The thread that underlies our approach to teaching all of arithmetic is that people talk about numbers but what they see are quantities.
For example, we have seen 3 fingers, 3 apples, 3 tally marks, 3 people,
etc.; but we have never seen “threeness'' itself.
In a phrase such as “3 apples”,
3 is an adjective that modifies the noun“apples”. We refer to such a phrase as a quantity. More formally:
A quantity is a phrase that consists of an adjective (in the
form of a number) that modifies a noun (usually referred to as a unit).
People in science talk about quantities, not numbers. That is, they will talk about 3 ounces, 3 grams,
3 pounds, etc., but never just about 3.
In the quantity “3 apples”, the adjective is 3 and the noun
(unit) it modifies is “apples”.
Our website is dedicated to helping you understand how we implement our goal
and what you can do to help students attain greater success in internalizing the basics of mathematics. What is important
to keep in mind is that we are not asking you to abandon anything that you prefer to do in class. Instead we are supplying
you with an additional tool; a tool that has worked very well for us.
Our Underlying Contention:
tend to see numbers as quantities. And if we allow students to visualize numbers as being quantities, all of arithmetic becomes
much easier to internalize and understand.