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?

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    $\begingroup$ This is just a personal opinion, therefore only a comment: For me, the numeracy is related to the mathematical education while number sense is a matter of talent. But I also feel a certain deal of overlapping, though. $\endgroup$ – Thinkeye Jun 2 '17 at 12:29

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.

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  • $\begingroup$ I think there's a grey area between the two, and you've done a good job here. When I encounter a student who offers an answer that defies my own common sense, I don't spend much time categorizing the source of the error. $\endgroup$ – JTP - Apologise to Monica May 29 '17 at 19:25
  • $\begingroup$ I don't see what is wrong with 0.03798 ± 0.00213. Why couldn't you determine that the true value of some quantity lies within such an interval? Would you change how you reported the results to an experiment if you did the calculations in a different base? $\endgroup$ – Steven Gubkin May 21 at 16:59

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