ZDM最新文献

Assessing students’ (mis)conceptions is a challenging task for teachers as well as for researchers. While individual assessment, for example through interviews, can provide deep insights into students’ thinking, this is very time-consuming and therefore not feasible for whole classes or even larger settings. For those settings, automatically evaluated multiple-choice (MC) items could be a solution. However, it is a challenge to design those items and to adapt them for other countries in a way that they adequately reveal students’ (mis)conceptions. In this article, we investigate the question whether it is valid to use a German adaption of a multiple-choice test developed in Australia for formative assessment of the letter-as-object misconception in Germany. For this, first semi-structured interviews with five German Year 8 students were conducted, and second, 616 students were asked for short written explanations. These data were analysed with regards to the students’ (mis)conceptions and compared with their automatic online diagnosis. In general, a high concordance between online SMART test results and students’ explanations was observed, confirming that useful diagnoses of student misconceptions can be obtained from such a short well-designed MC test.

Students’ mathematics self-efficacy (MSE) is strongly associated with learning behaviours and performance, and students’ future career choices. In our scoping review, we screened what substantive foci (conceptualization, directionality and role of MSE, change in MSE, and situational specificity of MSE) have been posed and which methodological approaches (participants, analytical methods, data sources, and congruence of measures) have been used in recent (2018–2022) studies of MSE. Studies of MSE were clearly in the mathematics domain with 21 of 49 included studies exploring specific mathematics areas. The key focus was on strength of MSE. International databases (i.e., PISA) have enabled broad generalization, while in-depth qualitative studies enable minute situation-specificity. Cross-sectional and longitudinal studies using hierarchically nested designs (i.e., students in classrooms) enable us to draw conclusions at both individual, classroom, and school levels. The current state-of-the-art indicates methodological advancement is rapid and we are likely to see further methodological-substantive synergies in the field of MSE in future studies. We see the potential and need for future mixed-methods studies that continue the focus on MSE as a multidimensional and dynamic concept. Careful consideration of the theoretical background of the construct of MSE continues to be important to bring the field forward.

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 metropolitan area were observed. Lessons were scored both live in the classroom and using video recordings. Live and video scoring was conducted by (different) trained observers. Ratings were obtained with a “hybrid” observational instrument that covers generic and subject-specific characteristics of teaching quality in mathematics classrooms. Generalizability analysis and paired t tests were performed to investigate mode effects. The findings showed that in live scoring, classroom management was rated lower, and cognitive activation was rated higher. Rankings of lessons or classrooms were very similar across modes, and reliabilities did not differ to a meaningful extent either, except for classroom management reaching better results for live ratings. This suggests that based on the present findings, classroom observation performed with our hybrid framework of teaching quality generalizes across observation mode only under certain circumstances. Further research is necessary to better understand the relation between observation mode and teaching quality ratings, as well as the impact of the scoring procedures. We discuss the implications of our findings for educational research and practice.

Prospective teachers bring countless stories of success and failure from different mathematics classrooms to their post-field teacher education courses. These reflective stories often glorify school mathematics classrooms and dominant traditions within, instead of confronting the marginalization of diverse groups in school environments. Mathematics teacher educators have a significant role to play in teaching prospective teachers to reflect critically on their field experiences and, in doing so, create spaces for disruption and disruptive pedagogies. Drawing on critical and equity-based theories applied within the fields of mathematics education and teacher education research, we propose a disruptive pedagogy analytical framework that enables us to study the roles and practices of mathematics teacher educators as they conduct their work in these post-field contexts of teacher education. In this paper, we introduce our disruptive pedagogy framework and present the results that followed from using it to analyze data from a research study in which mathematics teacher educators from across Canada and Norway were interviewed. We claim that our analytical framework can be used to identify those disruptive and transformative practices initiated by mathematics teacher educators—practices that are necessary to bring about shifts in inequitable and unjust classroom practices of school mathematics and in becoming a teacher. Unfortunately, however, results reported here point to the need for further shifts and growth toward more explicitly disruptive practices initiated by mathematics teacher educators in the post-field context.

High-quality instruction in preschool is important for children’s mathematical development. To date, the domain-specific elements constituting mathematics instruction quality and the factors associated with this quality are hardly studied, resulting in serious gaps in our insights into the topic. We aimed to address this gap by investigating (a) 43 preschool teachers’ mathematical questioning behavior during shared picture book reading, and (b) its association with picture book and teacher characteristics. We analyzed the number and the level of abstraction of mathematical questions when sharing a mathematical (i.e., written with explicit mathematical aim and content) and a non-mathematical (i.e., written without explicit mathematical aim and content) picture book, and their associations with teachers’ professional competence. For mathematical and non-mathematical picture books, teachers formulated mathematical questions, mainly at lower levels of abstraction. They formulated more, but proportionally less abstract, mathematical questions when sharing a mathematical versus a non-mathematical picture book. We found only limited evidence for associations between teachers’ questioning behavior and their professional competence. Our findings indicate that preschool teachers offer opportunities to engage in mathematical interaction during shared picture book reading, pointing to the potential of this activity to implement high-quality mathematics instruction. They further show that mathematical picture books enable more mathematical interaction than non-mathematical picture books, but not at higher levels of abstraction. Future studies are needed to replicate and complement our findings, with special attention for the contribution of teacher professional competence and the fit to children’s competency level.

