Gabriele Kaiser

• Doctor of Education
• Hamburg University

Zusammenfassung In dieser Längsschnittstudie mit zwei Messzeitpunkten wird die Veränderung der Berufsidentität von angehenden Grundschullehrkräften untersucht. Mithilfe eines Online-Fragebogens wurden Daten von Grundschullehramtsstudierenden mit den Fächern Mathematik und Deutsch zu Beginn ihres Studiums ( N = 151) und nach vier Semestern ( N = 101...

The ability to notice and interpret relevant aspects of classroom interactions is central to effective teaching and plays a critical role in teachers' professional development. This study investigated the development and testing of an AI chatbot (NiCo) designed to support preservice teachers' noticing skills. The chatbot was built using the GPT-4o...

This mixed-method study uses interviews and an online questionnaire to investigate the obstacles that hinder teachers’ implementation of mathematical modelling in everyday classrooms in China. Thirty high school mathematics teachers were interviewed, and 200 teachers completed an online questionnaire regarding their perceived obstacles. We identifi...

Although considerable research has been conducted on mathematical modelling and mathematical creativity separately, relatively few studies have explored their intersection. This study builds on the framework established by Lu and Kaiser to conceptualise creativity in mathematical modelling. In the paper an elaborated model of creativity that is uni...

Explanatory videos play an important role in the flipped classroom (FC) approach, which has become highly important especially since the COVID-19 crisis. In this qualitative study, we explore the potential of using explanatory videos (EVs) in mathematical modelling education as important component of FC and assess its merits and deficiencies. We fo...

This study investigated the effects of an innovative professional development program aimed at enhancing teacher noticing skills and professional knowledge in inclusive (mathematics) education in secondary algebra instruction. A total of 653 participants, comprising master’s students, teachers in preparatory service, and in-service teachers from Ge...

This study investigated the effects of an innovative professional development program aimed at enhancing teacher noticing skills and professional knowledge in inclusive (mathematics) education in secondary algebra instruction. A total of 653 participants, comprising master’s students, teachers in preparatory service, and in-service teachers from Ge...

In this paper we explore the importance of critical mathematical thinking (CMT) in mathematics education and present a framework for teachers' support of CMT development. The CMT framework consists of five key dimensions: mathematical capability, critical capability, evaluating, reasoning, and disposition. Together, these dimensions address the kno...

Teacher noticing has become widely accepted as a principal component of teacher competence; it is supported during university teacher education in many activities. However, only a few high-quality standardized measurement instruments exist that capture noticing and allow valid interpretations of how its development depends on factors within univers...

This scoping review provides an overview of standardized instruments used to measure teacher noticing. A systematic literature search identified 37 publications in English-language peer-reviewed journals describing 22 different test instruments. Regarding the underlying conceptualization of noticing, instruments commonly distinguish mental processe...

The teacher noticing construct is widely recognized in teacher competence and education research, particularly in the field of mathematics education. This paper surveys recent research on mathematics teacher noticing published between July 2019 and 2022, following an earlier literature review on teacher noticing across different disciplines. The st...

The *.zip folder contains Mplus input and output files for the three structural equation models we presented in the paper.

The *.zip folder contains Mplus input and output files for reproducing table 2 (measurement invariance across multiple groups) and figure 2 (structural equation model) in the paper.

Teaching methods to promote cooperative learning may shape mathematics teachers’ roles in the classroom, requiring a shift from direct supervision to delegating authority to small groups of students. While it is widely acknowledged that mathematics teachers’ beliefs play a crucial role in shaping their instructional practices and behaviors, there i...

The potential of tasks to foster mathematical learning and understanding is an important aspect of instruction and their implementation in teaching is thus often viewed to be positively related to the quality of instruction. Both the selection of tasks as well as their implementation in the classroom depend on many factors, with teachers’ knowledge...

Mathematical modelling is now a fundamental activity within general education. Its importance is evident from recent global events, which will impact on the lives of future generations. Events and phenomena, such as pandemics or the intensive debate before reaching consensus on the Paris climate agreement, show the need to make informed evidence-ba...

Review studies are vital for advancing knowledge in many scientific fields, including mathematics education, amid burgeoning publications. Based on an extensive consideration of existing review typologies, we conducted a meta-review and bibliometric analysis to provide a comprehensive overview of and deeper insights into review studies within mathe...

In this study, we examined the effects of teaching internships and related opportunities to learn, such as conducting lessons or reflecting on teaching practice, on the three facets of teacher noticing, perception, interpretation, and decision-making. Cross-lagged effects of these facets were examined to include reciprocal influences of the facets...

The increase in international migration and the global number of students learning mathematics through a language other than their home language makes migrants’ educational pathways a particularly urgent issue. The current paper focuses on the German context as Germany is currently one of the major immigration countries in the Western context. Beca...

