Gersten, R., & Chard, D. (1999). Number Sense Rethinking Arithmetic Instruction for Students with Mathematical Disabilities. The Journal of special education, 33(1), 18-28.
This article draws analogies between phonological awareness and number sense. Although it is written for a specific learning disabilities audience, the information within is useful for anyone who wants to learn more about how number sense is developed. The authors draw analogies between earlier research on ways to remediate mathematical disabilities and earlier research on reading disabilities. Their goal here is to provide a brief overview of phonological awareness concepts and number sense before introducing the concept of number sense, rather than to attempt to provide a comprehensive review of either topic.
Number sense is difficult to define but easy to recognize. Students with good number sense can move seamlessly between the real world of quantities and the mathematical world of numbers and numerical expressions. They can invent their own procedures for conducting numerical operations. They can represent the same number in multiple ways depending on the context and purpose of this representation. They can recognize benchmark numbers and number patterns: especially ones that derive from the deep structure of the number system. They have a good sense of numerical magnitude and can recognize gross numerical errors that is, errors that are off by an order of magnitude. Finally, they can think or talk in a sensible way about the general properties of a numerical problem or expression-- without doing any precise computation.
It is also likely that some students who are drilled on number facts and then taught various algorithms for computations may never develop much number sense, just as some special education students, despite some phonics instruction and work on repeated readings/fluency and accuracy, fail to develop good phonemic awareness or any sense of the purpose or pleasure of reading.