Search

Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling competencies. The study described in this paper was a systematic literature review of the literature on modelling competencies published over the past two decades. Based on a full-text analysis of 75 peer-reviewed studies indexed in renowned databases and published in English, the study revealed the dominance of an analytical, bottom-up approach for conceptualizing modelling competencies and distinguishing a variety of sub-competencies. Furthermore, the analysis showed the great richness of methods for measuring modelling competencies, although a focus on (non-standardized) tests prevailed. Concerning design and offering for fostering modelling competencies, the majority of the papers reported training strategies for modelling courses. Overall, the current literature review pointed out the necessity for further theoretical work on conceptualizing mathematical modelling competencies while highlighting the richness of developed empirical approaches and their implementation at various educational levels. [ABSTRACT FROM AUTHOR]

Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting. Specifically, we investigated if they even attend to invariant properties; what invariant properties they discern and discuss; and how DGE can support such discernment. Our analysis found that teachers tend to discern and discuss invariant properties mainly when they were probed to consider invariance. We also found four categories of invariant properties that seem to be important for a robust and rich understanding of geometric objects in the context of invariance and DGE. The use of DGE allowed teachers to see and interact with invariant properties, thus suggesting that accessing geometry dynamically may have structural affordances especially when exploring invariance. Teachers were able to enact different DGE movements to discern and discuss invariant properties, as well as to reason with and about them. We also saw that teachers' backgrounds and past experiences can play an important role in their descriptions of invariant properties. Possible future research directions and implications to teacher education are discussed. [ABSTRACT FROM AUTHOR]

Teaching mathematical modeling is a demanding task. Thus, fostering teachers' competencies in this regard is an essential component of teacher education. Recent conceptualizations of teachers' competencies include situation-specific skills based on the concept of noticing, which is of particular interest for the spontaneous reactions needed when teaching mathematical modeling. The study described in this paper aims to analyze the development of a video-based instrument for measuring teachers' noticing competencies within a mathematical modeling context and obtain evidence for the validity of the instrument. Three kinds of validity are examined in three different studies: content validity, elemental validity and construct validity. Indicators for content validity could be found through different expert ratings and implementation with the target group, where participants were able to perceive all relevant aspects. The qualitative analysis of participants' reasoning, which is consistent with the coded level, indicates elemental validity. Moreover, the results of the confirmatory factor analysis suggest construct validity with one overall factor of noticing competence within a mathematical modeling context. Taken together, these studies imply a satisfactory validity of the video-based instrument. [ABSTRACT FROM AUTHOR]

Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers' professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions. [ABSTRACT FROM AUTHOR]

This study addresses teachers' activity when working with digital technologies (DT) in their classrooms. We build upon a model that considers teaching as managing open dynamic situations. Within the model, teachers' activity is viewed as diagnosing students' mathematical activity, managing uncertainties due to the characteristics of the situation and decision-making about didactic interventions. The study extends our earlier work and focuses on teachers' interventions in DT-based lessons, as they manage disturbances caused by unexpected difficulties. Our first observation is that there is a substantial change in how teachers diagnose these difficulties compared to paper-and-pencil environments. Notably, they need to make more inferences about the pedagogical support that is provided. Second, we show that in such conditions, rather than facing the single dynamicity of the class as a whole, the teacher has to deal with multiple, open dynamic situations (small groups named mini-classes), which are themselves intertwined in the dynamics of students' interactions with technology. Moreover, even if teachers are able to make reliable inferences concerning an individual student's current difficulties, they must also be able to make inferences about the scope of such difficulties within the class as a whole. We present four case studies that illustrate the diverse approaches that teachers take when managing such open dynamic situations and use them to illustrate the concepts and analytical tools that are introduced. [ABSTRACT FROM AUTHOR]

This paper reports changes of the quality of instruction and students' attitudes towards mathematics at one high school during 3 years while teachers participated in a teacher community. The setting for this research was a small-sized high school in South Korea with 154 students and three mathematics teachers. I analyzed the teachers' mathematics classes based on types of interaction, types of questions, and mathematical quality in instruction. Their students' responses for the National Assessment of Educational Achievement study about attitudes towards mathematics were also analyzed. The findings show that this school, over all, improved the mathematical quality and changed the types of questions and the types of interactions towards students' participation in discussing, exploring, and probing mathematical meanings. The students' attitudes towards mathematics became more positive throughout the 3-year period. However, the changes in each teacher's mathematics instruction were different. This study discusses the challenges of having an effective teacher community and researching teachers as learners. [ABSTRACT FROM AUTHOR]

Integrated Science, Technology, Engineering and Mathematics (STEM) education is an emerging approach to improve students’ achievement and interest in STEM disciplines. However, the implementation of integrated STEM education depends strongly on teachers’ competence, which entails, among others, teachers’ attitudes. Nonetheless, not much is known about the factors that influence teachers’ attitudes toward teaching integrated STEM. Therefore this paper uses a survey method to get insight into the relationship between three groups of variables and teachers’ attitudes toward teaching integrated STEM: teacher background characteristics, personal attitudes and school context variables. The results of the multiple regression analyses reveal three variables that are positively linked with teachers’ attitudes: professional development, personal relevance of science and social context. Moreover two variables show a negative correlation: having more than 20 years of teaching experience and experience in mathematics. The results of this study provide valuable information about factors related to teachers’ attitudes toward teaching integrated STEM. Moreover, these results can be deployed by school administrators to guide them when implementing integrated STEM education in their school. [ABSTRACT FROM AUTHOR]

This paper focuses on kindergarten teachers' interactions with young children during mathematical learning activities involving the use of digital tools. We aim to characterise the teachers' roles and actions in these activities and extend considerations of teachers' orchestrations current in the research literature with regard to agency and mediation. Our analysis of teacher-children-digital tool interaction reveals that the kindergarten teachers took three roles in their work with young children, which we call Assistant, Mediator and Teacher roles. These roles were used interchangeably and purposefully by the kindergarten teachers. With regard to agency and mediation, we argue that agency is distributed over the human and non-human agents in the activity and that agency and mediation are interrelated. [ABSTRACT FROM AUTHOR]