Over the past two decades, the field of teacher noticing, which refers to how teachers observe and interpret classroom events, has received considerable attention in educational research. This chapter presents a review of the literature on mathematics teacher noticing, with a particular focus on longitudinal studies that use video-based interventio...

Improving the effectiveness of teacher professional development programmes is crucial for enhancing education, and assessing teacher professional competence is vital. This study aimed at adapting and validating instruments originally developed in Germany as part of a follow-up study to TEDS-M (Teacher Education Development Study-Mathematics), inten...

In educational research, teaching quality is extensively studied because of its role of a mediator between teacher characteristics and student learning. However, empirical evidence on differences between video and live scoring of teaching quality is rare. In the present study, thirty lessons from 15 secondary mathematics classrooms in a German metr...

The use of technology in mathematics education is becoming more common, and innovative technology applications are gaining attention. Augmented reality (AR), virtual reality (VR) and mixed reality (MR) offer attractive and novel instructional opportunities in a variety of subjects, including mathematics. As pre- and in-service teachers play a vital...

The teacher noticing construct is widely recognized in teacher competence and education research, particularly in the field of mathematics education. This paper surveys recent research on mathematics teacher noticing published between July 2019 and 2022, following an earlier literature review on teacher noticing across different disciplines. The st...

Tasks play an important role in mathematics education, as they provide opportunities for students to develop their competencies and to cognitively engage with the mathematical content. The potential for cognitive activation as a central feature of a mathematical task has been considered in numerous studies, mostly as a didactical analysis by means...

This paper compares and contrasts two approaches that are widely used in the English- and German-speaking discourse on mathematics teacher knowledge: ‘mathematical knowledge for teaching’ and ‘mathematics didactic knowledge’. It is proposed that these constructs are based on distinct theoretical and conceptual positions and origins. Mathematical kn...

To assess the effectiveness of teachers and teaching, it is necessary to develop an appropriate understanding of what makes a “good” teacher. According to the framework by Medley, this includes amongst others focusing on the knowledge, skills, and values that a teacher possesses. To appropriately describe these competencies, current research depart...

As a well-established educational area, mathematical modelling is strongly emphasized in many national curricula, and it is widely acknowledged that an important goal of mathematics education is to increase students' ability to deal with real-world problems. Contemporary mathematics curricula call for innovative methods and technological advances t...

Empirical research has demonstrated that mathematical errors originate from various causes that may have different implications for the learning process. Mathematical errors are an international phenomenon as all teachers from different cultural background must handle them every day during teaching-and-learning processes. When errors arise, teacher...

In recent years, teacher noticing has gained prominence as a theoretical construct in mathematics education, highlighting the dynamic, situational aspects of teaching that underlie instructional decisions and actions. This research forum explores innovative research approaches to teacher noticing in mathematics education, focusing on four key areas...

Diskrete Modelle als Potenzial beim mathematischen Modellieren Diskrete Mathematik und mathematische Modellierung haben viele Verbin-dungen. Wir beschreiben im Rahmen einer Fallstudie Modellierungsaktivi-täten mit Lernenden am Ende der Sekundarstufe I. Die Lösungsprozesse der Lernenden für dieses graphentheoretische Optimierungsproblem werden be-sc...

Teacher noticing has become widely accepted as a principal component of teacher competence; it is supported during university teacher education in many activities. However, only a few high-quality standardized measurement instruments exist that capture noticing and allow valid interpretations of how its development depends on factors within univers...

In this study, we investigated the professional identities of 490 pre-service teachers (PSTs) at the University of Hamburg, Germany. By distributing 100 percentage points, the PSTs assessed the relevance of the roles of subject specialist (SS), didactician (DD), and pedagogue (PD) for themselves currently (actual identity) and for an ideal teacher...

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 learn...

Teacher scaffolding is crucial to promote students’ cooperative learning processes, but little is known about the cognitive attention underlying teachers’ scaffolding behavior. This study aims to investigate the scaffolding behavior teachers exhibit while intervening in students’ cooperative learning and to explore the relation between teachers’ sc...

Teacher noticing, a situation-specific part of teachers’ professional competence, has gained much importance in the past two decades. The construct is believed to play a crucial role in the transfer of knowledge and skills into professional teaching performance. However, there is little empirical evidence on how the length of teachers’ teaching exp...

In recent decades, mathematical modeling has become mandatory in the school curricula in many countries around the world; however, the reality and the corresponding empirical evidence show that modeling is rarely implemented by teachers in mathematics lessons, for several reasons, one of which is that teachers are rarely educated to teach modeling...

This scoping review provides an overview of standardized instruments used to measure teacher noticing. A systematic literature search identified 37 publications in English-language peer-reviewed journals describing 22 different test instruments. Regarding the underlying conceptualization of noticing, instruments commonly distinguish mental processe...