The paper responds to the need for understanding trends and gaps in extant research related to adult education in mathematics and numeracy, given changing skill demands and skill gaps regarding adults, and related policy, theorizing, and practice trends. This paper presents the results of a scoping review of recent empirical research related to adult education in mathematics and numeracy, published in 22 selected journals from 2019 to 2022, including 15 journals in adult education and seven in mathematics education. The results show that only 39 relevant empirical studies were found among over 2300 research papers reviewed, and that few of those focus on practice-related of adult education in mathematics and numeracy. The results provide quantitative evidence suggesting that the field of adult numeracy education is under-researched, and help to identify gaps in empirical research involving adult numeracy, including on emerging topics such as on modeling and critical interpretation. The results also point to research opportunities that can strengthen theorizing and practice in both mathematics education and adult numeracy education.

Abstract

The integration of dynamic visualisations, feedback formats and digital tools is characteristic of state-of-the-art digital mathematics textbooks. Although there already is evidence that students can benefit from these technology-based features in their learning, the direct comparison between the use of a comparable digital and printed resource has not yet been sufficiently investigated. We address this research gap by contrasting the use of an enriched digital textbook that includes these features and comparable printed materials without them. To do so, we investigate the achievement of 314 students in a pretest-posttest control group design in a five-hour series of lessons on conditional probability. Using the Rasch model and mixed ANOVA, the results indicate that students can benefit from digital textbook features, especially compared to the use of comparable printed materials. In line with other studies on mathematical achievement and the use of digital resources, our study also shows differences between boys and girls. It seems that particularly girls benefit from the use of the digital textbook, whereas, for the boys, it does not seem to make a difference what kind of resources they use. The group and gender differences are discussed against the background of other studies considering that, especially in Bayesian situations, the way statistical situations are visualised can be decisive for a student’s performance.

Lesson study (LS), a teacher-oriented, student-focused professional development (PD) approach that originated in Japan, has spread globally. However, existing literature on the implementation of LS and its effectiveness provides inconsistent results, suggesting a need to review current research on LS. With a focus on LS in mathematics education, we examined 75 recent LS studies using Lewis’s (ZDM Mathematics Education 48:571–580, 2016. https://doi.org/10.1007/s11858-016-0792-x) framework to understand how LS is implemented and the pathways by which LS can impact teaching practice and student learning. We found that new developments have taken place in LS implementation, although challenges persist throughout its process. Regarding the implementation of LS, even though the examined LS studies generally contained four phases (study, plan, teach, and reflect), we found many LS lacked a research question, and the study of teaching materials was sometimes invisible. Across phases, studies shared a consensus that it is most critical to focus on students’ thinking and learning, yet reported challenges in maintaining this focus. In addition, the role of knowledgeable others (KOs) was recognized but inconsistently understood. Collaboration was also widely reported as a challenge. Finally, there were large variations in LS duration, with some LS implementing overly brief cycles. Regarding LS impact, the literature has more frequently reported changes in teachers’ knowledge and beliefs and less frequently in curriculum, learning community/professional norms, teaching practice, and student learning outcomes. The above challenges reflect a need for culturally relevant systemic support for developing sustainable and large-scale LS. We suggest future directions for continued research and practice improvement.

We explore the potential of merging numeracy and literacy, through using number stories to stimulate mathematical engagement with young, marginalized learners in their communities. Our data emerges from the Family Maths Storytime Programme (FMSP) run in partnership with teachers in two South African schools. The FMSP conducted sessions with caregivers of pre-Grade 1 learners that focused on supporting mathematical talk in the home centred around four number storybooks with linked activities and games. Drawing on Bourdieu’s notion of habitus and other socio-cultural theories emphasising opportunities for talk and reasoning for learning we explore: Did the FMSP enable the integration of home and school numeracy and literacy practices? If so, what evidence is there of such integrated practices? What is the nature of the described practices? Our analysis focuses on 20 caregiver interviews following their participation in the FMSP that was initially run after school in two English medium pre-Grade 1 classrooms. NVivo coding highlighted key themes across interviews. The findings show how modelling engagement with merged literacy and numeracy practices in the programme enabled changing practices, dispositions, and forms of capital in relation to engaging with these in the home. We highlight how supporting home-based and story inspired engagement with marginalised learners supports equity goals in contexts where learners from indigenous backgrounds often begin and remain mathematically behind grade expectations in school.

Mathematics education is inherent to the discourse of globalization, which often states that mathematical knowledge is universal. Certain global mathematical techniques and procedures found in many mathematics curricula around the world often discourage students to engage in creating their own mathematical knowledge. This suggests that dominant cultural values are defined as universal or at the very least labeled as normative, while peripheral mathematical knowledge is tagged as merely simplistic, primitivistic, folkloristic, and/or as forms of obsolete systems. Our main purpose here is to discuss how ethnomodelling promotes a holistic understanding of local and global approaches in mathematics education, which contributes to the development of a glocal comprehension of mathematical practices developed by members of distinct cultures, which means placing them at the center of the educational process. Through the development of ethnomodelling, this pedagogical action promotes connections between day-to-day knowledge and systematized school curricula. Thus, this theoretical article demonstrates how we might consider situating local mathematical practices (margins) at the center (glocal) of the mathematics education process by decentering globalized mathematical knowledge in the search for peace and social justice.