There are multiple parts to each practice. The parts help students develop the habit of mind that is the main practice. Remember that the practices are defined as ways to help students become mathematically proficient. As we look at each practice, think of ways we can help students to take ownership of these practices.
In the first video, students are learning how to read and solve a word problem. The Essential Questions asks, “How does rewriting a word problem help you solve the word problem?”
Observe how the teacher prompts students to make sense of the problem. What questions does she ask? Notice that the students are making sense of the problem and planning a solution pathway. When they begin to work on problems in their groups, they will be able to use these strategies in building their proficiency.
Mathematical Practice #1: Make sense of problems and persevere in solving them.
• Mathematically proficient (MP) students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.
• MP students analyze givens, constraints, relationships, and goals.
• MP students consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.
• MP students 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.
• MP 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.
• MP students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”
• MP students understand the approaches of others to solving complex problems and identify correspondences between different approaches.
As you look at your classroom, you probably see students with varying degrees of expertise in this practice. Our job, as educators, is to help students develop a habit of mind that helps them naturally think before they begin, make sense of what they are doing and persevere in their work.
• Do you give students enough time to ask themselves the meaning of the problem?
• Are students aware that there may be more than one entry point to a solution?
• Do they monitor their own progress?
As students take ownership of their learning and develop expertise using the mathematical practices, the content standards (knowledge, skills and understandings, procedural skills and fluency, application and problem solving) that are applied in the classroom will become externalized, thereby allowing students to grasp and achieve success in mathematics.