Improving the Effectiveness of Independent Practice with Corrective Feedback

In this action research study of my 8th grade Algebra class, I investigated the effects of teacher-to-student written corrective feedback on student performance and attitude toward mathematics. The corrective feedback was given on solutions for selected independent practice problems assigned as homework. Each problem being assessed was given a score based on a 3- point rubric and additional comments were written. I discovered that providing teacher-to-student written corrective feedback for independent practice problems was beneficial for both students and teachers. The feedback positively affected the attitudes of students and teacher toward independent practice work resulting in an improved quality of solutions produced by students. I plan to extend my research to explore ways to provide corrective feedback to students in all of my mathematics classes.

Space–time zero-inflated count models of Harbor seals

Environmental data are spatial, temporal, and often come with many zeros. In this paper, we included space–time random effects in zero-inflated Poisson (ZIP) and ‘hurdle’ models to investigate haulout patterns of harbor seals on glacial ice. The data consisted of counts, for 18 dates on a lattice grid of samples, of harbor seals hauled out on glacial ice in Disenchantment Bay, near Yakutat, Alaska. A hurdle model is similar to a ZIP model except it does not mix zeros from the binary and count processes. Both models can be used for zero-inflated data, and we compared space–time ZIP and hurdle models in a Bayesian hierarchical model. Space–time ZIP and hurdle models were constructed by using spatial conditional autoregressive (CAR) models and temporal first-order autoregressive (AR(1)) models as random effects in ZIP and hurdle regression models. We created maps of smoothed predictions for harbor seal counts based on ice density, other covariates, and spatio-temporal random effects. For both models predictions around the edges appeared to be positively biased. The linex loss function is an asymmetric loss function that penalizes overprediction more than underprediction, and we used it to correct for prediction bias to get the best map for space–time ZIP and hurdle models.