Digitized by Kansas Correctional Industries

Diagnostic paradigms are becoming an alternative to normative approaches in educational assessment. One of the principal objectives of diagnostic assessment is to determine skill proficiency for tasks that demand the use of specific cognitive processes. Ideally, diagnostic assessments should include accurate information about the skills required to correctly answer each item in a test, as well as any additional evidence about the interaction between those cognitive constructs. Nevertheless, little research in the field has focused on the types of interactions (i.e., the condensation rules) among skills in models for cognitive diagnosis. The present study introduces a Bayesian approach to determine the underlying interaction among the skills measured by a given item when comparing among models with conjunctive, disjunctive, and compensatory condensation rules. Following the reparameterization framework proposed by DeCarlo (2011), the present study includes transformations for disjunctive and compensatory models. Next, a methodology that compares between pairs of models with different condensation rules is presented; parameters in the model and their distribution were defined considering former Bayesian approaches proposed in the literature. Simulation studies and empirical studies were performed to test the capacity of the model to correctly identify the underlying condensation rule. Overall, results from the simulation study showed that the correct condensation rule is correctly identified across conditions. The results showed that the correct condensation rule identification depends on the item parameter values used to generate the data and the use of informative prior distributions for the model parameters. Latent class sizes parameters for the skills and their respective hyperparameters also showed a good recovery in the simulation study. The recovery of the item parameters presented limitations, so some guidelines to improve their estimation are presented in the results and discussion sections. The empirical studies highlighted the usefulness of this approach in determining the interaction among skills using real items from a mathematics test and a language test. Despite the differences in their area of knowledge and Q-matrix structure, results indicated that both tests are composed in a higher proportion of conjunctive items that demand the mastery of all skills.

The 4-H Interaction Evaluation Model was developed to illustrate relationships between the 4-H program, as a sub-system, and a larger society as a greater system. The model specifically focused upon cognitive, affective and psychomotor skill development of 4-H boys and girls. Research instruments were designed to assess 4-H member outcomes of the cognitive and affective domains for 4-H members at two levels within the clothing, beef and photography projects.A random sample of 4-H boys and girls enrolled during 1975 in six selected project divisions participated in the study. Selected 4-H members resided in 12 counties in each of three states, Indiana, Nebraska and Missouri. Research instruments were administered as a pre-measurement of existing skill levels to participating 4-H members during May and as a post-measurement of terminal skill levels during September, 1975.Two major hypotheses were developed. Hypothesis I was an inclusive hypothesis of all skills classified as cognitive skills and stated that no significant mean score increases between pre-measurement and post-measurement would occur. Hypothesis II was an inclusive hypothesis stating that no significant mean score differences on three attitudinal sub-scales would occur between the two administrations of the attitude sub-scales.The resulting data were analyzed to determine the proportion of 4-H members performing the specified skills adequately at the time of each administration of the research instrument and the significance of observed mean score differences for each skill assessed. A correlated t test for significance utilizing a one-tailed test was used to test all skills contained under Hypothesis I. A correlated t test for significance utilizing a two-tailed test was used to test attitudinal sub-scale changes under Hypothesis II. All skills contained as sub-hypotheses were rejected at the .05 level of confidence.The following conclusions were based upon the findings of the study:1. Attitude of 4-H members toward the 4-H project division generally change little during one project year.2. Criterion levels established for attitude sub-scales generally are within reach of the 4-H member.3. Terminal 4-H project mean attitude sub-scale scores are generally lower at advanced levels than first year levels indicating that advanced 4-H members hold a more positive attitude toward the project than first year members.4. Attitudinal changes are more likely to occur within the beef and photography projects than in the clothing project. No significant differences were observed in the three attitude sub-scales in the clothing project levels.5. Criterion levels established for cognitive objectives are either too high for all but ten of the cognitive objectives studied or the project experiences are inadequate to guarantee 4-H member achievement.6. Among the three beginning 4-H project divisions, increased levels of measured cognitive achievement occurred most frequently in the clothing project and least frequently in the photography project difference among the three projects is not observable for the advanced divisions. 7. Measured cognitive gains are more frequent for beginning project divisions in Indiana and Nebraska while for Missouri, the gains are more frequent for advanced project divisions.8. Generally, a larger number of 4-H members can reach specified criterion levels for objectives on the post-test than on the pretest.9. Except for the beef project in Indiana, the increase in percentage of 4-H members reaching criterion levels from pre-test to post-test is greater for beginning project divisions than advanced project divisions.10. A total of 43 of the 220 objectives developed for the study are inappropriate, evaluation items utilized are inadequate or the attendent project division programs need major revision because terminal cognitive mean scores were lower than entering cognitive mean scores.

Mathematical connection has received increasing attention and become one major goal in mathematics education. Two types of connections are distinguished: (a) between-concept connection, which cuts across two concepts; and (b) within-concept connection, which links two representations of one concept. For example, from the theoretical probability to experimental probability is a between-concept connection; generate a graph of a circle from its equation is a within-concept connection. Based on the directionality, unidirectional and bidirectional connections are discerned. Bidirectional connection portrays a pair of a typical and a reverse connection. The benefits of connections, especially bidirectional connections, are widely endorsed. However, researchers indicated that students and even teachers usually make unidirectional connections, and underlying reasons may be the curriculum and cognitive aspects. Previous studies have reported differences in learning opportunities for bidirectional connections in U.S. and Chinese textbook problems, but few have explored the high school level. This study addressed this issue by comparing the directionality of mathematical connections and textbook-problem features in popular U.S. (the UCSMP series) and Chinese (the PEP-A series) high school mathematics textbook problems. The results indicated that the between-concept condition and unidirectional connections dominated textbook problems. Mathematical topic, contextual feature, and visual feature were most likely to contribute to different conditions of connections. Overall, problems dealing with quadratic relations from Chinese textbooks presented a vigorous network of more unique and total between-concept connections with balanced typical and reverse directions than the U.S. counterparts. Problems from U.S. textbooks showed a denser network of (a) within-concept connections in two topics and (b) between-concept connections in probability and combinatorics than the Chinese counterparts, but still exhibited an emphasis on specific concepts, representations, and directionality. The study reached a generalized statement that the new-to-prior knowledge direction was largely overlooked in textbook problems. The results have implications for adopting graph theory and Social Network Analysis to visualize and evaluate mathematical connections and informing mathematics teachers and textbook authors to pay attention to the new-to-prior knowledge connection.