Modeling, Measuring and Fostering (Pre-Service) Teachers’ Professional Knowledge to Integrate Technologies in Mathematics Education

Abstract

Mathematics plays a pivotal role in our rapidly changing world as it drives technological progress, facilitates scientific breakthroughs, and cultivates critical thinking necessary for addressing complex global challenges. Acquiring mathematical knowledge is therefore considered crucial in educational policy. In this context, digital technologies hold the potentials to support students in gaining a profound understanding of mathematics. For these potentials to unfold, however, technologies must be integrated effectively in the classroom by the teacher. Against this background, teachers’ professional knowledge is a regarded as a crucial pre-requisite for implementing technologies in a way that supports students’ conceptual understanding of mathematics. This professional knowledge of teachers is prominently subsumed under the term Technological Pedagogical Content Knowledge (i.e., TPCK), a knowledge component which extends beyond other knowledge components such as Pedagogical Content Knowledge (i.e., PCK) and Technological Knowledge (i.e., TK). Despite its relevance for education and beyond, however, little is known about the precise nature of mathematics-specific TPCK which is likely a result of the predominant use of self-reports in respective studies which have shown to induce validity issues. Also, the lack of reliable test-based instruments to assess mathematics-specific TPCK impedes the investigation of the relationship between TPCK and other knowledge components, leaving the theoretical underpinnings of TPCK unclear. Additionally, insights into how to effectively prepare (pre-service) teachers to teach with technologies in mathematics are limited as self-reported data only provides distal proxy for competence growth. Against this background, the present dissertation’s overarching goal was to provide a comprehensive investigation into the nature of mathematics-specific TPCK with a specific focus on how such knowledge could be assessed in an objective way, and how it could be fostered within mathematics-specific short-term interventions. To address these objectives, I conducted a total of three studies. In the first study, I extended beyond mathematics to various subject domains and conducted a comprehensive systematic review of prior TPCK interventions based on 166 primary studies. The aim of this study was to discern whether TPCK has predominantly been conceptualized from a pedagogical, technological, or subject-specific perspective. Moreover, within a subsequent meta-analysis, I investigated the effectiveness of TPCK-interventions. In contrast to prior meta-analyses, I included only studies in this meta-analysis that applied test-based instrument to adequately capture competence growth. In the second study, I focused on mathematics-specific TPCK, proposing it to be knowledge necessary to provide high-quality instruction with technologies in mathematics. Using a self-developed and piloted instrument to assess mathematics-specific TPCK (consisting of text vignettes describing specific mathematical teaching problems), I empirically examined the relationship between TPCK, PCK and TK and investigated whether PCK is a sub-facet of TPCK or whether TPCK is a distinct knowledge component. In study three, I developed a mathematics-specific intervention to investigate whether evidence-based short-term interventions could be successful in developing pre-service teachers’ TPCK. Across these studies, I carefully considered contextual variables such as participants’ motivational characteristics and demographics, too, in order to obtain an even more comprehensive picture on mathematics-specific knowledge regarding technology integration. The collective findings from this dissertation indicate that TPCK has primarily been approached and viewed from a technology-cantered perspective, as opposed to a subject-specific perspective (study 1). Additionally, while mathematics-specific PCK and TPCK are statistically related, they seem to be distinct knowledge components, highlighting the necessity to specifically focus on mathematics-specific TPCK in pre-service teacher training (study 2). Lastly, it seems possible to foster pre-service teachers’ mathematics-specific TPCK in an intervention, that adheres to principles from both general education research and mathematics education (study 3).