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Background and Context: In today's increasingly digital world, it is critical that all students learn to think computationally from an early age. Assessments of Computational Thinking (CT) are essential for capturing information about student learning and challenges. When programming is used as a vehicle to foster CT skills, assessment of CT skills needs to measure understanding of programming concepts alongside general problem-solving practices applicable in contexts beyond programming. Objective: In this paper, we discuss the development of and results from separate validated assessments of programming concepts and generic CT practices for 4th-6th grade students. Method: An Evidence-Centered Design approach was used for the development and validation of the assessments, that were used with 15,000 upper elementary students in Hong Kong. Findings: Results from assessment implementation indicate that the assessments worked as designed and reveal student challenges with CT concepts and practices. Implications: These results point to the utility of our assessment as a curricular tool and the need for emphasizing certain CT concepts and practices in future curricular initiatives and teacher professional development.

Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic--the proportion of common variance (PCV)--into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues [(mathematical characters omitted)] overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as [mathematical characters omitted], even with a relatively large sample size of 5,000. Finally, we investigated the use of [mathematical characters omitted] in combination with R-PA and concluded that practitioners can gain additional information from [mathematical characters omitted] and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors.

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The proper reference distribution of eigenvalues assesses the kth factor based on comparison datasets with k-1 underlying factors. Two methods that use the proper reference distribution are revised PA (R-PA) and the comparison data method (CDM). We compare the accuracies of these methods using Monte Carlo methods by manipulating the factor structure, factor loadings, factor correlations, and number of observations. In the 17 conditions in which CDM was more accurate than R-PA, both methods evidenced high accuracies (i.e.,>94.5%). In these conditions, CDM had slightly higher accuracies (mean difference of 1.6%). In contrast, in the remaining 25 conditions, R-PA evidenced higher accuracies (mean difference of 12.1%, and considerably higher for some conditions). We consider these findings in conjunction with previous research investigating PA methods and concluded that R-PA tends to offer somewhat stronger results. Nevertheless, further research is required. Given that both CDM and R-PA involve hypothesis testing, we argue that future research should explore effect size statistics to augment these methods.

Inferences about student knowledge, skills, and attributes based on digital activity still largely come from whether students ultimately get a correct result or not. However, the ability to collect activity stream data as individuals interact with digital environments provides information about students' processes as they progress through learning activities. These data have the potential to yield information about student cognition if methods can be developed to identify and aggregate evidence from diverse data sources. This work demonstrates how data from multiple carefully designed activities aligned to a learning progression can be used to support inferences about students' levels of understanding of the geometric measurement of area. The article demonstrates evidence identification and aggregation of activity stream data from two different digital activities, responses to traditional assessment items, and ratings based on observation of in-person non-digital activity aligned to a common learning progression using a Bayesian Network approach.

The standardized generalized dimensionality discrepancy measure and the standardized model-based covariance are introduced as tools to critique dimensionality assumptions in multidimensional item response models. These tools are grounded in a covariance theory perspective and associated connections between dimensionality and local independence. Relative to their precursors, they allow for dimensionality assessment in a more readily interpretable metric of correlations. A simulation study demonstrates the utility of the discrepancy measures' application at multiple levels of dimensionality analysis, and compares them to factor analytic and item response theoretic approaches. An example illustrates their use in practice.

Past research suggests revised parallel analysis (R-PA) tends to yield relatively accurate results in determining the number of factors in exploratory factor analysis. R-PA can be interpreted as a series of hypothesis tests. At each step in the series, a null hypothesis is tested that an additional factor accounts for zero common variance among measures in the population. Integration of an effect size statistic—the proportion of common variance (PCV)—into this testing process should allow for a more nuanced interpretation of R-PA results. In this article, we initially assessed the psychometric qualities of three PCV statistics that can be used in conjunction with principal axis factor analysis: the standard PCV statistic and two modifications of it. Based on analyses of generated data, the modification that considered only positive eigenvalues ( π ^ SMC : k ′ + Λ ^ ) overall yielded the best results. Next, we examined PCV using minimum rank factor analysis, a method that avoids the extraction of negative eigenvalues. PCV with minimum rank factor analysis generally did not perform as well as π ^ SMC : k ′ + Λ ^ , even with a relatively large sample size of 5,000. Finally, we investigated the use of π ^ SMC : k ′ + Λ ^ in combination with R-PA and concluded that practitioners can gain additional information from π ^ SMC : k ′ + Λ ^ and make more nuanced decision about the number of factors when R-PA fails to retain the correct number of factors. [ABSTRACT FROM AUTHOR]

