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Is there a difference between numeracy and number sense, or are they synonymous? In my language they are often both translated to the same word (tallforståelse).
I'm thinking that perhaps numeracy describes a competency, while number sense is more about having a "feel" for numbers or understanding relations between numbers. Is this how the terms are used in education literature?
This answer could be totally wrong. It just describes the shades of meaning that the terms have for me.
To me, "number sense" feels more specific and has the connotation of describing someone who habitually and competently makes sense out of numerical relationships. For example, I teach my students to do order-of-magnitude estimates (Fermi problems), and once I posed a problem of estimating the amount of blood sucked by a flea. One of my students estimated a liter. This student lacked number sense. He wasn't in the habit of thinking about whether numbers made sense, and/or he wasn't competent enough to tell that this particular number didn't make sense.
Another example of lacking number sense is when someone writes the result of an experiment as $0.03798\pm 0.00213$, not understanding that it doesn't make sense to express the result to the 100,000ths place when the uncertainty is in the thousandths place.
"Numeracy" feels to me more like a broad term that describes facility with numbers. For example, someone who is numerate should understand that a hamburger with a 1/3 pound patty contains more meat than one with a 1/4 pound patty. (There was a famous ill-fated advertising campaign that didn't anticipate how many people figured 1/4 pound to be more meat, since 4 is greater than 3.)
A numerate person can estimate, without reaching for a calculator, that \$12 is about 1% of \$1000.
A numerate person may not have memorized what 7x6 is, but if necessary they can reconstruct it in a few seconds by doing (7x3)x2. If someone lacks numeracy, then not only do they not have 7x6=42 memorized, but they can't reconstruct that fact.
I have just been exploring numeracy (and literacy), which I find quite fascinating. Numeracy seems to be the application of mathematics in a range of different contexts, not just in mathematics classes and maths scenarios. The Australian education literature and formal definitions seems to have gone that way. However, number sense is a specific subsection or part of the overall numeracy umbrella concept.
https://www.australiancurriculum.edu.au/f-10-curriculum/general-capabilities/numeracy/
While numeracy focuses a broad application, number sense is a cognitive ability or internal familiarity with estimations and quantities. There is an inherent sense some people are great at eyeballing and getting a sense of numbers but there is a learnt part of number sense too. Guessing the number of candies in a jar would be a number sense example maybe? Number sense seems a more arithmetic concept, more concrete and definite.
The flip side of innumeracy includes people with difficulty with number sense, dyscalculia, different levels of mathematical competency (learnt) and also universal finding that humans are basically innumerate with large numbers and probabilities.
