Possessing number sense permits a child to achieve everything from understanding the meaning
of numbers to developing strategies for solving complex math problems; from making simple
magnitude comparisons to inventing procedures for conducting numerical operations; and from
recognizing gross numerical errors to using quantitative methods for communicating, processing,
and interpreting information.
Researchers have identified the following components and features of number sense:
1) A faculty permitting the recognition that something has changed in a small
collection when, without direct knowledge, an object has been removed or
added to the collection.
2) Elementary abilities or intuitions about numbers and arithmetic.
3) Ability to approximate or estimate.
4) Ability to make numerical magnitude comparisons.
5) Ability to decompose numbers naturally.
6) Ability to develop useful strategies to solve complex problems.
7) Ability to use the relationships among arithmetic operations to understand
the base-10 number system.
8) Ability to use numbers and quantitative methods to communicate,
process, and interpret information.
9) Awareness of various levels of accuracy and sensitivity for the reasonableness
of calculations
10) A desire to make sense of numerical situations by looking for links between
new information and previously acquired knowledge.
11) Possessing knowledge of the effects of operations on numbers.
12) Possessing fluency and flexibility with numbers.
13) Can understand number meanings.
14) Can understand multiple relationships among numbers.
15) Can recognize benchmark numbers and number patterns.
16) Can recognize gross numerical errors.
17) Can understand and use equivalent forms and representations of numbers
as well as equivalent expressions.
18) Can understand numbers as referents to measure things in the real world.
19) Can move seamlessly between the real world of quantities and the mathematical
world of numbers and numerical expressions.
20) Can invent procedures for conducting numerical operations.
21) Can represent the same number in multiple ways depending on the context
and purpose of the representation.
22) Can think or talk in a sensible way about the general properties of a numerical
problem or expression—without doing any precise computation.
23) Engenders an expectation that numbers are useful and that mathematics
has a certain regularity.
24) A non-algorithmic feel for numbers.
25) A well-organized conceptual network that enables a person to relate
number and operation.
26) A conceptual structure that relies on many links among mathematical
relationships, mathematical principles, and mathematical procedures.
27) A mental number line on which analog representations of numerical
quantities can be manipulated.
28) A nonverbal, evolutionarily ancient, innate capacity to process approximate
numerosities.
29) A skill or kind of knowledge about numbers rather than an intrinsic process.
30) A process that develops and matures with experience and knowledge
HOME Curriculum Fees Schedules Testimony Consultants Contact Us Resources