Zdm-Mathematics Education最新文献

In this paper, we discuss the theoretical background of mathematical modelling and its connection to citizenship education. Citizenship education in this context means that young people are equipped with competencies to respond as responsible citizens in situations relevant for society. To outline the connection between mathematical modelling and citizenship education in theory, we discuss the aims of mathematical modelling, modelling competences and the connection between numeracy and modelling. Based on these reflections we present an extended modelling cycle that specifically highlights modelling steps relevant to citizenship education. To show how the theoretical connection between mathematical modelling and citizenship education can be used in teaching practice, we describe three different examples of modelling tasks and analyse them with the help of the extended modelling cycle. We argue that the three tasks support different learning aims in relation to citizenship education and require modellers to carry out different steps of the extended modelling cycle. As an example of context, we used the pandemic caused by COVID-19, as it affected the quality of human life greatly, as all students in the Western world experienced.

This paper introduces this special issue aiming to deepen and extend research on mathematics teachers' work, from a resource perspective, by taking language and culture into account, and exploring two questions: How are teachers' interactions with resources interpreted and modeled across contexts? And, What challenges and insights emerge through recent efforts to engage these models in cross-cultural (and linguistic) research? The fields of resources, language and culture in mathematics education are each extensive, and we do not attempt to survey comprehensively across them. We have chosen instead to propose three approaches on resources in mathematics teachers' work that developed somewhat contemporaneously from three different countries with differing linguistic, curricular, and social contexts, corresponding to the work of the three guest editors. The models developed through these approaches are driven by the educational, and so cultural and material conditions of the time and the location of each author, and allow us to propose preliminary answers to our two guiding questions. We then move to pull the threads from these models together, and discuss the contributions to this Special Issue. This results in more robust and nuanced responses to our questions, and in identifying two themes that emerge from research that sit at the convergence of studies of teachers' interactions with resources, languages, and cultures: an invisibility-visibility dialectic and a local-global tension. Finally, this study leads us to consider a new region of mathematics education research.

In March 2020, many schools worldwide were closed due to the COVID-19 pandemic. This closure confronted mathematics teachers with the challenging transition to emergency remote teaching (ERT). How did students experience ERT, and how did these experiences relate to context variables and to their teachers' beliefs and practices? In particular, what didactic approaches and formative assessment practices did secondary mathematics students experience, and which beliefs did they hold concerning digital mathematics education? How were these student experiences and beliefs related to student context variables (gender, need to support family, personal home equipment), teacher beliefs, delivery modes, and student appreciation of mathematics? To investigate these issues, we set out online questionnaires for mathematics teachers and their students in Flanders-the Dutch-speaking part of Belgium-, Germany, and the Netherlands. Data consisted of completed questionnaires by 323 mathematics teachers and 2126 of their students. Results show that even though students preferred regular face-to-face teaching, they were content with the quality of their teachers' distance mathematics teaching. Students reported that they were taught new topics often, but did not experience teachers initiating peer feedback. High student appreciation of mathematics, good home environment, and more synchronous delivery of ERT were related to ERT experiences and more positive beliefs concerning digital mathematics education. These findings have implications for ERT teaching strategies in future, as well as for hybrid teaching practices.

When the COVID-19 pandemic began, many universities switched to fully online teaching. This unexpected switching to online teaching was challenging for both teachers and students, and restrictions that were put in place because of pandemic made this challenge even greater. However, new ways of teaching might also open new opportunities for students' learning. The research question driving our study was as follows: how do students regulate their learning and specifically their choice of resources and peer learning in university mathematics classes that are fully taught online as offered during the COVID-19 pandemic? We report on a longitudinal, qualitative study in which students recorded a brief audio diary twice a week over one whole semester (14 weeks). We focused on three students who completed 70 interviews in total and finished the semester with varying degrees of success. The results show how the students structured their studying (e.g., the roles that deadlines or synchronous teaching events played). They illustrate the strengths and limitations of digital materials provided by the lecturer and the use of complementary media. Further, the pandemic uncovered the double-edged role of simple, often anonymous exchanges (e.g., via Discord servers), with few binding forces for either side, and the significance of stable learning partnerships for students' success. Our research highlights aspects that should be focal points when comparing traditional instruction and online instruction during the pandemic from a self-regulatory perspective. Practical implications refer to how these aspects can be combined sensibly in fully online courses, but also in blended learning contexts.

