Analyzing prospective mathematics teachers’ diagnostic processes in a simulated environment

Abstract

Diagnostic competences are an essential facet of teacher competence. Many studies have investigated the quality of teachers' judgments of students' competences. However, little is known about the processes that lead to these judgments and about the ways to promote these processes in the early phase of teacher training. The aim of the research project on which we report in this paper was to develop a simulated computer-based environment that allows assessing and promoting the diagnostic processes of prospective teachers. In the simulated environment, 'virtual third-graders' solve mathematical problems. Participants are asked to diagnose the students' competence levels according to a theoretical model, which has been empirically validated. Participants can repeatedly select mathematical problems of varying difficulty levels, assign them to a virtual student, and then receive the student's written solution. In this paper, we present the conceptualization of the simulated environment. We also report on the results of a pilot study with 91 prospective primary school mathematics teachers to analyze whether the environment allows an assessment of individual differences in diagnostic processes. The majority of participants rated the environment as authentic and as one in which they could become immersed. Overall, participants were fairly accurate in their diagnoses concerning the student's competence level. However, log data and participants' written notes indicated that there was large variability in their diagnostic processes. Participants varied greatly in the number of mathematical problems they assigned to a student during their diagnostic process, and in how strongly the difficulty of these problems deviated from the student's true competence level. Overall, the data suggest that the simulated environment has the potential to assess diagnostic processes in a valid way. We discuss open questions and issues for further development.

Erforschung potenzieller Entwicklungsverläufe diagnostischer Fähigkeiten angehender Chemielehrkräfte hinsichtlich Lernendenvorstellungen – Die Bedeutung individueller Vorstellungen über Lernendenvorstellungen

“…Für eine Analyse von komplexen Lernendenmerkmalen unter einer fachdidaktischen Perspektive erweist sich diese Art von Videos als eher ungeeignet (von Aufschnaiter und Rogge 2010; Wildgans-Lang et al 2020). Es empfiehlt sich daher, die Komplexität der gezeigten Situationen einerseits zu reduzieren und andererseits auf einzelne Inhalte zu fokussieren (Olson et al 2016;Wildgans-Lang et al 2020). Dies kann bspw.…”

“…Diagnostische Prozesse im Unterrichtsgeschehen sind hochgradig komplex (Heitzmann et al 2019). Zu Zwecken der Förderung diagnostischer Fähigkeiten ist der Einsatz von unterrichtsrealistischen Lernumgebungen daher weniger zielführend (Wildgans-Lang et al 2020). Vielmehr ist eine Reduktion dieser Komplexität bei gleichzeitiger Fokussierung auf einzelne Inhalte bzw.…”

“…Vielmehr ist eine Reduktion dieser Komplexität bei gleichzeitiger Fokussierung auf einzelne Inhalte bzw. Lernende notwendig (Dannemann et al 2019;Heitzmann et al 2019;Wildgans-Lang et al 2020). Larkin (2012) zufolge ist die Fähigkeit Lernendenvorstellungen zu antizipieren und ihren Ursprung zu verstehen eine grundlegende Voraussetzung, um mit ihnen im späteren Berufsalltag umzugehen.…”

Expertise in developing students’ expertise in mathematics: Bridging teachers’ professional knowledge and instructional quality

“…The first theme, addressed in various contributions, involves the construction and validation of instruments aimed at assessing teachers' situated professional knowledge, ranging from scenario-based questionnaires (Gasteiger et al 2020) to video-based assessments (Blömeke et al 2020;Kersting et al 2020;Krauss et al 2020) and online simulation environments (Charalambous 2020;Wildgans-Lang et al 2020). Moderate correlations have been observed between teachers' performances on these measures of situated knowledge and paper-and-pencil tests that are developed following a cognitive perspective on teacher knowledge (Charalambous 2020;Gasteiger et al 2020;Krauss et al 2020).…”

Pre-service mathematics teachers’ knowledge of functions: a mixed methods sequential explanatory study

“…It has also been revealed that there exists a link between Subject-Matter Knowledge (CCK, SCK) and Pedagogical Content Knowledge (KCS). KCS improves instructional quality of mathematics teachers(Ünver, Özgür, and Güzel, 2020;Wildgans-Lang et al, 2020; Yang et al, 2020) Thus, mathematics teacher education providers in Zambian colleges of education and universities are urged to design educational courses that are aimed at addressing secondary school mathematics. The said courses should have special focus on the concept of a function because it is a central topic in secondary school mathematics and in advanced university mathematics.…”