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The potential of tasks to foster mathematical learning and understanding is an important aspect of instruction and their implementation in teaching is thus often viewed to be positively related to the quality of instruction. Both the selection of tasks as well as their implementation in the classroom depend on many factors, with teachers' knowledge and skills as one of the most important ones. The present study aims to analyze the relations between different aspects of task potential, the quality of instruction, and teachers' competence in order to investigate whether task potential can be seen as an indicator for teaching quality, for teacher competence, or as an independent construct in models of educational effectiveness. To this end, we draw on data from the TEDS-Validate study, namely tests of mathematics teachers' competence (n = 31) observations in their classrooms (n = 60), and an in-depth analysis of all tasks used in the respective lessons (n = 2490). Multiple regression analysis suggests that while some facets of task potential are related to either teaching quality or teacher competence, the potential of tasks emerges as an independent construct with some characteristics predicting the teaching quality of the respective lessons. Implications of these results for the role of tasks in educational effectiveness research are discussed.

In educational research, teaching quality is extensively studied because of its role of a mediator between teacher characteristics and student learning. However, empirical evidence on differences between video and live scoring of teaching quality is rare. In the present study, thirty lessons from 15 secondary mathematics classrooms in a German metropolitan area were observed. Lessons were scored both live in the classroom and using video recordings. Live and video scoring was conducted by (different) trained observers. Ratings were obtained with a "hybrid" observational instrument that covers generic and subject-specific characteristics of teaching quality in mathematics classrooms. Generalizability analysis and paired t tests were performed to investigate mode effects. The findings showed that in live scoring, classroom management was rated lower, and cognitive activation was rated higher. Rankings of lessons or classrooms were very similar across modes, and reliabilities did not differ to a meaningful extent either, except for classroom management reaching better results for live ratings. This suggests that based on the present findings, classroom observation performed with our hybrid framework of teaching quality generalizes across observation mode only under certain circumstances. Further research is necessary to better understand the relation between observation mode and teaching quality ratings, as well as the impact of the scoring procedures. We discuss the implications of our findings for educational research and practice.

In the existing multidimensional extensions of the log-normal response time (LNRT) model, the log response times are decomposed into a linear combination of several latent traits. These models are fully compensatory as low levels on traits can be counterbalanced by high levels on other traits. We propose an alternative multidimensional extension of the LNRT model by assuming that the response times can be decomposed into two response time components. Each response time component is generated by a one-dimensional LNRT model with a different latent trait. As the response time components--but not the traits--are related additively, the model is partially compensatory. In a simulation study, we investigate the recovery of the model's parameters. We also investigate whether the fully and the partially compensatory LNRT model can be distinguished empirically. Findings suggest that parameter recovery is good and that the two models can be distinctly identified under certain conditions. The utility of the model in practice is demonstrated with an empirical application. In the empirical application, the partially compensatory model fits better than the fully compensatory model.

As digitalisation is becoming increasingly important in educational settings, teachers' key competencies -- in particular, their professional knowledge regarding the integration of information and communication technology (ICT) in the classroom -- warrant targeted development. Aside from their general pedagogical knowledge (GPK), teachers' technological pedagogical knowledge (TPK) and technological knowledge (TK) are becoming increasingly necessary for mastering professional teaching-related tasks (as outlined in the well-known technological pedagogical content knowledge (TPACK) model). To date, however, the question of whether these knowledge facets are discrete or interrelated -- at least, on the basis of standardised assessments -- has remained largely unanswered. In the present study, therefore, a sample of 619 preservice teachers (320 bachelor's and 299 master's students in their second semesters) were considered via an online survey with three different knowledge tests. In this article, we investigate hypotheses concerning the structures of those knowledge facets and further hypothesise that initial teacher education learning opportunities relate to preservice teachers' GPK, TPK, and TK. Our findings reveal that the three knowledge facets can be empirically separated. Master's students outperform bachelor's students in all three tests, however, with effects varying from strong (GPK) to medium (TPK, TK). As expected, pedagogical learning opportunities -- surveyed through students' self-reports -- directly correlate with GPK. By contrast, technological pedagogical and technological learning opportunities are not correlated with TPK and TK, respectively. We discuss the findings' implications for future initial teacher education design -- in particular, the evident need to update the curriculum to meet the needs of the current era of digitalisation.

Spatial orientation and spatial navigation are important abilities. However, large individual differences are common in these spatial abilities, yet satisfying explanations about the origin of such differences are lacking. In this work, we measured the eye-tracking data of 26 participants who freely explored a large city (244 buildings) in an immersive virtual reality for 150 min. After the exploration, participants performed a pointing-to-building task in the same city. For the analysis, we transform the eye-tracking data into gaze-graphs and calculate graph-theoretical measures. We then model participants' mean task performance with a linear model using global gaze-graph measures (R²=0.41). Moreover, a linear model with graph diameter only results in an R² of 0.4; thus, graph diameter can explain 40% of the variance in the mean task performance of participants. Overall, our results show visual behavior, specifically gaze-graph diameter, to be a strong predictor of individual differences in spatial navigation performance.

The Xorde Avesta is considered a collection of shorter Zoroastrian liturgies. Until recently, neither the architecture of the manuscripts in which the Xorde Avesta was handed down was analyzed in detail, nor was the relationship between manuscript and practice adequately described. This article develops the thesis that the representation of the Xorde Avesta in manuscripts and liturgical practice can be understood from the point of a ritual structuring of circular units of time.

The teacher noticing construct is widely recognized in teacher competence and education research, particularly in the field of mathematics education. This paper surveys recent research on mathematics teacher noticing published between July 2019 and 2022, following an earlier literature review on teacher noticing across different disciplines. The study presented here analyzed 118 English-language articles published in peer-reviewed journals, focusing on conceptualizations, research methods, and relationships with other constructs, including teacher knowledge and beliefs. The findings suggest that the cognitive-psychological perspective on noticing, which emphasizes a set of cognitive processes, remains the predominant conceptualization. Recent research on noticing is characterized by a high proportion of studies based on small samples and qualitative research methods. While several studies have demonstrated the interrelatedness of noticing and professional knowledge, the relationship between noticing and beliefs and between noticing and instructional quality has rarely been addressed. Based on these findings, we highlight noteworthy contributions and critical shortcomings, and suggest directions for future research.