The mathematical medium of data visualization and other data representations (DV) has served as a primary means of communicating about the COVID-19 crisis. DVs about the pandemic are highly visible across news journalism and include an increasingly innovative and diverse set of representational forms. These representational forms employ multimodal, interactive, and narrative elements, among others, that create new possibilities for data storytelling. Building on current efforts to expand the teaching and learning of data practices in K-12 mathematics education, we argue that innovative DVs create new opportunities for teaching and learning mathematics, particularly during times of crisis. We illustrate our argument using three examples of innovative DVs from news journalism. We discuss how these DVs could serve as complementary resources alongside conventional graphs to support students as they use mathematics and mathematical representations to make sense of crises such as the COVID-19 pandemic. Our commentary seeks to bring current trends in data representation to bear in mathematics education. Leveraging such trends offers artifacts useful for teaching and opens up space for elevating emotion and experience as important aspects of mathematics curricula.

Understanding the structure, antecedents, and outcomes of students' emotions has become a topic of major interest in research on mathematics education. Much of this work is based on the Achievement Emotions Questionnaire-Mathematics (AEQ-M), a self-report instrument assessing students' mathematics-related emotions. The AEQ-M measures seven emotions (enjoyment, pride, anger, anxiety, shame, hopelessness, boredom) across class, learning, and test contexts (internal structure). Based on control-value theory, it is assumed that these emotions are evoked by control and value appraisals, and that they influence students' motivation, learning strategies, and performance (external relations). Despite the popularity and frequent use of the AEQ-M, the research leading to its development has never been published, creating uncertainty about the validity of the proposed internal structure and external relations. We close this gap in Study 1 (N = 781 students, Grades 5-10, mean age 14.1 years, 53.5% female) by demonstrating that emotions are organized across contexts and linked to their proposed antecedents and outcomes. Study 2 (N = 699 students, Grade 7 and 9, mean age 14.0 years, 56.9% female) addresses another deficit in research on the AEQ-M, the lack of evidence regarding the assumption that emotions represent sets of interrelated affective, cognitive, motivational, and physiological/expressive components. We close this gap by evaluating extended AEQ-M scales, systematically assessing these components for five core mathematics emotions (enjoyment, anger, anxiety, hopelessness, boredom). Our work provides solid grounds for future research using the AEQ-M to assess emotions and their components in the domain of mathematics.

Due to the COVID-19 pandemic, educational institutions at all levels closed their doors and began to operate remotely. In this paper, we analyze the educational experiences of preservice mathematics teachers (PMTs) enrolled in mathematics teacher education programs from three South American universities, as the pandemic was unfolding. An exploratory study was conducted, based on an inductive and thematic qualitative text analysis of narratives written by 24 PMTs. Based on the study, we report on the following aspects: (1) experiences of PMTs in the passage to remote education (RE) mode (considering characteristics of remote classes-interactions, the rhythm of the class, teaching work-time management, home-classroom fusion, and physical and psychological discomfort), and (2) opportunities and limitation experienced by PMTs in relation to the use of technologies. The results of the study suggest the need to rethink teacher education programs regarding the integration of technologies in mathematics classes, the opportunities offered by hybrid education, and teacher education for distance teaching.

Emotions and motivation are important for learning and achievement in mathematics. In this paper, we present an overview of research on students' emotions and motivation in mathematics. First, we briefly review how early research has developed into the current state-of-the-art and outline the following key characteristics of emotions and motivation: objects, valence, temporal stability (vs. variability), and situational specificity (vs. generality). Second, we summarize major theories in the field (the control-value theory of achievement emotions, expectancy-value theory of achievement-related motivation, self-determination theory of human motivation, and social-cognitive theory of self-efficacy). Third, we present an overview of instructional characteristics that have been shown to foster emotions and motivation. Fourth, we provide an overview of the contributions to the special issue on "Emotions and Motivation in Mathematics Education and Educational Psychology." Finally, we suggest directions for future research in the field with respect to advancing theory, improving measurement, and considering diversity and inclusion.

[This corrects the article DOI: 10.1007/s11858-022-01447-2.].

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary decisions and policies which do, in fact, affect society as a whole. The mathematical tools that are used derive from nonlinear systems of difference equations (possibly viable at a high school level, using spreadsheets or adequate software) as well as nonlinear systems of ordinary differential equations (therefore using mathematical tools and software well within the reach of undergraduate students of many courses). This purpose is accomplished by motivating students and learners to study existing SIR-type models and modifying them in order to have a fully understandable translation of dynamics for infectious diseases such as COVID-19 in several different realistic scenarios, that is to say, situations that consider social distancing policies, widespread vaccination programmes, as well as possible and even probable results when in the presence of negationist postures and attitudes. Several modelling choices referring to real-life situations are shown and explored. These models are analysed and discussed, implicitly proposing similar attitudes and evaluations in learning environments. Conclusions are drawn, stimulating further work using the described mathematical tools and resources.

Supplementary information: The online version contains supplementary material available at 10.1007/s11858-022-01447-2.