K-12 Standards for Mathematical Practices

One of the major differences between the previous curriculum frameworks and new Massachusetts Mathematics Curriculum Frameworks is the incorporation of the 8 Mathematical Practices.  These practices are habits of mind that all successful mathematical thinkers use to solve problems. 

Bill Calum, the lead writer of the Common Core State Standards for Mathematics, structured the practices into four groups. 

• Overarching habits of mind-(MP1 and MP6)
• Reasoning and Explaining-(MP2 and MP3)
• Modeling and tools-(MP4 and MP5)
• Structuring and generalizing-(MP7 and MP8)

Students at all grades are expected to develop proficiency with these practice standards along with an understanding of the content standards. Students will gain experience with these practices through class discussions, collaboration with peers to solve problems, and tasks that provoke different levels of student thinking.  These practices are not meant to be a check list of skills to be learned individually. Students will use multiple practices when solving a single problem.

Here is a summary of the Mathematical Practices

MP1. Make sense of problems and persevere in solving them.

Students explain their thought processes in solving a problem, analyze the given information, explore ways to represent and solve the problem, and check to make sure their answer makes sense.  Students try several approaches in finding a solution and do not give up.

MP2. Reason Abstractly and Quantitatively

Students work with numbers and symbols out of context, and then work with and make sense of numbers and quantities in context.  Students represent relationships using diagrams and models.

MP3. Construct Viable Arguments and Critique the Reasoning of Others

Students communicate their reasoning and justify their conclusions by providing evidence. Students listen to arguments of their peers to determine whether their reasoning is correct or flawed, and correct any flaws.

MP4. Model with Mathematics

Students apply the mathematics that they learn to everyday life.  Additionally, students represent situations by writing equations that model the problems or by writing problems that represent the given situation.

MP5. Use Appropriate Tools Strategically

Students select available tools that can be used to solve problems including number lines, bar diagrams, graphs, manipulative materials, and technology.  Students use mental math and estimation to detect possible errors in their thinking or tool use.

MP6. Attend to precision

Students are precise and accurate in problem solving and in communicating mathematically. Students can speak, read, write, and listen with mathematical precision.  Students correctly use mathematical vocabulary, symbols, and units of measure.  Students’ calculations are accurate and efficient.

MP7. Look For and Make Use of Structure

Students look for and understand parts, wholes, and patterns in numbers and shapes. They leverage their prior knowledge to solve problems that behave in similar ways. They break down complicated problems to surface the structure of the problem.

MP8. Look For and Express Regularity in Repeated Reasoning

Students see the overall process of problems and notice repetitive calculations and find general methods in computation. They delve into the details of the problem while maintaining the big picture.

by Chritina Cardella, Department Chair for Mathematics, Melrose Public Schools

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