Using the quantum theory of atoms in molecules a near complete combined directed spanning quantum topology phase diagram (QTPD) was constructed from the nine (H2O)5 reaction-pathways and five unique Poincaré-Hopf solutions that were found after an extensive search of the MP2 potential energy surface. Two new energy minima that were predicted from earlier work are found and include the first (H2O)5 conformer with a 3-DQT quantum topology. The stress tensor Poincaré-Hopf relation indicated a preference for 2-DQT (H2O)5 topologies as well as the presence of coupling between shared-shell OH BCPs to the hydrogen-bond BCPs that share an H NCP. The complexity of the near complete combined QTPD was explained in terms of the O...O bonding interactions that were found in six of the nine (H2O)5 reaction-pathways and for all points of the combined QTPD. The stabilizing role of the O...O bonding interactions from the values of the total local energy density was explored. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The nature of the bonding interactions including the intramolecular SS interactions in tetrasulfur tetranitride, S4N4 are probed by performing very large amplitude vibrations of all of the 18 normal modes of vibration. The QTAIM and stress tensor point properties are -then investigated and found to be highly dependent on the mode of vibration. A considerable degree of metallicity ξ( rb) is found for the SS and SN bonding interactions. A unique bonding feature is found for a small amplitude vibration of the most anharmonic mode of this investigation, mode 2, where the SS bond critical point (BCP) transforms from a closed-shell SS BCP to a shared-shell SS BCP. We find 17 new unique QTAIM topologies for the molecular graphs corresponding to the 18 modes of vibration along with seven 'missing' topologies that are mapped onto a spanning 2-D Quantum topology Phase Diagram (QTPD). In addition, eleven unique topologies existing on 3-D QTPDs are found due to the presence of non-nuclear attractors (NNAs). We use the stress tensor eigenvalues to explain the invariance of the numbers and types of QTAIM critical points. The applicability of both the stiffness S and stress tensor stiffness Sσ are also explored. Two new bond measures are introduced, a polarizability P and the stress tensor polarizability Pσ which are derived from the stiffness S and stress tensor stiffness Sσ, respectively. © 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The objective was to offer guidelines for applied researchers on how to weigh the consequences of errors made in evaluating measurement invariance (MI) on the assessment of factor mean differences. We conducted a simulation study to supplement the MI literature by focusing on choosing among analysis models with different number of between-group constraints imposed on loadings and intercepts of indicators. Data were generated with varying proportions, patterns, and magnitudes of differences in loadings and intercepts as well as factor mean differences and sample size. Based on the findings, we concluded that researchers who conduct MI analyses should recognize that relaxing as well as imposing constraints can affect Type I error rate, power, and bias of estimates in factor mean differences. In addition, fit indexes can be misleading in making decisions about constraints of loadings and intercepts. We offer suggestions for making MI decisions under uncertainty when assessing factor mean differences. [ABSTRACT FROM PUBLISHER]

Parallel analysis (PA) assesses the number of factors in exploratory factor analysis. Traditionally PA compares the eigenvalues for a sample correlation matrix with the eigenvalues for correlation matrices for 100 comparison datasets generated such that the variables are independent, but this approach uses the wrong reference distribution. The proper reference distribution of eigenvalues assesses the k th factor based on comparison datasets with k -1 underlying factors. Two methods that use the proper reference distribution are revised PA (R-PA) and the comparison data method (CDM). We compare the accuracies of these methods using Monte Carlo methods by manipulating the factor structure, factor loadings, factor correlations, and number of observations. In the 17 conditions in which CDM was more accurate than R-PA, both methods evidenced high accuracies (i.e.,>94.5%). In these conditions, CDM had slightly higher accuracies (mean difference of 1.6%). In contrast, in the remaining 25 conditions, R-PA evidenced higher accuracies (mean difference of 12.1%, and considerably higher for some conditions). We consider these findings in conjunction with previous research investigating PA methods and concluded that R-PA tends to offer somewhat stronger results. Nevertheless, further research is required. Given that both CDM and R-PA involve hypothesis testing, we argue that future research should explore effect size statistics to augment these methods., Competing Interests: Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Using the quantum theory of atoms in molecules a near complete combined directed spanning quantum topology phase diagram (QTPD) was constructed from the nine (H 2 O) 5 reaction-pathways and five unique Poincaré-Hopf solutions that were found after an extensive search of the MP2 potential energy surface. Two new energy minima that were predicted from earlier work are found and include the first (H 2 O) 5 conformer with a 3-D QT quantum topology. The stress tensor Poincaré-Hopf relation indicated a preference for 2-D QT (H 2 O) 5 topologies as well as the presence of coupling between shared-shell OH BCPs to the hydrogen-bond BCPs that share an H NCP. The complexity of the near complete combined QTPD was explained in terms of the O…O bonding interactions that were found in six of the nine (H 2 O) 5 reaction-pathways and for all points of the combined QTPD. The stabilizing role of the O…O bonding interactions from the values of the total local energy density was explored. © 2016 Wiley Periodicals, Inc., (© 2016 Wiley Periodicals, Inc.)