This month, I’m sharing ideas for teaching with the Common Core mathematical practice standards. And, for my Texas readers, I will be correlating them to the mathematical process standards of the TEKS. The mathematical practice standards are included in each grade level’s Common Core State Standards. They include important processes, practices, and proficiences that are important for the development of every successful mathematician. These standards were derived from the work of The National Council of Teachers of Mathematics, NCTM, and The National Research Council.
For today’s Transformation Tuesday, I want to focus on Mathematical Practice Standard 1: Make Sense of Problems and Persevere in Solving Them. An excerpt for this standard, from http://www.corestandards.org/Math, is provided below.
CCSS.MATH.PRACTICE.MP1: Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”
This standard correlates with Texas Mathematical Process Standard TEKS 1B which states, “use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.” (Source: Texas Education Agency)
The component of the mathematical practice standard that really jumps out at me is the part that states, “students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.” This tells us that students must be able to restate the question and decide how and where to get started. No brainer right? But, what about when our students can’t restate the problem or they don’t know how to get started? How do we help them? It’s all about questioning!
Using purposeful questions in the classroom is essential to helping students become “mathematically proficient” problem solvers. NCTM (2014) suggests that teachers use “purposeful questions to assess and advance students’ reasoning and sense making.” In addition, George Polya (1945), who is attributed with establishing the basic 4-step problem solving model used by many educators and resource creators, states that there are two goals of questioning during problem solving:
1. to help students solve a problem.
2. to help students develop the ability to solve future problems on their own.
So what? What does that mean for us?
While asking good questions seems easy enough, asking purposeful questions takes both forethought and planning. In order to meet George Polya’s goals, we must strike a balance between asking questions that give too much away and asking questions that do not give enough support to enable the student to move forward in his/her thinking.
Thinking about and planning the questions to ask students while problem solving will help support their success as mathematicians. When designing instructional experiences with problem solving, consider how your students will interpret the problem and where they might want to begin. This will help you determine what questions you should be prepared to ask when students are stuck and need help moving forward.
To support your work in this area, I’ve created a “Questions to Stimulate Student Thinking Flipchart.” This resource tool can be placed in a lesson planner so that it is easy to access when planning. The flipchart is separated into six different processes: Understand the Problem, Choose a Strategy, Develop a Process, Represent the Solution, Evaluate & Extend, and Reflect & Connect. Each layer includes questions to help students advance their thinking at various points in the problem solving process. Once assembled, the flipchart becomes a portable tool that can be referred to and utilized during instruction to help students advance their thinking and move forward in the problem solving process.
Freebie Alert! Grab your free copy of my “Questions to Stimulate Student Thinking Flipchart” here!
- NCTM (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: National Council of Teachers of Mathematics.
- Polya, George (1945). How to solve it. Princeton, NJ: Princeton University Press