Mathematical Language and the Common Core

As we are implementing the common core math standards and the standards of mathematical practice we want to keep in mind how those standards apply to our instruction.  One way we can do that is to model the use of precise language in our teaching.  In an article by Valerie Faulkner, Why the Common Core Changes Math Instruction, she discusses old math language habits we may have and offers a new phrase to use instead.  The following examples are all taken from her article.

Instead of  defining equality as "same as" define it as "same value as."
For example: 3 + 4 tells a different math story than 4 + 3, but they have the same value of 7.

Instead of calling digits "numbers" clearly explain the difference between numbers/numerals and digits.
For example: 73 is a numeral that represents the number 73 and has two digits 7 and 3.

Instead of saying addition makes things bigger show addition is about combining.
The "addition makes things bigger" statement becomes a problem when students are introduced to negative numbers.

Instead of saying subtraction makes things get smaller show that subtraction is about difference.
Again, "subtraction makes thing get smaller" is a problem with the introduction of negative numbers.

Instead of referring to "the answer" ask students to use "the model", "the relationships", "the structure", or to "justify their answer."
When the goal is to find an answer we forget about the most important part of the problem - How did we do that? and Why did we do that?

Just as we are asking students to be more precise in their use of vocabulary, so must teachers.  Through our modeling students will learn how to speak and write using specific and correct mathematical language.

Below are some prompts to help get your students talking about math, how they arrived at their solution, and asking others about their work.  This is an easy way to build in some of the standards of mathematical practice, particularly construct viable arguments and critique the reasoning of others.
Please let me know if you would like a hard copy of the prompts.