What about the FACTS?
Unless a child has successfully experienced, understood and ultimately learned the principles of counting they cannot learn the facts. They can memorize them, maybe, with a lot of practice but… they won’t ever understand them in such a way that they can apply them in a purposeful manner.
Principles of Counting
Stable Order Principle:
Child consistently counts numbers without skipping any. (Example: 1, 2, 3, 4, 5 …)
Expectancy varies with age.
Order Irrelevance Principle:
Maintaining the same amount despite different starting points.
Conservation Principle:
Maintaining quantity irregardless of the spatial orientation.
Example: XXXXXX XX
(Both are six.) X
XXX
Abstraction Principle: Quantity remains the same despite the size and the shape of the objects. Example: XXX @^$ … Each group is still 3
One to One Correspondence: 1 to 1 counting of objects
Cardinality Principle: How much – quantity; maintaining amount without having to recount; the last number you say is the “name” of that group (quantity) *Children do not naturally know this, they have to experience it and learn it!
Movement is Magnitude Principle: Being able to tell what one more or less is.
Example: 1 more than 23 is 24; (real life connections – ladder, growth chart, thermometer, stairs)
Unitizing Principle: Making bundles or being able to tall; equal bundles should not have to be counted individually; eventually applying this principle to place value or digit value.
Subitizing: Coined in 1949 by E.L. Kaufman et al. refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning sudden) and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range. Number judgments for larger set-sizes were referred to either as counting or estimating, depending on the number of elements present within the display, and the time given to observers in which to respond (i.e., estimation occurs if insufficient time is available for observers to accurately count all the items present).
"Subitizing is a fundamental skill in the development of students' understanding of number" (Baroody 1987, 115). Students can use pattern recognition to discover essential properties of number, such as conservation and compensation. They can develop such capabilities as unitizing, counting on, and composing and decomposing numbers, as well as their understanding of arithmetic and place value-all valuable components of number sense.
Unless a child has successfully experienced, understood and ultimately learned the principles of counting they cannot learn the facts. They can memorize them, maybe, with a lot of practice but… they won’t ever understand them in such a way that they can apply them in a purposeful manner.
Principles of Counting
Stable Order Principle:
Child consistently counts numbers without skipping any. (Example: 1, 2, 3, 4, 5 …)
Expectancy varies with age.
Order Irrelevance Principle:
Maintaining the same amount despite different starting points.
Conservation Principle:
Maintaining quantity irregardless of the spatial orientation.
Example: XXXXXX XX
(Both are six.) X
XXX
Abstraction Principle: Quantity remains the same despite the size and the shape of the objects. Example: XXX @^$ … Each group is still 3
One to One Correspondence: 1 to 1 counting of objects
Cardinality Principle: How much – quantity; maintaining amount without having to recount; the last number you say is the “name” of that group (quantity) *Children do not naturally know this, they have to experience it and learn it!
Movement is Magnitude Principle: Being able to tell what one more or less is.
Example: 1 more than 23 is 24; (real life connections – ladder, growth chart, thermometer, stairs)
Unitizing Principle: Making bundles or being able to tall; equal bundles should not have to be counted individually; eventually applying this principle to place value or digit value.
Subitizing: Coined in 1949 by E.L. Kaufman et al. refers to the rapid, accurate, and confident judgments of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning sudden) and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range. Number judgments for larger set-sizes were referred to either as counting or estimating, depending on the number of elements present within the display, and the time given to observers in which to respond (i.e., estimation occurs if insufficient time is available for observers to accurately count all the items present).
"Subitizing is a fundamental skill in the development of students' understanding of number" (Baroody 1987, 115). Students can use pattern recognition to discover essential properties of number, such as conservation and compensation. They can develop such capabilities as unitizing, counting on, and composing and decomposing numbers, as well as their understanding of arithmetic and place value-all valuable components of number sense.