In the present longitudinal study, cross-lagged path models were applied to investigate the potential reciprocal relationships between senior secondary school students’ motivation and their cognitive engagement, using data from 623 Chinese senior secondary school students across 2 years. The 623 students completed self-reported measures of motivati...

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) normal . However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we attempt to give so...

The capacity to use mathematics critically is essential for making decisions and forming judgements about challenges facing society, including those related to the economy, health and the environment. Critical Mathematical Thinking (CMT) involves the use of mathematical techniques and reasoning to address complex real-world problems in a wide range...

Introduction 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...

Teacher quality is a critical factor that influences instructional quality and student learning outcomes. Recently, the authors have proposed broadened views of teacher competence that include dispositions, such as knowledge, and more situation-specific aspects, such as noticing, and span from the dispositions of teachers to their performance in th...

Many students are becoming increasingly disengaged in school, particularly in mathematics. This is an important problem as lack of engagement may threaten students' achievement and performance in mathematics. A flipped learning pedagogy, which encourages students to take an active role in learning mathematics, has become a widely researched topic i...

Flipped classroom (FC) is a widely accepted, innovative pedagogy designated to enhance students’ learning by changing the paradigm of instruction. It has the potential to adapt learning to the students’ needs, interests, and mutual expectations by using the advantages of both online and face-to-face learning, which strengthens the quality of the in...

This study investigates the relations between working environment and teachers' job satisfaction, perceived work‐related stress, as well as work‐related self‐efficacy. The sample consisted of 226 mathematics teachers from German secondary schools. About 55% were female and they had been teaching for 13 years on average. We used self‐reported measur...

Flipped learning pedagogy (FLP) is an innovative approach with the potential to engage students in mathematics education. The current review aims to explore the opportunities and pitfalls of FLP in mathematics education. The results demonstrate that FLP is a promising approach that has numerous benefits for mathematics teaching and learning, althou...

Educators sometimes effect changes in education through the implementation of new ideas, and sometimes extraordinary circumstances force them to change their educational approaches, as during the COVID-19 crisis. Although we live in a digital age, the limited use of technology in education, particularly prior to the COVID-19 pandemic, and teachers'...

Although strong references to expertise in different theoretical approaches to teacher noticing have been made in the last decades, empirical knowledge about the development of teacher noticing from novice to expert level is scarce. The present study aims to close this research gap by comparing three different groups of mathematics teachers with di...

Existing research indicates inconsistent or at best weak predictive effects of teacher knowledge on student achievement. Data from Germany were used to examine the relation between teachers' content and pedagogical content knowledge, their perception, interpretation, and decision-making skills, the instructional quality implemented in class, and st...

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 publi...

As mathematics has been seen for decades as a stereotyped male domain, gender differences in mathematics learning have received strong attention from the public and academia. In China, the issue of gender equity in education is a particularly interesting topic to most families with the implementation of the one-child policy since the late 1970s. Th...

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we el...

Understanding students’ thinking and learning processes is one of the greatest challenges teachers face in the classroom. Misconceptions and errors have the potential to be a rich source of information for identifying students’ thinking and reasoning processes. However, empirical studies show that pre-service teachers (PSTs) and teachers find it ch...

Teaching effectiveness is a core issue in educational research; however, there is little consensus about the most important results of classroom teaching from an international perspective. The effectiveness of teaching has remained a ‘black box’ for a long time. In the secondary study described in this paper we used empirical data for Shanghai take...

The diagnostic competence in error situations is the competence needed by teachers to identify, interpret and then manage error situations in a way that promotes students’ mathematical understanding (Heinrichs & Kaiser, 2018). The development of preservice teachers’ (PST) diagnostic competence in error situations can begin in initial teacher educat...

Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open...

This study examined how expert and novice (preservice) teachers solved mathematical modelling tasks as well as how they noticed written artifacts of student thinking that were in response to the mathematical modelling tasks. Some teachers in both groups were aware of the openness and underdetermination of the modelling tasks and that these characte...

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 competencie...

In der vorliegenden Studie wird untersucht, wie sprachbezogene Merkmale von Lehramtsstudierenden und in universitären Lerngelegenheiten von ihnen genutzte Studieninhalte mit ihrem Wissenserwerb zusammenhängen. Es wurden das deutschdidaktische Wissen von N = 320 angehenden Lehrkräften mit Fach Deutsch und das erziehungswissenschaftliche Wissen von N...

Mathematical modeling and applications are an important part of curriculum and considered to be important for students’ current and future lives. In this contribution, we focus on mathematical modeling from a cognitive prospective. Following embedding the cognitive perspective within the discourse of mathematical modeling, we describe some of the c...

