Selecting Mathematical Tasks for Assessing Student's Understanding: Pre-Service Teachers' Sensitivity to and Adaptive Use of Diagnostic Task Potential in Simulated Diagnostic One-To-One Interviews

Teachers' diagnostic competences are regarded as highly important for classroom assessment and teacher decision making. Prior conceptualizations of diagnostic competences as judgement accuracy have been extended to include a wider understanding of what constitutes a diagnosis;novel models of teachers' diagnostic competences explicitly include the diagnostic process as the core of diagnosing. In this context, domain-general and mathematics-specific research emphasizes the importance of tasks used to elicit student cognition. However, the role of (mathematical) tasks in diagnostic processes has not yet attracted much systematic empirical research interest. In particular, it is currently unclear whether teachers consider diagnostic task potential when selecting tasks for diagnostic interviews and how this relationship is shaped by their professional knowledge. This study focuses on pre-service mathematics teachers' selection of tasks during one-to-one diagnostic interviews in live simulations. Each participant worked on two 30 mins interviews in the role of a teacher, diagnosing a student's mathematical understanding of decimal fractions. The participants' professional knowledge was measured afterward. Trained assistants played simulated students, who portrayed one of four student case profiles, each having different mathematical (mis-)conceptions of decimal fractions. For the interview, participants could select tasks from a set of 45 tasks with different diagnostic task potentials. Two aspects of task selection during the diagnostic processes were analyzed: participants' sensitivity to the diagnostic potential, which was reflected in higher odds for selecting tasks with high potential than tasks with low potential, and the adaptive use of diagnostic task potential, which was reflected in task selection influenced by a task's diagnostic potential in combination with previously collected information about the student's understanding. The results show that participants vary in their sensitivity to diagnostic task potential, but not in their adaptive use. Moreover, participants' content knowledge had a significant effect on their sensitivity. However, the effects of pedagogical content and pedagogical knowledge did not reach significance. The results highlight that pre-service teachers require further support to effectively attend to diagnostic task potential. Simulations were used for assessment purposes in this study, and they appear promising for this purpose because they allow for the creation of authentic yet controlled situations

Cognitive and Motivational Person Characteristics as Predictors of Diagnostic Performance: Combined Effects on Pre-Service Teachers' Diagnostic Task Selection and Accuracy

The acquisition of diagnostic competences is an essential goal of teacher education. Thus, evidence on how learning environments facilitate pre-service teachers' acquisition of corresponding competences is important. In teacher education, approximations of practice (such as simulations) are discussed as being learning environments that can support learners in activating acquired knowledge in authentic situations. Simulated diagnostic interviews are recommended to foster teachers' diagnostic competences. The conceptualization of diagnostic competences highlights the importance of cognitive and motivational characteristics. Motivational learning theories predict that the activation of acquired knowledge in learning situations may be influenced by motivational characteristics such as individual interest. Although teachers' diagnostic competences constitute an increasing research focus, how cognitive and motivational characteristics interact when shaping the diagnostic process and accuracy in authentic learning situations remains an open question. To address this question, we report on data from 126 simulated diagnostic one-on-one interviews conducted by 63 pre-service secondary school mathematics teachers (students simulated by research assistants), studying the combined effects of interest and professional knowledge on the diagnostic process and accuracy. In addition to the main effect of content knowledge, interaction effects indicate that participants' interest plays the role of a door-opener for the activation of knowledge during simulation-based learning. Thus, the results highlight the importance of both, cognitive and motivational characteristics. This implies that simulation-based learning environments should be designed to arouse participants' interest to support their learning or to support less interested learners in activating relevant knowledge

Simulation-based learning environments: do they affect learners’ relevant interests?

The use of simulation-based learning environments to foster professional competences attracts more and more research. The role of participants’ interest for learning is quite undisputable also in this context. Recent research findings emphasize that interest may trigger the activation of professional knowledge during participation in a simulation. Using data from N = 81 pre-service teachers who participated in four simulations over one semester, this contribution investigates how characteristics of the simulation (roleplay vs. video) and participants’ perception of the simulation affect the development of participants’ interests. Results reveal that, beyond the perception of the simulation, development of participants’ interests is weakly related to simulation characteristics

Simulationsbasierte Lernumgebungen: Beeinflussen diese das Interesse der Lernenden?

Zur Förderung professioneller Kompetenzen von (angehenden) Lehrkräften wird vermehrt der Einsatz simulationsbasierter Lernumgebungen diskutiert. Wie auch in anderen Lernkontexten spielt dabei das Interesse der Lernenden eine zentrale Rolle. Forschungsergebnisse deuten darauf hin, dass die Aktivierung relevanter Wissensaspekte während simulationsbasiertem Lernen mit dem Interesse der Teilnehmenden zusammenhängt (Kron et al., 2022). Unklar ist, ob dieses Interesse durch Eigenschaften der Simulation auch beeinflusst werden kann. Dieser Beitrag untersucht Effekte unterschiedlicher Präsentationsformate von Simulationen und deren Erleben auf das Interesse der Lernenden

Die Reifung der GABAergen Inhibtion und die Änderung des Verhältnisses an inhibitorischen und exzitatorischen Neuronen in neokortikalen Neuronenkulturen

81 Seiten, Illustrationen, Diagramm

From Religion to Dialectics and Mathematics

Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory (German: Ausdehnungslehre) in 1844