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
Teacher noticing has become a prominent construct in research on teacher education and professional development; however, the current state of research is quite diverse, with different theoretical ...foundations and a variety of research designs. The study described in this paper provides a systematic review of the literature on teacher noticing published over the past two decades. Based on a full-text analysis of 182 articles published in renowned databases and peer-reviewed Englishscholarly journals, the study reveals the dominance of a cognitive-psychological perspective of teacher noticing, especially in combination with qualitative studies. Although teacher noticing has been described as a holistic concept in many earlier articles, more recent studies from the last decade tend to differentiate teacher noticing into different facets. Overall, qualitative studies with small sample sizes are prevalent, which allows for fine-grained analysis but limits the generalizability of findings. This study highlights the limitations of the current discussion, such as the prevalence of teacher noticing mainly in the field of mathematics education and the low representation of work from parts of the world other than North America and Europe. In addition, the studies under consideration in this literature review are examined in depth in terms of their findings on improving teachers’ noticing through interventions and on comparisons between experts and novices, which allows for a discussion of the implications of learning to notice for teacher education and professional development.
•Full text analysis of 182 articles on the topic of teacher noticing.•Dominance of qualitative studies on noticing as theoretical foundation.•Recent studies differentiate sub-facets of noticing.•Dominance of studies with small sample sizes, which limit the generalizability of findings.•Predominance of U.S. and European studies without consideration of cultural differences.•Improvement of teacher noticing through interventions.•Expert-novice differences in teacher noticing.
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
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
Mathematics classrooms are typically characterized by considerable heterogeneity with respect to students' knowledge and skills. Mathematics teachers need to be highly attentive to students' ...thinking, learning difficulties, and any misconceptions that they may develop. Identification of potential errors and appropriate ways to approach them is crucial for attaining positive learning outcomes. This paper explores which knowledge and affective-motivational skills teachers most require to effectively identify and approach students' errors.
To address this research question within the German follow-up study of the Teacher Education and Development Study in Mathematics (TEDS-M), 131 primary school mathematics teachers' ability to identify students' errors was assessed based on (a) a digitalized speed test showing different students' solutions in a written notation and (b) three video vignettes that showed different scenes from mathematics classes. These scenes dealt, among other things, with children who struggled with the lesson's mathematical content. Teachers were asked to analyze students' thinking and to determine how best to react. In addition, teachers' mathematics pedagogical content knowledge, mathematical content knowledge, and beliefs were assessed in separate tests and served as predictors for teachers' abilities to identify, analyze, and deal with students' errors.
The results indicate that all components are interrelated. However, path analysis reveals that teachers' ability to deal with students' errors is mainly predicted by their constructivist beliefs while their ability to quickly identify typical students' errors is largely dependent on their mathematics content knowledge.
The results show the central filtering function of beliefs. Teachers who believe that students must shape and create their own learning processes are more successful in perceiving and analyzing student errors in classroom situations. They may understand errors as learning opportunities and - thus - pay specific attention to these occurrences.
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
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
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
Recent research on the professional competencies of mathematics teachers, which has been carried out during the last decade, is characterized by different theoretical approaches on the ...conceptualization and evaluation of teachers' professional competencies, namely cognitive versus situated approaches. Building on the international IEA Teacher Education and Development Study in Mathematics (TEDS-M) and its follow-up study, TEDS-FU, the paper compares cognitive and situated approaches on professional competencies of teachers. In TEDS-FU, the cognitive oriented framework of TEDS-M has been enriched by a situated orientation including the novice-expert framework and the noticing concept as theoretical approaches on the analyses of classroom situations. Correspondingly, the evaluation instruments were extended by using video vignettes for assessing teachers' perception, interpretation, and decision-making competencies in addition to cognitive oriented knowledge tests. The paper discusses the different kinds of theoretical frameworks and the consequences for the evaluation methods, the strengths, and weaknesses of both approaches. Furthermore, connecting the results of TEDS-FU with TEDS-M allows comprehensive insight into the structure and development of the professional competencies of mathematics teachers, the complex interplay between the different facets of teachers' competencies, and the high relevance of teaching practice for the development of these competencies. The analyses show on the one hand that both approaches—cognitive and situated—are needed for a comprehensive description of teachers' professional competencies. On the other hand, it is shown that both approaches can be integrated in a productive way. The paper closes with prospects on further studies coming even closer to the real classroom situation.
PDF
