Adjusting Math Terms for the Common Core World

Valerie Faulkner of North Carolina State University argues for a shift in the mathematical language we use.  The Common Core should give us pause and force us to reconsider the terminology and vocabulary we employ in describing certain skills and concepts.  Here are a few examples:

Old Habit (eliminate)                                     New Habit (adopt)

Defining equality as “ same as”                   Defining equality as “same value as”

Calling digits numbers                                    Clearly distinguishing between digits, numbers and numerals

Addition makes things bigger                      Addition is about combining

Subtraction makes things get smaller      Subtraction is about difference

Let’s borrow from the tens place               Use regrouping, trading, decomposing

Multiplication makes things bigger          Teach 3 structures of multiplication

Divison makes things smaller                     Teach the different structures of divisions,

Doesn’t go into                                                 Prepare students for later learning by using accurate language

Saying “and” means decimal point         Don’t create false rules for language using and

Canceling out                                                   Explicitly use and discuss the idea behind simplifying

Referring to “the answer”                           Use the model or the relationships to justify your answer

Guess-and-check as a strategy                 Teach systematic math representations


Old habits die hard, but this is food for thought as many districts get farther into implementing the Common Core.

Identity Confusion: The Problem with the Equal Sign

Henry Borenson explains how we use the = sign in two very different ways.  The first way is operational, for example 10 + 15 = ______.  The second way we use the sign is relational, indicating equivalence between two sets of expressions, each of which includes one or more operations, for example 8 + 4 =_____ + 5.  But in 1999 a study of hundreds of first through six graders only 5%  solved problems like this correctly.

Borenson believes that because of this study we can conclude that the relational meaning  of the equal sign is not something that students find intuitive or self evident. When asked to fill in the answer to the problems above most students said that 12 belongs in the space because the answer follows the equal sign.  The equal sign seems to trigger the operational definition in most students’ minds. Some students thought the  + 5 was just there to confuse them.

Borenson recommends  introducing students in the second or third grade to the idea of balanced equations using concrete objects rather than numbers and the equal sign. Once students get the idea the equal sign can be introduced with the balancing explanation. Studies have shown that if the relational meaning of the equal sign is introduced in this way students are much more likely to grasp both ways.

How to Encourage a Love of Mathematics

Here’s Lisa Medoff from Stanford University suggesting eight helpful ways that educators can build students’ tenacity with a subject that frustrates many of them: math!

  • Empathize. It helps to imagine a situation where you are out of your confort zone and feeling frustrated and agry.


  • Know your stuff. Be sure to spend time mastering the topic and walking students through their own self-doubts and frustrations.


  •  Use a variety of activities and supports. Get students working in groups with structured, hands-on, real world activities with the teacher circulating to troubleshoot and provide one-on-one support.


  • Convey the “growth” mindset. Let the students know that some may have to work at it harder and they will approach the problem differently, but they can all master math.


  •  Answer all questions respectfully. Even if the question has been asked before, you might say, “ I am glad you asked me again to make sure you understood.


  • Be intentional about homework. Think about how many problems students need to practice, which problems will be most helpful, will help be needed, etc.


  • Reframe the purpose of quizzes and test. Make it clear to the students that the test are not to determine how smart the student is but to show how well the teacher taught the information.


  • Praise effort and reinterpret mistakes. Students should learn to see success as the result of effective effort and mistakes as a sign that more work is needed.


Developing Non-Cognitive Skills

Here’s an interesting perspective: Kentucky math teacher, Alison Wright, described how two students in her Algebra II class reacted to a quiz that was returned. One student looked at the test, rolled her eyes, threw the paper on the floor, and complained the test was not fair and should not count. The second student read the comments, reworked the problems to find her mistakes and stayed after class to discuss the test.

After some research Wright came up that a new approach that she is going to implement in her class this year.

·        Teach students that wrong answers are a helpful part of the learning process.  Many students shut down because they are afraid of having the wrong answer and failing.

·        Use cooperative group work as often as possible. By doing this students develop social skills necessary for teamwork while constructing arguments and providing valuable feedback to each other in a nonthreatening environment.

·        Use “A” and “Not Yet” as the only two possible grades. Wright believes this will help students that have bad reactions to failing grades.


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