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 ha...

Although the effects of professional development programs on teachers’ noticing skills have attracted considerable interest among mathematics education researchers, little is known about the developmental process of prospective teachers’ noticing skills within initial teacher education. This paper examines the extent to which prospective teachers’...

Innovative technologies such as Flipped classrooms (FCs) can change the perspective of mathematics teaching and provide different experiences and new ideas. In a qualitative case study, we examined the characteristics of feedback provided by a mathematics teacher in two different secondary mathematics classrooms, comparing non-FCs and FCs. The resu...

The flipped classroom (FC) approach has become an increasingly popular research topic in recent years. The core idea of FC is to transfer lectures out of the classroom with the help of digital technologies and to allocate in-class time for active learning. The purpose of the presented case study was to investigate student engagement in a flipped se...

Results of a systematic literature survey on modelling competencies and possible consequences for ICTMA

It is widely assumed that teachers play a key role in providing high-quality learning opportunities to students and fostering students’ learning. Yet it is still unclear how specific teacher knowledge facets as part of their professional competence contribute to classroom processes and learning outcomes. Focusing on mathematics education at the sec...

This book documents ongoing research and theorizing in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical...

The title of this book is Mathematical ModellingMathematical modellingEducation in West and East, arising from the ICTMA-19 conference with the same theme. It is argued that since both mathematics itself and mathematics education are human products, and solving problems in real-life context is at the heart of mathematical modellingMathematical mode...

Discussions on numeracy and the value of numerical skills and practices have a long tradition, historically dating back to the 16th century and the practical arithmetic of Adam Ries, which was characterized by the perspective of enlightenment. This critical enlightened perspective has only been taken up to a limited extent in the reception of numer...

Task design constitutes a growing core of research in mathematics education. In particular , task design in Dynamic and Interactive Mathematics Learning Environments (DIMLEs) has become very popular, although it remains under-researched. This study aims to systematically analyze the current state of research on task design in DIMLEs. The literature...

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 vi...

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 inves...

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...

Das „Handbuch Lehrerinnen- und Lehrerbildung“ bietet aus fachlicher, fachdidaktischer, bildungswissenschaftlicher und schulpraktischer Perspektive einen umfassenden forschungsbasierten Überblick zu allen Bereichen der Lehrerinnen- und Lehrerbildung. Das von 174 Autorinnen und Autoren erarbeitete Orientierungswissen wird in 107 Beiträgen präsentiert...

This paper considers various approaches to classroom observation that combine generic and mathematics content-specific dimensions of instructional quality. Using results from previous research in which three research teams each analysed the same three mathematics lessons (from fourth-grade mathematics classrooms in the USA) using different framewor...

Zusammenfassung Die deutschsprachige Unterrichtsforschung unterscheidet bereits seit längerem drei Basisdimensionen der Unterrichtsqualität: Effiziente Klassenführung, konstruktive Unterstützung und Potential zur kognitiven Aktivierung. Da die drei Basisdimensionen als fächerübergreifende Konzeptualisierung der Unterrichtsqualität gelten, stellt si...

The usage of metacognitive strategies can help students to avoid or to overcome cognitive barriers during modelling processes. For imparting relevant metacognitive strategies and supporting students during the modelling process, it is necessary that teachers act on a meta-meta level and monitor their students’ usage of metacognitive strategies. The...

This latest contribution from members of the ICTMA research community focusses on how students, teachers, tertiary educators, and researchers make sense of mathematical modelling and applications educational research and practice. Innovative approaches in modelling educational research and research into and evaluation of teaching practice are showc...

Metacognitive competency can be described as a sub-competence of mathematical modelling competence. Although there is consensus about its relevance, until now research on metacognition in modelling processes is very limited. In particular, students’ perspective on metacognitive competencies has not been examined yet. The present study aims at inves...

(A Survey paper which opens a ZDM Mathematics Education special issue on “Numeracy, learning, and vulnerability in adult life”). 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...

Although research on teachers’ noticing in mathematics education has significantly increased over the last decade, little is known about the relationship between teachers’ noticing and teachers’ knowledge as an influential basis of their professional noticing. This paper examines this relationship based on a study involving 203 in-service Chinese m...

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 s...

Zusammenfassung. Der in der TEDS-M-Studie (Teacher Education and Development Study: Learning to Teach Mathematics) entwickelte Test zur Erfassung pädagogischen Wissens am Ende der Lehramtsausbildung hat sich in diversen Untersuchungen als zuverlässiges Messinstrument erwiesen, für das eine Reihe von Ergebnissen vorliegt, die die Validität der Testw...

The TEDS-Validate project has been carried out within the research program derived from Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M). In this chapter, we describe the aim of the study, which is related to the question of whether research findings brought forward by measurement instruments to test professional comp...