Developing individual in society gLecture 5 : 12/11/2020 Numbers Lecturer: Fenja Ziegler There is no known date when the idea of measuring quantitatively was created. Two types of numbers: Cardinal: Provide plurality of items, one, two, three etc. Provides for simple day-to-day needs, probably came first. Ordinal: Provides the order of items. First, third, second. Possibly for ritual or ceremonial needs. Numbers probably began with contrasts. Such as being able to differentiate between the number of wolves dependent upon the number of howls, which would have aided survival. Contrast lead to similarity and correspondence. Similarity is recognising two similar items, such as two hands, or two nights. Some expressions still exist today when such methods did not exist. I.e., yoke of oxen, murder of crows, school of dolphins. Correspondence is recognising two unsimilar objects as a pair, such as the sun and moon. Numbers were created to be a minimal set, from 0-9, enabling us to create any number using any combination of this set. Children and numbers - Piaget was the first to test the idea of numbers in children. - Presented 2 rows of counters of equal number, asked the children if they were the same amount or not. - When one row was spread out, but still an equal number, when the children were asked again, they said the spread out row was longer. < 7 years. - Piaget said children have no sense of numbers, counting or maths. Do infants know numbers? (starkey ff cooper) numerical relations - Conducted habituation studies in 5-6 mo. old infants. - Shown 2 circles until habituated, as well as moving them in different positions. - Then change the number of circles, so 3 circles. If the child show renewed interest, it suggests the child perceive 2 as different to 3.
Do infants understand relational knowledge? I.e. 3 > 2, etc. (Cooper) - 10-14 mo. old children, habituation study. - Shown a greater than image until habituated. I.e. 4 squares compared to 2 squares. - In test, shown a less than, equal to, and novel greater than scenario. - Found 10 mo. old children dishabituate for equal to. But do not understand greater or less than. - 14 mo. old children dishabituate for all 3 test conditions. Criticism that this is surprise, NOT dishabituation. (Wynn) Tested impossible mathematical scenarios when adding/subtracting with children. - Had a 1+1 condition, with a possible and impossible scenario, and the same with a 2- 1 condition. - Found the children look longer at the out-come, which is not mathematically correct, the impossible outcome. I.e. 1+1 = 1, or 2-1 = 2. - Expected the correct mathematical outcome. Two hypotheses - Perceptual hypothesis: Infants can do the tasks, but not through an understanding of numbers. - Numerical hypothesis: The idea that children have an innate understanding of numbers. Perceptual (Clearfield ff Mix) children completed the tasks through length, not numbers. [perceptual] Claimed that the children recognised the variances in the different represented 'numbers' in these tasks.