Akademik Veri Yönetim Sistemi
Sunum, ss.175-176, 2023
Previous research showed that the development of children’s understanding on micro-infinity (infinity
associated with unlimited division) starts at the age of 11 with mapping a physical quantity onto the
number which is understood as infinitely divisible (i.e., Smith, Solomon & Carey, 2005). However, in
the studies conducted with younger children, micro infinity was investigated through the concrete
object division tasks, which might lead children to use their prior knowledge about physical rules
(i.e., infinite division of concrete objects can not be observed unlike the theoretical division of numbers).Thus, these rules may precede the abstract understanding of micro-infinity. However, little is
known about how younger children understand infinity concepts and infinitesimals (a quantity that is
closer to zero than any standard real number, but that is not zero) without the bias of physical rules.
In this preregistered study, we asked 1) When does children’s understanding of micro-infinity develop,
2) Whether understanding of micro-infinity is affected by knowledge of concrete object divisibility and
3) If the manipulation of physical rules in accordance with the nature of micro-infinity helps children
to profess micro-infinity and infinitesimals in early ages.
Children (N = 80) aged 7, 8, 10, and 11 are displayed to an animation in which a target keeps eating
a cake while biting half of it continually. For half of the children (Fantastic Group Condition), the
scenario takes place in a fantastic world where different physical rules can be applied (i.e., a cake
which can change the eater’s size). In that animation, the target keeps eating half of the cake and
shrinks by half the size. For the other half of the children (Control Group), the story takes place in a
typical world where the target always bite half of the cake in hand without shrinking. In the Fantastic
Group, shrinking of the target makes it possible to observe the continuous division of the object and
it is more suitable for the nature of micro infinity and the concept of infinitesimals.
After the animations are displayed, children are asked, ‘If the target kept biting half of the cake, would
the cake ever disappear completely or always a half piece of cake remain?’. Children’s answers are
coded as -1 or +1 (for negative and positive answers). Also, children who give negative answers are
asked ‘Then, how many times do you think the target could bite the cake?’ Children’s answers are
coded on an interval scale.
We hypothesize that listening to different scenarios (i.e., Fantastic Group vs. Control Group) about
the object divisibility will affect children’s understanding of micro-infinity and the concept of infinitesimals. We expect that children in the Fantastic Group Condition understand micro infinity and the
concept of infinitesimals at an earlier age than children in the Control Group. The findings of our study might help us gain a deep insight into the children’s understanding of different infinity dimensions and their relation to the physical rules of the world.