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Online mentoring can be useful for supporting girls in science, technology, engineering, and mathematics (STEM). Yet, little is known about the differential effects of various online mentoring formats. We examine the general and relative effectiveness of three online mentoring formats, one-on-one mentoring, many-to-many group mentoring, and a hybrid form of the two. All three formats were implemented in different years in the Germany-wide online-only mentoring program, CyberMentor, whose platform enables communication and networking between up to 800 girls (in grades 5-13) and 800 women (STEM professionals) each year. We combined longitudinal mentee data for all first-year participants (N = 4017 girls, M age  = 14.15 years) from 9 consecutive mentoring years to evaluate and compare the three mentoring formats. Overall, all formats effected comparable increases in mentees' STEM activities and certainty about career plans. However, mentees' communication behavior and networking behavior on the mentoring platform differed between the three formats. Mentees in the hybrid mentoring format showed the most extensive STEM-related communication and networking on the platform. We also analyzed the explanatory contributions of STEM-related communication and networking on interindividual differences in the developmental trajectories of mentees' STEM activities, elective intentions in STEM, and certainty about career plans, for each format separately., (© 2020 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals LLC on behalf of New York Academy of Sciences.)

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities. The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural equation modeling. The results showed no direct effect of the intervention on student modeling competence. However, they did reveal that the intervention had a significant effect on teacher beliefs about learning (constructivist and socio-constructivist view) and an effect of these teacher beliefs about learning on student modeling competence. Further, the results showed that students' gains in modeling competence is not only mediated by teacher beliefs, but also influenced by individual factors. Implications for teaching as well as limitations of the study are discussed.

This paper reports upon particular aspects of a study carried out by Delice in 2003, the main aim of which was to compare the performance of students in the 16-19 age group from Turkey and England on trigonometry of "A-level standard" and then to compare the curriculum and assessment provision in each country to seek possible explanations for differences in performance. Overall, the Turkish students did much better with the algebraic, manipulative aspects of trigonometry, the English students did better with the application of trigonometry to practical situations. The comparison of curriculum and assessment provision in the light of these results raises several issues about the current A-level mathematics syllabus. It may be that there is a tendency to think that mathematics is very much the same in any country, however this research supports previous work [Kawanaka, T., Stigler, J.W. and Hiebart, J. (1999) Studying Mathematics Classrooms in Germany, Japan and the United States: Lessons from the TIMSS Video Study] where mathematics was indeed found to be taught and learnt differently and the roles of teachers and students were different across three countries (Germany, Japan and the USA). The paper begins by briefly describing the research and presenting some of the results. There then follows a discussion of these results within the context of curriculum and assessment provision within each country. Finally, issues for the current A-level syllabus arising out the results are presented.

Feedback is an important component of interactive learning software. A conclusion from cognitive learning theory is that good software must give the learner more information about what he did. Following the ideas of constructivist learning theory the user should be in control of both the time and the level of feedback he receives. At the same time the feedback system must identify and review different possible solution strategies in an open learning environment. The interactive geometry software Cinderella offers an easy-to-use programming interface. It can be used to implement application specific feedback by the author of learning units. In this paper we present two exemplary learning units implementing two kinds of interactive feedback: feedback on demand and immediate feedback. The presented units come from discrete mathematics and from the theory of line reflections and congruencies in geometry. The units are implemented in a process-oriented design. Various directly given or hidden hints help the students to understand the mathematical principles behind the given problems. Our tools analyses the student's solution processes automatically and generates additional feedback on demand. The second learning environment can also be used in conjunction with recording of user actions. This allows additional feedback given later by the teacher whenever the automatic feedback system fails in analyzing the users' learning processes. First experiences using the units in teaching are presented.

Data about processes and outcomes of preschool teacher education is scarce. This paper examines the opportunities to learn (OTL) of prospective preschool teachers (N = 1,851) at different types and stages of preschool teacher education and their relation to general pedagogical knowledge (GPK), mathematics pedagogical content knowledge (MPCK), and mathematical content knowledge (MCK) with standardized tests. Process indicators in terms of OTL and outcome indicators in terms of knowledge varied substantially across teacher education types and stages. Controlling for preschool teachers' background, multilevel models revealed that OTL in general pedagogy and mathematics pedagogy provided during teacher education were significantly related to GPK and MPCK. Effect sizes reached up to 2 thirds of a standard deviation. OTL in mathematics pedagogy were in turn significantly related to the type of institution that offered a program in favor of pedagogical colleges compared with vocational schools. OTL were also significantly related to program stage in favor of the last year of preschool teacher education compared with the beginning. Process characteristics in terms of OTL mediated fully or partly structural characteristics of teacher education such as type of institution or program stage. These results suggest that the OTL provided are more important than whether prospective preschool teachers were at the beginning or the end of their program or whether they were prepared at vocational schools or pedagogical colleges (although entrance differences have still be taken into account). It may be an important responsibility of policymakers then to ensure that all prospective preschool teachers receive sufficient OTL.

