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MATHEMATICS ~ MRS. MICHELLE MARINI ~ February 2017

 

 

math

Adjusting Mathematical Language to Help Students Become Better

Valerie Faulkner (North Carolina State University) presents a number of changes in the
way elementary mathematics is conceived in the Common Core. Implementing the new
standards means letting go of a lot of old habits so students may build accurate
mathematical ideas. Research supports that precise definitions are imperative in
learning mathematics because opportunities for miscommunication exist if the words and
symbols are interpreted incorrectly or used in imprecise ways (Devlin 1998).
Oftentimes, I reflect on my own experiences as a math student. I remember some ideas
seemed inconsistent and confusing because the “rules” or language used would change.
At Tashua, we hope to support students in their development of accurate, meaningful
and consistent mathematical understandings. In order to do this we have to shed some
old habits…
• Old habit to eliminate: Defining equality as “same as.”
The problem: This is mathematically incorrect and leads to misconceptions.
New habit to adopt: Defining equality as “same value as.”
For example, 3 + 4 tells a different math story than 4 + 3, but they yield the same value of 7.
• Old habit to eliminate: Calling digits “numbers.”
The problem: Failing to distinguish between digits, numbers, and numerals
New habit to adopt: Clearly distinguishing between numerals and numbers (which are
essentially the same) and digits.
For example, 73 is a numeral that represents the number value 73 (7 tens and 3 ones) and has
two digits: 7 and 3.
• Old habit to eliminate: “Addition makes things get bigger.”
The problem: When negative numbers are introduced, the old habit has to be debugged.
New habit to adopt: Addition is about combining.
• Old habit to eliminate: “Subtraction makes things get smaller.”
The problem: As with addition, negative numbers make this wrong.
New habit to adopt: Subtraction is about difference.
• Old habit to eliminate: When borrowing, saying, “We don’t have enough ones so we need to
go to the next place.”
The problem: Students don’t understand that in the number 10, there are ten ones, but in the
decimal system, we don’t “see” them.
New habit to adopt: “We can’t see the ones we need, and we need to find those ones.”
• Old habit to eliminate: “You can’t take a big number from a little number.”
The problem: The statement is intended to help elementary students deal with borrowing, but
it’s mathematically inaccurate and leads to problems later on.
New habit to adopt: “We could take a larger number from a smaller number, but we would get
a negative number. You will learn about these later, but right now we will learn to solve this
problem using all positive numbers.”
• Old habit to eliminate: “Let’s ‘borrow’ from the tens place.”
The problem: This doesn’t prepare students for more-difficult borrowing and fractions.
New habit to adopt: Use “regrouping,” “trading,” or “decomposing” instead.
• Old habit to eliminate: Multiplication “makes things bigger.”
The problem: This is true only when using positive whole numbers and will confuse students
later on.
New habit to adopt: Teach the three structures of multiplication: repeated addition; finding
how many unique possibilities there are when matching one set with another; and finding a total
amount or area when two sides are known.
• Old habit to eliminate: Referring to “the answer.”
The problem: If the goal is to find answers, there’s a tendency to forget the most important
part: How did we do that? Why did we do that? How did you know that?
New habit to adopt: Use “the model” or “the relationships” or “the structure” or “justify your
answer.”

Michelle Marini Math Specialist

Tiger Times February 2017