. Provide students with word problems and real-world scenarios and encourage a variety of tools and strategies. Discuss appropriate behavior for respectful dialogue. Give students individual think time before discussing with a partner. Set a timer for three minutes for individual think time. Frame math challenges that are clear and explicit. Check in periodically to check student clarity and thought process. If students are stuck, scaffold the problem to a simpler problem. Ask students, how the problems are similar and how they are different. Set up structures requiring students to connect different forms of the problem (equation to graph, table, etc.) Students share out different strategies for solving the problem.	What do you know about the problem? What is being asked? What problems have we solved before like this problem? How might talking to ______ help you? What might be another way to solve this problem? How is ____ strategy like yours? How is it different? How might a number line help you? How is your graph connected to your equation? How does your equation match the problem? How might acting out the story help you solve the problem? What made you decide to use that strategy? What made you choose that operation?

Possible Activities:

1.     Be a math detective - Discuss the job of detectives, " To look for clues/evidence and solve mysteries." 2.     Provide story problems and allow students to struggle with solutions. 3.     Ask students to show three ways to solve the problem (Give individual think time prior to group) 4.     Look at different student work (remove names and replace with Student 1 and Student 2) Ask, "what is this mathematician thinking or trying to figure out." 5.     Provide real world, high quality tasks. 6.     Keep in mind the level of cognitive demand from this practice:      - Explain, analyze, make conjectures, monitor, evaluate, check their answers.

"Struggling in mathematics is not the enemy any more than sweating is in basketball, it's a clear sign you are in the game."  - Kim Sutton