Numeracy is the ability to execute standard whole number operations or algorithms correctly, consistently, and fluently and estimate, accurately and efficiently, both mentally and on paper, using a range of calculation strategies and means.
Acquisition of numeracy depends on proficiency in numbersense – the flexible use of number relationships and numerical information in various contexts. Those with numbersense can represent and use a number in multiple ways depending on the context and purpose. In computations and operations, they can decompose and recompose numbers with ease and fluency.
Numeracy is the gateway to higher mathematics beginning with the study of algebra and geometry. But, many individuals never reach this gateway because of difficulties with mastering numeracy. Some difficulties are caused by environmental factors:
- lack of appropriate number experiences,
- ineffective instruction and a fragmented curriculum,
- inefficient conceptual models and strategies,
- lack of appropriate skill development, and
- low expectations.
For example, teaching arithmetic facts by sequential counting (“counting up” for addition, “counting down” for subtraction, “skip counting” on number line for multiplication and division), though advocated by many researchers and educators, is not an efficient strategy because one-to-one counting only turns most children into counters – that’s all.
Other difficulties in mastering numeracy are due to individual capacities and learning disabilities. Among those who exhibit learning problems in mathematics, some struggle in certain aspects of mathematics (e.g., procedures, conceptual processes). Some have difficulty in arithmetic, algebra, or geometry. Others display symptoms of dyscalculia, which manifests as poor number concept – difficulty in estimating the size and magnitude of numbers, lack of understanding and fluency in number relationships, and inefficiency of numerical operations.
A learning disability may manifest as deficits in the development of prerequisite skills: following sequential directions, spatial orientation/space organization, pattern recognition and extension, visualization and visual perception, and deductive and inductive thinking. These deficits may affect learning in different aspects of mathematics, for example, a few isolated skills in one concept or procedure or several areas of arithmetic and mathematics. Some learning problems fall in the intersection of quantity, language, and spatial thinking.
Because of the range of mathematics disabilities, we cannot always identify a cause or effect, and no one explanation adequately addresses the nature of learning problems in mathematics.