Understanding MP 2: Reason abstractly and quantitatively
The Common Core’s Mathematical Practice 2, Reason abstractly and quantitatively, calls for students to make sense of quantities and their relationships in problem situations. Students de-contextualize – translate the actions and events described in a problem into models or numbers and symbols that they can manipulate. They also contextualize – interpret the meaning of the numbers, symbols, and units of measure in their work in terms of what they represent in the original problem. Students are able to imagine a problem context for an abstract problem, enabling them to make sense of the mathematics and judge the reasonableness of their answer. They understand the properties of operations, numbers, and geometric objects and use them flexibly. MP 2 is closely related to several other Practices, especially MP 4, Model with Mathematics.
Why is reasoning important?
Reasoning is the foundation of mathematics. It is one of the principal vehicles for developing understanding, exploring new ideas, and constructing new knowledge. Through reasoning we are able to analyze and solve problems, assess our results, and generally make sense of mathematical situations. Students who can reason are often able to find their own way through problems, even when their memory of procedures and rules fails them.
How should we develop reasoning?
Like other Mathematical Practices, MP 2 is best addressed in the context of doing worthwhile mathematics. Rich problems and investigations provide authentic opportunities for students to develop the number sense and operation sense that support understanding. Teachers can help students develop reasoning by asking guiding questions; by encouraging students to visualize problems and search for connections with previous work; by modeling a variety of tools and representations and having children compare them; and by fostering the development of math language and providing numerous opportunities for students to share their thinking.
How can these resources help?
The resources in this collection are intended to help teachers and math specialists understand the intent and scope of MP 2 and plan for successful attainment in the classroom. They include: documents and websites that help us interpret the practice and appreciate its importance; a webcast and videos that illustrate teachers fostering reasoning in a problem context; and articles suggesting effective instructional strategies. A companion Classroom Collection includes resources to help teachers foster this practice with their students.