Revisiting the Introductory Challenge

What’s arithmetic?  Here’s the complete answer—as it exists in one good source at present. (It will be different later.)

It’s an answer neither Sam nor Jessica’s mom could possibly have provided.

Here is the first paragraph from Wikipedia’s article, “Arithmetic”:

Arithmetic or arithmetics (from the Greek ἀριθμός arithmos, “number”) is the oldest and most elementary branch of mathematics. It consists of the study of numbers, especially the properties of the traditional operations between them — addition, subtraction, multiplication and division. Arithmetic is an elementary part of number theory, and number theory is considered to be one of the top-level divisions of modern mathematics, along with algebra, geometry, and analysis. The terms arithmetic and higher arithmetic were used until the beginning of the 20th century as synonyms for number theory and are, sometimes, still used to refer to a wider part of number theory. (

Here is the definition from the Oxford English Dictionary:

The science of numbers; the art of computation by figures. (This dictionary also tells us that the first occurrence of the word “arithmetic” in written English took place in the year 1305!)

In thinking about these definitions, try to answer the following questions:

  • How well did these definitions fit with the understanding of “arithmetic” you had before you read them?
  • What features of “arithmetic” did the definitions help you understand?
  • What was useful?
  • What do you think about the fact that arithmetic is (only) 700 years old?

Then, either alone, or with an interested friend or co-worker, create a description of “arithmetic” in just two sentences that you could share with one of your students.  Remember: you’re creating this description to help a child get some idea of what arithmetic is! If you are working in a group, discuss your descriptions.

Some of the interesting things to talk about might be:

  • What is it about the child you’re thinking of that influenced what you wrote?
  • What do you want the child to take away from what you say about arithmetic?
  • How does your description differ from the two descriptions listed above?