In this paper, the state of research on the assessment of competencies in higher education is reviewed. Fundamental conceptual and methodological issues are clarified by showing that current controversies are built on misleading dichotomies. By systematically sketching conceptual controversies, competing competence definitions are unpacked (analytic/trait vs. holistic/real-world performance) and commonplaces are identified. Disagreements are also highlighted. Similarly, competing statistical approaches to assessing competencies, namely item-response theory (latent trait) versus generalizability theory (sampling error variance), are unpacked. The resulting framework moves beyond dichotomies and shows how the different approaches complement each other. Competence is viewed along a continuum from traits that underlie perception, interpretation, and decision-making skills, which in turn give rise to observed behavior in real-world situations. Statistical approaches are also viewed along a continuum from linear to nonlinear models that serve different purposes. Item response theory (IRT) models may be used for scaling item responses and modeling structural relations, and generalizability theory (GT) models pinpoint sources of measurement error variance, thereby enabling the design of reliable measurements. The proposed framework suggests multiple new research studies and may serve as a “grand” structural model.

It is widely assumed that teachers play a key role in providing high-quality learning opportunities to students and fostering students’ learning. Yet it is still unclear how specific teacher knowledge facets as part of their professional competence contribute to classroom processes and learning outcomes. Focusing on mathematics education at the secondary level, this study investigates the links between teachers’ pedagogical competence (i.e., cognitive pedagogical facets of their professional competence), instructional quality, and students’ mathematics achievement. The sample comprises mathematics teacher and student data from 59 classrooms in Germany. Student mathematics achievement was measured across two time points (grade 7 and 8). Teachers’ pedagogical competence was tested using two tests measuring their general pedagogical knowledge (GPK) and situation-specific classroom management expertise (CME). Instructional quality was measured using observational rating data from in vivo rating in mathematics classrooms. Research questions on the relation of teachers’ competence and students’ mathematics achievement were answered using multilevel models. Results from multilevel regression analyses indicate that both GPK and CME predict instructional quality. Direct statistical effects on students’ mathematical progress were identified, whereas no indirect statistical effects via instructional quality could be identified. Although teachers’ measured pedagogical competence is not subject-specific, it serves as a significant predictor for cognitive activation as an indispensable part of quality-oriented mathematical teaching and learning processes in the lower secondary mathematics classroom, and it contributes to students’ mathematical progress.

This chapter examines how crucial input and process characteristics of schooling are related to cognitive student outcomes. It was hypothesized that teacher quality predicts instructional quality and student achievement, and that instructional quality in turn predicts student achievement. The strengths of these relations may vary across countries, making it impossible to draw universal conclusions. However, similar relational patterns could be evident within regions of the world. These hypotheses were investigated by applying multi-level structural equation modeling to grade four student and teacher data from TIMSS 2011. The sample included 205,515 students from 47 countries nested in 10,059 classrooms. Results revealed that teacher quality was significantly related to instructional quality and student achievement, whereas student achievement was not well predicted by instructional quality. Certain characteristics were more strongly related to each other in some world regions than in others, indicating regional patterns. Participation in professional development activities and teachers’ sense of preparedness were, on average, the strongest predictors of instructional quality across all countries. Professional development was of particular relevance in Europe and Western Asian/Arabian countries, whereas preparedness played an important role in instructional quality in South-East Asia and Latin America. The ISCED level of teacher education was on average the strongest predictor of student achievement across all countries; this characteristic mattered most in the Western Asia/Arabia region.

In this paper we examine the relationship between teachers’ knowledge, beliefs and instructional practices based on a study with 495 Chinese pre-service mathematics teachers. The results indicate that Chinese pre-service mathematics teachers tend to hold mixed beliefs about the nature of mathematics, and a constructivist view about mathematics teaching and learning, and that they are inclined to report that their teaching is inquiry-oriented. Mathematical content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) were found not to correlate with the teachers’ self-reported instructional practice, in contrast to pre-service mathematics teachers’ beliefs, which showed a stronger association with their self-reported inquiry-oriented instructional practice. Moreover, pre-service teachers’ dynamic beliefs about the nature of mathematics, and constructivist beliefs about mathematics teaching and learning, acted as mediators between pre-service mathematics teachers’ MCK, MPCK and instructional practice respectively.

Academic resilience refers to students’ capacity to perform highly despite a disadvantaged background. Although most studies using international large-scale assessment (ILSA) data defined academic resilience with two criteria, student background and achievement, their conceptualizations and operationalizations varied substantially. In a systematic review, we identified 20 ILSA studies applying different criteria, different approaches to setting thresholds (the same fixed ones across countries or relative country-specific ones), and different threshold levels. Our study on the validity of these differences and how they affected the composition of academically resilient students revealed that the classification depended heavily on the threshold applied. When a fixed background threshold was applied, the classification was likely to be affected by the developmental state of a country. This could result in an overestimation of the proportions of academically resilient students in some countries while an underestimation in others. Furthermore, compared to the application of a social or economic capital indication, applying a cultural capital indicator may lead to lower shares of disadvantaged students classified as academically resilient. The composition of academically resilient students varied significantly by gender and language depending on which indicator of human capital or which thresholds were applied reflecting underlying societal characteristics. Conclusions drawn from such different results depending on the specific conceptualizations and operationalizations would vary greatly. Finally, our study utilizing PISA 2015 data from three countries representing diverse cultures and performance levels revealed that a stronger sense of belonging to a school significantly increased the chances to be classified as academically resilient in Peru, but not in Norway or Hong Kong. In contrast, absence from school was significantly associated with academic resilience in Norway and Hong Kong, but not in Peru.