Effective mathematics involves two distinct acts:
- Parsing and writing mathematical symbols to create meaningful messages
- Applying an understanding of mathematical relations and objects
It seems to me that we have two terms at our disposal: Numeracy and mathematical literacy. It also seems to me that these two terms are used somewhat interchangeably. (“What is numeracy?”)
I recommend that we stop blurring these terms. Two terms, two acts: The logician in me says we should apply one to each.
To that end, I suggest these definitions:
- Mathematical literacy: The ability to read and write statements about mathematics in an acceptably meaningful way, e.g., being able to see “2 + 2 = 4” and think “two plus two equals four”, and being able to see a room that is ten feet by twenty feet and write “10′ * 20′ = 200 sq. ft.”.
- Numeracy: The ability to use mathematics effectively, including having a number sense and basic reasoning skills and being able to apply and construct mathematical constructs that are relevant to solving personal, real-world problems.
