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Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of number they operate on. Integer arithmetic restricts itself to calculations with positive and negative whole numbers. Rational number arithmetic involves operations on fractions that lie between integers. Real number arithmetic includes calculations with both rational and irrational numbers and covers the complete number line. Another distinction is based on the numeral system employed to perform calculations. Decimal arithmetic is the most common. It uses the basic numerals from 0 to 9 and their combinations to express numbers. Binary arithmetic, by contrast, is used by most computers and represents numbers as combinations of the basic numerals 0 and 1. Some arithmetic systems operate on mathematical objects other than numbers, such as interval arithmetic and matrix arithmetic.
A serial number is a unique identifier used to uniquely identify an item, and is usually assigned incrementally or sequentially.
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics, therefore, excludes topics in "continuous mathematics" such as calculus and analysis.
Numeracy is the ability to understand, reason with, and to apply simple numerical concepts. The charity National Numeracy states: "Numeracy means understanding how mathematics is used in the real world and being able to apply it to make the best possible decisions...It's as much about thinking and reasoning as about 'doing sums'". Basic numeracy skills consist of comprehending fundamental arithmetical operations like addition, subtraction, multiplication, and division. For example, if one can understand simple mathematical equations such as 2 + 2 = 4, then one would be considered to possess at least basic numeric knowledge. Substantial aspects of numeracy also include number sense, operation sense, computation, measurement, geometry, probability and statistics. A numerically literate person can manage and respond to the mathematical demands of life.
Dyscalculia is a disability resulting in difficulty learning or comprehending arithmetic, such as difficulty in understanding numbers, learning how to manipulate numbers, performing mathematical calculations, and learning facts in mathematics. It is sometimes colloquially referred to as "math dyslexia", though this analogy is misleading as they are distinct syndromes.
Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.
Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. It is the primary model for standards-based mathematics.
Numerical cognition is a subdiscipline of cognitive science that studies the cognitive, developmental and neural bases of numbers and mathematics. As with many cognitive science endeavors, this is a highly interdisciplinary topic, and includes researchers in cognitive psychology, developmental psychology, neuroscience and cognitive linguistics. This discipline, although it may interact with questions in the philosophy of mathematics, is primarily concerned with empirical questions.
The following outline is provided as an overview of and topical guide to the human self:
Number systems have progressed from the use of fingers and tally marks, perhaps more than 40,000 years ago, to the use of sets of glyphs able to represent any conceivable number efficiently. The earliest known unambiguous notations for numbers emerged in Mesopotamia about 5000 or 6000 years ago.
The following outline is provided as an overview of and topical guide to thought (thinking):
In human developmental psychology or non-human primate experiments, ordinal numerical competence or ordinal numerical knowledge is the ability to count objects in order and to understand the greater than and less than relationships between numbers. It has been shown that children as young as two can make some ordinal numerical decisions. There are studies indicating that some non-human primates, like chimpanzees and rhesus monkeys have some ordinal numerical competence.
Counting in prehistory was first assisted by using body parts, primarily the fingers. This is reflected in the etymology of certain number names, such as in the names of ten and hundred in the Proto-Indo-European numerals, both containing the root *dḱ also seen in the word for "finger".
The numerosity adaptation effect is a perceptual phenomenon in numerical cognition which demonstrates non-symbolic numerical intuition and exemplifies how numerical percepts can impose themselves upon the human brain automatically. This effect was first described in 2008.
The approximate number system (ANS) is a cognitive system that supports the estimation of the magnitude of a group without relying on language or symbols. The ANS is credited with the non-symbolic representation of all numbers greater than four, with lesser values being carried out by the parallel individuation system, or object tracking system. Beginning in early infancy, the ANS allows an individual to detect differences in magnitude between groups. The precision of the ANS improves throughout childhood development and reaches a final adult level of approximately 15% accuracy, meaning an adult could distinguish 100 items versus 115 items without counting. The ANS plays a crucial role in development of other numerical abilities, such as the concept of exact number and simple arithmetic. The precision level of a child's ANS has been shown to predict subsequent mathematical achievement in school. The ANS has been linked to the intraparietal sulcus of the brain.
Number sense in animals is the ability of creatures to represent and discriminate quantities of relative sizes by number sense. It has been observed in various species, from fish to primates. Animals are believed to have an approximate number system, the same system for number representation demonstrated by humans, which is more precise for smaller quantities and less so for larger values. An exact representation of numbers higher than three has not been attested in wild animals, but can be demonstrated after a period of training in captive animals.
Spatial ability or visuo-spatial ability is the capacity to understand, reason, and remember the visual and spatial relations among objects or space.
Plant arithmetic is a form of plant cognition whereby plants appear to perform arithmetic operations – a form of number sense in plants.
Lisa Feigenson is Professor of Psychological and Brain Sciences at Johns Hopkins University and co-director of the Johns Hopkins University Laboratory for Child Development. Feigenson is known for her research on the development of numerical abilities, working memory, and early learning. She has served on the editorial board of Cognition and the Journal of Experimental Psychology: General.
References
- ↑ Piazza, M. (2010). "Neurocognitive start-up tools for symbolic number representations". Trends in Cognitive Sciences. 14 (12): 542–551. doi:10.1016/j.tics.2010.09.008. PMID 21055996. S2CID 13229498.
- ↑ "Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities".
- ↑ Berch, Daniel B. (2005). "Making Sense of Number Sense: Implications for Children With Mathematical Disabilities". Journal of Learning Disabilities. 38 (4): 333–339. doi:10.1177/00222194050380040901. PMID 16122065. S2CID 1657049.
- ↑ "Stages in Development of Number Sense - Harvard Education Letter".
- ↑ "Number Systems". www.math.twsu.edu.
- ↑ Dantzig, Tobias. Number: The Language of Science. New York: Macmillan Company, 1930.
- ↑ "Understanding a Child's Development of Number Sense".
- ↑ "UIL Number Sense".
- 1 2 "Unit 1: Number and Number Sense" (20-day lesson), STPSB.org, St. Tammany Parish School Board, Covington, LA (USA), 2009, overview webpage: ST-MathGrade7Unit-topics.
- ↑ "Freakonomics.com".