The study explored the relationships among instructional leadership, professional learning community components, and teacher self-efficacy in the context of mainland China. Study subjects were 1082 elementary school teachers participating in a questionnaire survey. The results showed that instructional leadership had significant effects on the five professional learning community components, four of which, collaborative activity, collective focus on student learning, de-privatized practice, and reflective dialogue, positively predicted teacher self-efficacy. Analysis showed that collaborative activity, de-privatized practice, and reflective dialogue significantly mediated the effects of instructional leadership on teacher self-efficacy. Implications for school leadership and teacher learning are discussed.

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Modeling of the variogram is a critical step for most geostatistical methods. However, most of the prevalent variogram-based solutions are designed without sufficient consideration of the effect of the interpolation process on their application. This paper proposes an automated variogram modeling framework, which simultaneously considers the fit of the experimental variogram and interpolation accuracy in the modeling variogram interpolation result. The variogram modeling framework can be treated as a nonlinear optimization problem with two sub-goals. The first is to optimize the goodness of fit between the experimental and theoretical variogram values under the conditions of their designated parameters. Second, we seek to optimize the difference between measured values and the associated kriging estimates with the candidate variogram model. A typical case study was chosen using a public dataset to test the proposed method, which was implemented using a genetic algorithm, and its performance was compared with the ones of other commonly applied variogram modeling approaches. As expected, the traditional variogram modeling method that only considers fitting standard experimental variograms showed severe sensitivity to errors in data and parameters; classical cross-validation modeling results tended to overlook the experimental variograms. By contrast, the proposed method succeeded in producing variogram models with robust, high-quality kriging estimates and favorable fitness of experimental variograms in a more powerful and flexible way.

Many geoscience problems involve predicting attributes of interest at un-sampled locations. Inverse distance weighting (IDW) is a standard solution to such problems. However, IDW is generally not able to produce favorable results in the presence of clustered data, which is commonly used in the geospatial data process. To address this concern, this paper presents a novel interpolation approach (DIDW) that integrates data-to-data correlation with the conventional IDW and reformulates it within the geostatistical framework considering locally varying exponents. Traditional IDW, DIDW, and ordinary kriging are employed to evaluate the interpolation performance of the proposed method. This evaluation is based on a case study using the public Walker Lake dataset, and the associated interpolations are performed in various contexts, such as different sample data sizes and variogram parameters. The results demonstrate that DIDW with locally varying exponents stably produces more accurate and reliable estimates than the conventional IDW and DIDW. Besides, it yields more robust estimates than ordinary kriging in the face of varying variogram parameters. Thus, the proposed method can be applied as a preferred spatial interpolation method for most applications regarding its stability and accuracy.