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"Gabriele Kaiser"
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Flipped classroom as a reform-oriented approach to teaching mathematics
Innovative methods can change the paradigm of teaching mathematics and inspire teachers to espouse new ideas and gain new experiences. The flipped classroom (FC) is currently an innovative pedagogical approach that has high potential to transform the teaching of mathematics. In the case study described in this paper, we investigated one mathematics teacher's transformation of teaching in two mathematics classrooms through implementing interventions based on FC methods; furthermore, we identified several key points of FC design as well as challenges and opportunities afforded by teaching mathematics in FCs. The results of the study showed that the tasks posed by the teacher, the implemented discourse, teacher feedback and scaffolding, and the teaching-learning environment were changed in FCs, although the approaches used by the teacher to analyze the tasks and students' learning were similar to those used in non-FCs, which points out the strengths of traditional teaching approaches. The study indicates that although teaching mathematics in FCs created some difficulties for teaching, well-designed FCs offered a great opportunity to promote students' mathematical thinking and understanding. Overall, the results highlight that through FC, teachers can develop students' mathematical potential with FCs. [Author abstract]
Journal Article
Architecture in Austria in the 20th and 21st centuries
Revised, updated and expanded by nearly 100 projects, this new edition of the catalog for the 'a_show,' Architekturzentrum Wien's (Az W) permanent exhibition on Austrian architecture of the 20th and 21st century, has become a stand-alone reference book. Its scope extends beyond the themes of the exhibition. Apart from condensing the current discourse on Austrian architecture of the last 150 years, it also documents relevance and singularity of the Az W collection. Featuring more than 2300 images and plans, accompanied by explanatory texts structured chronologically as well as thematically the book points out both historical connections and contemporary tendencies. Paired with a timeline, offering also an overview of all relevant media since 1836, brief biographies, and an index, this is the authoritative survey of modern and contemporary Austrian architecture.
Book
Competence Measurement in (Mathematics) Teacher Education and Beyond: Implications for Policy
Teacher education and the professional development of teachers has become a prominent topic in recent policy discussions worldwide. However, many educational changes have been carried out without clear reference to the results of empirical studies evaluating the efficiency of teacher education programs. This paper aims to contribute to this discussion. It provides an overview on the current knowledge derived from empirical research on the structure of the professional competence of teachers and competence development during teacher education. First, a description of a theoretical framework for the professional competence of teachers and their impact of competence measurement with pre- and in-service mathematics teachers is given. Then, the competence development of teachers at the transition from teacher education into teaching practice and the relation to instructional quality and student learning gains is described. Finally, implications for policy are outlined, emphasizing the necessity of a sound knowledge base in teacher education, which has to be complemented by professional noticing accounting for situated facets of teacher competence. Due to the dynamic acquisition of teacher competence through practical learning opportunities in early career teaching, strong professional development measures are needed.
Journal Article
Can mathematical modelling work as a creativity-demanding activity? An empirical study in China
Creativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-
solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling has recently been introduced as one of the six core competencies in the Chinese mathematical curriculum and is built on
students' ability to solve real-world problems using mathematical means. As mathematical modelling is characterised by openness regarding the understanding of complex real-world problems and the complex relationship between the real
world and mathematics, for the strengthening of creativity, mathematical modelling activities seem to be adequate to accomplish this purpose. In this paper, we describe a study with 71 upper secondary school students, 50 pre-service
mathematics teachers, and 66 in-service mathematics teachers, based on an extended didactical framework regarding mathematical modelling as a creativity-demanding activity. The results of the study indicate a significant correlation
between modelling competencies and creativity aspects. Especially significant correlations between the adequacy of the modelling approaches and the two creativity aspects of usefulness and fluency could be identified, as well as a
significant negative correlation between usefulness and originality. The results of the correlational analysis of relationships among the four criteria were not always consistent in the three participant groups. Overall, the results have
implications for the promotion of creativity for various expertise groups and demonstrate the dependency of the modelling activities on the mathematical knowledge of the participants and the mathematical topic with which they are
dealing. [Author abstract]
Journal Article
Mathematics teacher learning to notice : a systematic review of studies of video-based programs
Teacher noticing has become increasingly acknowledged as a fundamental aspect of teacher professional competence. Teacher education scholars have examined how the development of noticing might be supported both in initial teacher
education and in professional development. In mathematics teacher education, several studies have explored the use of video as a supporting tool for teacher noticing. It remains unclear how this body of work builds on the various
theoretical perspectives of noticing prevalent in the literature, thus broadening our understanding of noticing. Furthermore, the field has not examined systematically the extent to which research has leveraged the affordances of digital
video technologies, and whether scholars have employed different research methods to answer questions that are critical to teacher educators. This survey paper reviews studies published in the last two decades on programs centered on
