Absolute and Relative Judgment Accuracy: Early Childhood Teachers' Competence to Evaluate Children's Mathematical Skills

This study examined absolute and relative judgment accuracies of German early childhood (EC) teachers with respect to the mathematical skills of the children under their supervision. The two types of judgment accuracies are crucial prerequisites for pacing activities in EC education and offering differentiated educational activities adapted to individual skill levels of children. Data from 39 EC teachers and 268 children were analyzed using multilevel modeling. Teachers rated the skills of children on a structured observation instrument (“Kinder Diagnose Tool,” KiDiT). Children were assessed on their mathematical skills with a standardized test (“Mathematische Basiskompetenzen im Kindesalter,” MBK-0). On average, 65% of the variation in judgments of teachers on the KiDiT could be explained by MBK-0 scores of children, which suggest that teachers are—on average—able to rank children within their groups. Teachers were also able to judge the mathematical level of skills of children as assessed by the MBK-0. Neither mathematical content knowledge (MCK) of teachers nor their mathematics pedagogical content knowledge (MPCK) or general pedagogical knowledge (GPK) moderated the relationship between judgments of teachers and test scores of children or the relationship between the level of the judgments and the level of test scores. Conclusions for future research and practice are drawn.

PURE ABSTRACTION’S CRITIQUE

Classical philosophy considers the concepts of abstraction and concreteness and as categories of logic, and as an immediately given, sensuously perceived and represented whole. These categories are opposed to each other as some existence of the object of “simple” and the object of “complex” both for their perception in sensation and for understanding in thinking. At the same time it is assumed that there is a certain object of the “original” “simple” element of all that exists, on the basis of which conditions are created for the manifestation of signs of a change in the states and properties of the existence of all that exists, and which “gives rise” to the emergence, development, improvement of objects in a given field of existence in possibility and reality. In this hypothesis signs of contradiction between the possibilities of representing the existence indefinitely small “simple” object (element) and the inability to know about the existence indefinitely large “simple” object (element). Therefore both the categories of the logic of the concept of concrete and abstract have the character of a relative judgment that provides an explanation of the properties of thinking in the processes of experiences of the being of the thinker. However those who think in the given field of existence in the possibility and reality are able to feel and think the signs of their existence in the experience of sensory perception and verbal thinking, and for their limited changes in properties and states, observations and thoughts about the concept of the object of “pure abstraction”, and all objects accessible to observation and thinking for them exist specifically. Object existing in this field, available for experience, is concrete, and object existing outside of experience is “purely abstract”. To attempt to introduce the concept of the object matter of “pure abstraction” is necessary to “get out” of the idea of the existence of a specific space of the object in the experiment and the “look” on all things like a “point of view” of all that exists in the “absence” of his being a thinking observer. In the presence of an observer, everything observed becomes, in his representations, a clearly ordered and formalized concrete concept.

Running head: Relative judgment. When the relative judgment theory proved to be false

A commonly accepted theory is that when witnesses can identify culprits in lineups, they will concentrate on him. On the other hand, when they cannot they compare between lineup members and choose the person most similar to the culprit. Therefore they will divide their gaze more equally between foils. An eye tracker was used with a 48-person lineup (four screens with twelve photos in each) in an attempt to demonstrate the superiority of gaze behavior over the verbal response. Surprisingly witnesses usually concentrated on some foil as much as they did on the target. Alternate theories are required to explain the reduction of false identifications in sequential lineups. The advantage of large lineups was demonstrated. Police may use them in conjunction with eye trackers to find culprits that witnesses focus on despite saying that they are absent, the only known method to increase correct identifications.