The way we represent mathematical problems in writing often introduces new and

confused ways of thinking about numbers without really talking it through. One such

case we saw in class happens when children are asked to move to using directional

numbers from just counting objects. For example, the familiar way of writing "take

away," like $"8-5=>3",$ gets confused when we write a "negative number," like $"-5".$ A

student will try to use their knowledge by thinking, "Take five from what? There is

only one number." We can untangle this by making clear there are two types of

"minus" operations: The

minus tells you to find the opposite of a single number,

while the

unary; binary

binary; unary

real; fake

fake; real