mathematics teacher noticing that used video as a supporting tool for teacher learning. Thirty-five peer-reviewed papers written in English were identified and coded along three dimensions: (1) theoretical perspectives; (2) use of video
technologies; and (3) research questions and methods. This review summarizes important findings and highlights several directions for future research. Most studies involved pre-service teachers, and only a few centered on in-service
teachers. Developers of the large majority of programs took a cognitive psychological perspective and focused on the attending/perceiving and interpreting/reasoning facets of noticing. Few studies used video-based software and few
studies used grouping, and even fewer used randomized grouping. Evidence of program effects on responding and decision making, and on instructional practice, is limited and should be extended in the future. [Author abstract]
Journal Article
Numeracy, adult education, and vulnerable adults : a critical view of a neglected field
This survey paper examines selected issues related to the intersection of three broad scholarly areas: numeracy, adult education, and vulnerability. Numeracy encompasses the ways in which people cope with the mathematical, quantitative, and statistical demands of adult life, and is viewed as an important outcome of schooling and as a foundational skill for all adults. The focus on vulnerability stems from the realization that concerns of policy makers and educators alike often center on populations seen as vulnerable. The paper is organized in five sections. After a brief introduction, Section 2 examines adult numeracy, focusing on five numeracy domains (health, financial, digital, civic, and workplace numeracy), literacy-numeracy linkages, functional and critical aspects of numeracy, and the centrality of numeracy practices, and notes sources of vulnerability for each of these. Section 3 sketches formal, non-formal and informal contexts in which adults learn or develop their numeracy, and examines factors that may be potential sources of vulnerability, including systemic factors and dispositional and affect factors. Section 4 reflects more broadly on the concept of vulnerability, introduces selected aspects of the papers published in this issue of ZDM Mathematics Education, and points to findings regarding adult learners who may be deemed vulnerable. The closing section summarizes conclusions and research directions regarding the intersection of the three core domains. Overall, the paper points to emerging research needs and educational challenges that are relevant to scholars, practitioners, and policy makers interested in developing the numeracy of adults as well as in the mathematics education of younger learners. [Author abstract]
Journal Article
Growth of professional noticing of mathematics teachers : a comparative study of Chinese teachers noticing with different teaching experiences
The last decade has witnessed increasing interest in the study of teacher noticing in mathematics education research; however, little is known about the growth of teacher noticing and how it is influenced by teaching practice.
Departing from the expert-novice-paradigm, in this paper we address this research gap by a cross-sectional study that investigates how Chinese mathematics teachers' noticing is affected by their developmental stage, measured by the
length of their teaching experience. The study included 152 pre-service teachers at the end of their initial teacher education, 162 early career teachers with one to five years' teaching experience, and 123 experienced mathematics
teachers with more than 15 years' teaching experience, who participated in a video-based assessment of their noticing competency conceptualized by the sub-facets of perception, interpretation, and decision-making. Our findings indicate a
nearly linear growth in teacher noticing among Chinese mathematics teachers, with significant differences identified between pre-service and experienced teachers and only small differences between pre-service and early career teachers.
Analyses using the method of Differential Item Functioning (DIF) further suggest that pre-service and early career teachers demonstrated strengths in aspects more related to reform-oriented or Westernized approaches to mathematics
teaching, such as working with open-ended tasks, identifying characteristics of cooperative learning, and mathematical modeling tasks. By contrast, experienced teachers demonstrated strengths in perceiving students' thinking, evaluating
teachers' behavior, and analyzing students' mathematical thinking. Our findings further highlight that the three sub-facets of teacher noticing develop differently within the three participating groups of teachers. These findings suggest
that teaching experience acts as one influential factor in the development of teacher noticing in the Chinese context. [Author abstract]
Journal Article
Relationship between pre-service mathematics teachers' knowledge, beliefs and instructional practices in China
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. [Author abstract]
Journal Article
Exploring the Benefits and Drawbacks of AR and VR Technologies for Learners of Mathematics: Recent Developments
Despite the growing interest in the field, the overall impact of augmented reality (AR) and virtual reality (VR) on mathematics learning remains unclear, with previous studies reporting mixed results. Moreover, to date, no systematic review has evaluated the potential of AR/VR in mathematics education, including its benefits and drawbacks for learners. To address this gap, the present systematic literature review aims to identify research trends, determine characteristics and methodologies, and explore the potential benefits and drawbacks of AR/VR technologies in mathematics learning based on existing empirical studies. In accordance with the PRISMA guidelines, we analyzed 59 peer-reviewed journal articles published in English that focused on AR/VR implementation in mathematics education. The review determined that geometry was the most widely studied topic of mathematics, with several studies focusing on the use of AR/VR to assist students with learning disabilities. The present review offers evidence for the potential of AR/VR potential in consolidating learners’ socio-emotional, cognitive/meta-cognitive, and pedagogical development in mathematics learning. Nevertheless, a few issues, including technological glitches, cost, start-up effort, health issues, and unfamiliarity with AR/VR, pose challenges to the successful application of AR/VR in the classroom. This systematic review contributes to the existing body of knowledge in the field and recommends avenues for future research.
Journal Article