Learning the Natural Numbers as a Child

Abstract

How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the initial segment of the natural numbers on the basis of the Fregean definitions, but do not learn the natural number structure as a whole on the basis of Hume's principle. Therefore, we need to account for some of the consistency of our number concepts with the Dedekind‐Peano axioms in other terms.

Absence perception and the philosophy of zero

“…We would still use zero as a numerosity property to track absences of objects, absence perception and number cognition would still be features of our cognitive make-up, it is just that additional epistemological steps would need to be made in connecting the epistemology to the relevant cognition. Similar remarks apply to Buijsman ( 2017 )’s account of the natural numbers as understood through Hume-style principles. Even if the epistemology is not exactly as we have described it, the underlying account of zero as a property of collections related to absence perception can be transferred to these cases.…”

“…This has been pursued in the cognitive sciences by Núñez 38 who argues that cultural factors are important in determining our epistemology of number (rather than it being “hardwired” by numerosity cognition and then integrated via bootstrapping procedure). In the philosophical literature, Buijsman ( 2017 ) argues that since numerical core cognition is available to infants, bootstrapping procedures fail to explain the ontogenetic delay in infants progressive understanding of the meanings of the numerals “1”, “2”, and “3”.…”

Ethnomathematics: Mathematical Concept in the Local Game of Tong Tong Galitong Ji for High School

“…Hence, the nth term is = 11 + ( − 1)1 or = 10 + , with being a natural number. Natural numbers or in this game are used when the players say ji, ro, lu, and so on (Buijsman, 2019). The quantity of the punishment can be expressed in the form of a linear function (Moss, Boyce, & Lamberg, 2020).…”

How numerals support new cognitive capacities

“…My reason for bringing up this ability is that I think that the acquisition of number concepts relies heavily on it. As I have defended in Buijsman (2017), it is possible to acquire the number concept one on the basis of the ability to distinguish collections with one item from those with more than one item. In effect, this means that children are able to determine that a collection has exactly one item.…”

“…I am not suggesting that children construct such mental models. Instead, I suggest that they recognize the common factor to situations where the word 'two' is correctly applied purely on the basis of an iterated application of this ability to distinguish between one item and more than one item [see Buijsman (2017) for more details on this account of number concept acquisition].…”