Effective Mathematics Teaching Practice 1: Establish Mathematics Goals to Focus Learning

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NCTM's first effective teaching practice is to establish goals to focus learning. The most poignant aspect of this teaching practice is that mathematics teachers must be more focused on meaningful shifts in student understanding rather than just what students are expected to be doing. This is the difference between a learning goal and a performance goal. Compare the following goal statements:

Goal A: Students will recognize that the area of the square built on the hypotenuse of a right triangle is equal to the sum of the areas of the squares built on the legs and will conjecture that c²=a²+b².
Goal B: Students will be able to (SWBAT) use the Pythagorean Theorem (c²=a²+b²) to solve a series of missing value problems.

Goal A is a learning goal, as it describes the reasoning and understanding we want students to learn as the result of instruction. Goal B is a performance goal, as it falls short of describing what learning is being done and instead essentially says, “Students will solve problems using a theorem.” While part of the lesson activity may include solving a series of problems, our goals should focus on the learning to be developed, not the tasks to be performed. Doing so sets up everything for the rest of the lesson: the tasks that are chosen, the representations students use, questions to be asked, the focus of classroom discussion, and assessment strategies.

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One of the ways NCTM (2014, p. 16) summarizes the practice of establish mathematics goals to focus learning is by describing a set of actions expected of teachers and students that indicate engagement in this teaching practice.