Barbie caught a lot of flack back in the '90s for declaring, "Math class is tough!" Today we find ourselves in the disorienting position of defending her.
We recently got a note from an anonymous "math lover" who insists the words "math" and "arithmetic" do not mean the same thing, despite the fact that many people use them interchangeably.
But many dictionaries define arithmetic as "a branch of mathematics." Which means even simple addition and subtraction are, technically, math. But are the words interchangeable? We turned to Dr. Math for an answer. (Dr. Math is actually a group of experts gathered through Drexel University to answer math questions via e-mail at mathforum.org/dr.math/.)
"Any place you really mean 'arithmetic,' it's probably fine to use 'math' instead," the good doctor answered. "For example, parents at the dinner table asking their child, 'What did you learn in math today?' is perfectly fine, no matter what math class the child is actually taking in school, because what is meant will be understood by those at the table."
This does not work in reverse, however.
"Most people will understand arithmetic to be a specific type of math, and will not equate it with math itself," says Dr. Math. "We can't refer to calculus as arithmetic, even though calculus contains arithmetic operations in it."
How about a non-math analogy to send the point home?
"You can refer to everything at the zoo as an 'animal' because they all belong to the animal kingdom —reptiles, amphibians, even insects and invertebrates," says Dr. Math. "But you couldn't use a more specific word like "mammal" to refer to animals in general."
Or, as the MathMedia Educational Software folks put it, "Arithmetic is to mathematics as spelling is to writing." Not one and the same, exactly. But certainly crucial to the other's survival.
Barbie was clearly onto something.
Math vs. arithmetic
Yes, there is a difference. Words Work adds it up with help from Dr. Math.
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