William M. Bart

An Ordering-Theoretic Method to Determine Hierarchies Among Items.

more closely mirror its algebraic framework. Ordering theory has as its primary intent either the testing of hypothesized hierarchies among items or the determination of hierarchies among items. In ordering theory, response patterns for bivalued items are viewed as atoms in a boolean algebra with as many generators as there are items being considered. An ordering (formerly termed a tree) is the union of the obtained atoms and indicates the logical relationships among the items. Ordering theory shares with classical models the item response matrix, but does not use summation across subject rows to express in the form of the correct responses of a subject his standing on the trait measured. This is the first departure of ordering theory from older models of measurement. These models invariably assume that the trait measured is linearly ordered and can be measured with a simple additive model-e.g., a summative score (Gulliksen,

A functional MRI study of high-level cognition. I. The game of chess.

Chess is a game that involves many aspects of high level cognition and requires sophisticated problem solving skills. However, there is little understanding of the neural basis of chess cognition. This study employed functional magnetic resonance imaging (fMRI) to identify cortical areas that are active during the analysis of chess positions compared with a spatial task with matched visual stimuli. Bilateral activation was revealed in the superior frontal lobes, the parietal lobes, and occipital lobes. Some small areas of activation were observed unilaterally in the left hemisphere. The left hemisphere showed more activation than the right. Results are discussed in relation to a similar brain imaging study on the game Go.

An Ordering Theoretic Method of Multidimensional Scaling of Items

A method for the multidimensional scaling of dichotomous item data is presented which is derived from ordering theory. This method is related to the methodological multivariate extension of Guttmans scalogram analysis developed by Coombs and his students. An example is provided and comparison is provided between the data analytic results of the ordering theoretic method and those of the method of Coombs and his students for their conjunctive model. Some relationships of this method to conventional psychometric data analytic procedures are discussed.

Construction and Validation of Formal Reasoning Instruments

This report describes the construction and validation of paper-and-pencil instruments to test for formal operational thought. Three structurally parallel tests in three content areas and four Piagetian formal thought tasks were administered to 90 scholastically above-average adolescents of 13, 16, and 19 yr. Items were six-choice logic items with abstruse and absurd content. The reasoning tests had substantial content validity, modest concurrent validity, and limited construct validity. These formal reasoning tests could be employed by educators to select students who are capable of abstract conceptualization and theoretically might profit from a curriculum emphasizing symbolic and verbal instruction and an abstract mode of learning.

Scholastic Achievement and Family Marital Structure: Bedouin-Arab Adolescents From Monogamous and Polygamous Families in Israel

Abstract In a sample of Bedouin-Arab adolescents from monogamous and polygamous families in the Negev region of Israel, the authors examined scholastic achievement levels in the subjects of Arabic, English, Hebrew, and mathematics. There were no significant differences in the scholastic achievement levels in those 4 disciplines between adolescents from monogamous families and those from polygamous families. There was, however, a significant interaction between gender and family marital structure for Hebrew scores: Polygamous family structures tended to engender higher Hebrew scores for the male participants, whereas monogamous family structures tended to engender higher Hebrew scores for the female participants. However, the major overall finding was that polygamous family marital structures did not affect deleteriously the scholastic achievement levels of the Bedouin-Arab participants.

The effect of task characteristics on conceptual conflict and information processing in online discussion

A key guidance factor of computer-supported collaborative learning (CSCL) is the specification of a discussion task. Aspects of the discussion task may affect the quality of group discussion for higher-order learning. This experiment investigated the effects of two aspects of discussion task on asynchronous text discussion of an online higher-education course. Groups completed discussion assignments that varied in degree of task context and outcome specification. Content analysis was used to assess conceptual conflict and level of information processing indicated in the online discussions. Results indicate that conceptual conflict is associated with higher-order discussion, but differences in task context and product do not have large effects on the quantity or quality of online discussion.

Some results of ordering theory for guttman scaling

Some of the ramifications of the linear order assumption underlying much of measurement theory are discussed. Ordering theory is then described as an alternative deterministic measurement model that does not make the linear order assumption. With this theory which emanates from Guttmans scalogram analysis, one can examine the ordering properties of sets of test items. One finding of ordering theory for Guttman scaling is that the probability of four or more items forming a Guttman scale is very small. Another finding of ordering theory is that the range of Guttman scales possible for a set of n items is between I and either C(n, n/2) if n is even or C(n, n+1/2) if n is odd. A third finding of ordering theory is that Guttman scales can be classified according to a certain matrix decomposition method.

On the effect of chess training on scholastic achievement

What are the effects of chess training—especially on scholastic achievement among school-aged students? Can chess instruction facilitate the acquisition of scholastic competency? The current state of the research literature is that chess training tends not to provide educational benefits. This article provides a critical review of research on the effects of chess training on the scholastic achievement levels of school-aged students.

The Hierarchical Structure of Formal Operational Tasks.

The hierarchical structure of the formal opera tional period of Piagets theory of cognitive develop ment was explored through the application of or dering theoretic methods to a set of data that sys tematically tapped the various formal operational schemes. The results suggest that the tasks within some schemes are empirically equivalent. While the response patterns were quite varied, the results do suggest that some common structure may underlie performance on the tasks, thus supporting Piagets notion of the integrative structure of the period.

The Effect of "Origami" Practice on Size Comparison Strategy among Young Japanese and American Children

Abstract This study explored the effect of origami practice on size comparison strategies among young Japanese and American children. Forty-six Japanese children and 48 American children, 4 to 6 years old, received three different treatments. Specific treatment children folded origami paper triangles, superimposing the paper shapes to achieve congruence; general treatment children folded traditional origami forms; and control children engaged in conversation with an experimenter. In each task of the pretest and the posttest, children in all conditions were asked to judge the relative sizes of two figures. It was found that the girls under the specific treatment condition increased their strategy of superimposition significantly more than those under the control condition. In addition, the number of children changing their dominant strategy to superimposition or adjustment by two dimensions after the specific or general treatment sessions was significantly larger than that of children changing their strate...