Mr. Botha
Question 1
My understanding of mathematical cognition is how children learn mathematics. In this article the authors state that children have a notion of quantity already before they acquire number words and that the carry out quantifying estimations long before they can calculate with precision (Feigenson, Dehaene & Elizabeth Spelke, 2004). Children are born with the ability to compare and discriminate small number of objects. Very early in their development they can represent quantities and even undertake operations with them. Infants and toddlers can only manage very small quantities or somewhat larger ones with limited precision (Butterworth, 1999; 2005; Deheane, 1997;Feigenson, 2004; Xu, 2005).
Feigenson, Dehaene & Elizabeth Spelke, 2004 review evidence that two distinct core systems of numerical representations are present in human infants and in other animal species and therefore do not emerge through individual learning or cultural transmission. These two systems are automatically deployed, are tuned only to specific types of information and continue to function throughout the lifespan. However the two core systems are limited in their representational power. Nether systems support concepts of fractions, square roots, negative numbers or even exact integers. The construction of natural, rational and real numbers depends on arduous processes that are probably accessible only to educated humans in a subset of cultures but which nevertheless are rooted in the two systems that are these authors current focus and that account for humans’ basic number sense.
Humans have two number systems: a system for small, exact numbers and an approximate number system. The two core systems are: Core system 1: Approximate representations of numerical magnitude (representations of larger quantities). With tests Spelke realized that even in infancy children exhibit numerical knowledge. They can discriminate between 8 versus 16 dots. In other words they know which one is
My understanding of mathematical cognition is how children learn mathematics. In this article the authors state that children have a notion of quantity already before they acquire number words and that the carry out quantifying estimations long before they can calculate with precision (Feigenson, Dehaene & Elizabeth Spelke, 2004). Children are born with the ability to compare and discriminate small number of objects. Very early in their development they can represent quantities and even undertake operations with them. Infants and toddlers can only manage very small quantities or somewhat larger ones with limited precision (Butterworth, 1999; 2005; Deheane, 1997;Feigenson, 2004; Xu, 2005).
Feigenson, Dehaene & Elizabeth Spelke, 2004 review evidence that two distinct core systems of numerical representations are present in human infants and in other animal species and therefore do not emerge through individual learning or cultural transmission. These two systems are automatically deployed, are tuned only to specific types of information and continue to function throughout the lifespan. However the two core systems are limited in their representational power. Nether systems support concepts of fractions, square roots, negative numbers or even exact integers. The construction of natural, rational and real numbers depends on arduous processes that are probably accessible only to educated humans in a subset of cultures but which nevertheless are rooted in the two systems that are these authors current focus and that account for humans’ basic number sense.
Humans have two number systems: a system for small, exact numbers and an approximate number system. The two core systems are: Core system 1: Approximate representations of numerical magnitude (representations of larger quantities). With tests Spelke realized that even in infancy children exhibit numerical knowledge. They can discriminate between 8 versus 16 dots. In other words they know which one is
References: Dahaene, S.( 2011). The number sense: How the mind creates mathematics. UK: Oxford University Press. Feigenson, L; Dehaene, S & Spelke E. (2004). Core systems of number. Cognitive Science, 8, 307-314. Reys, R., Lindquist, M., Lambdin, D., Smith, L., Suydam, M. (2001). Helping children learn mathematics.United States: John Wiley &Sons. Inc