The Programme for the International Assessment of Adult Competencies (PIAAC) has recently drawn additional attention to "mathematical literacy" as an important influential factor for individuals' life chances. High levels of mathematical literacy have thereby been linked to using mathematics in daily and working life frequently. In this paper, based on the data from Germany, we focus on the construct "use of mathematics" in two ways: First, we analyze in depth how it can be utilized to describe different groups of adults. Second, we investigate its role as predictor of mathematical competence and mediator of other relevant background variables. Results show that three groups of adults can be distinguished that use mathematics differently in daily and working life. However, the construct can sensibly be described as unidimensional. In a path model, "use of mathematics" turns out to be the strongest predictor of mathematical competence. In addition, it mediates effects of the mathematical requirements of the job, duration of education, and gender.

The paper presents results from a computer-based assessment in which 171 early career mathematics teachers from Germany were asked to anticipate typical student errors on a given mathematical topic and identify them under time constraints. Fast and accurate perception and knowledge-based judgments are widely accepted characteristics of teacher competence. The item-wise length of anticipation time, the complexity of mathematical topics and the frequency of right or wrong given answers were used as indicators for teacher competence. The data revealed that anticipation time and the complexity of mathematical topics were related with each other. The groups of test persons with correct and incorrect answers behaved contrarily to the length of the anticipation time. Whereas test persons with correct answers needed more time to anticipate typical errors with an increasing complexity of the errors, the test persons giving false answers responded very quickly, even with an increasing error complexity. This finding confirms results of the expertise research, which emphasize that expert teachers focus more intensively if this is required by a complex task.

This paper examines how a certain threshing machine was developed and improved by Jobst Heinrich Voigt and Gottfried Wilhelm Leibniz between 1699 and 1700. While this machine was based on various mechanical principles and instruments, including the pinned drum mechanism first noted by Georg Philipp Harsdörffer, it was later reconceptualized as a 'mathematical' machine. I claim that such a positioning was not unique to this machine, but part of a wider movement during the 18th century that considered various artisanal instruments as mathematical, as well as agricultural and artisanal knowledge as scientific. Examining the development and subsequent reception of this machine, I show that during the first decades of the 18th century these conceptions gave rise to a double image of this machine, and hence of agricultural knowledge in general: on the one hand, this machine was considered as more efficient and productive (while still in need of improvement); on the other hand, it was viewed, either implicitly or explicitly, as something that should be studied by mathematicians, thus reflecting a changing image of mathematics., Competing Interests: Declaration of competing interest No competing interests to declare., (Copyright © 2024 Elsevier Ltd. All rights reserved.)

This paper investigates the impact of early noncognitive skills on social outcomes in adolescence. The child's attention span, approach, prevailing mood and distractibility in early childhood may be crucial predictors for school achievements, health risk behavior, delinquency and autonomy as adolescent. We investigate this issue using a longitudinal epidemiological cohort study of 384 children at risk from the Rhine-Neckar region in Germany. Our results indicate that noncognitive skills in early childhood are important predictors of educational success, tobacco and alcohol use, delinquency and autonomy in adolescence. In particular, the attention span has emerged as a dominant factor among noncognitive skills regarding educational performance, health behavior and delinquency in our study. Further, we find that boys with low noncognitive skills have significantly lower social outcomes compared with girls.

Using Progress in International Reading Literacy Study 2001 and Programme for International Student Assessment 2003 data for Germany, this paper examines whether second-generation immigrants and girls are graded worse in math than comparable natives and boys, respectively. Once all grading-relevant characteristics, namely math skills and oral participation, are accounted for, pupils should obtain same school grades. Results of a matching approach and class fixed effects regressions suggest that second-generation immigrants have grade disadvantages in primary education which could bias their secondary school track choice. Regarding secondary school, most immigrants are not affected by grade discrimination and girls enro lled in upper-secondary school are systematically graded better.

Whereas several studies investigated the effects of implementation of state-wide exit exams on student achievement, there is still little known about the impacts of the exams on students' self-regulated learning. This paper examines the question as to whether the implementation of state-wide high school exit exams is associated with a change in the self-regulated learning of students in mathematics or English. We conducted a standardized questionnaire survey of students in two German states for a period of 3 years. In mathematics no significant effects of the immediate introduction of state-wide exit exams were identified. In English the results show significant positive and negative effects. The results are discussed and implications for further research are given. (Contains 3 tables.)

This essay paper discusses the decline in the numbers of students studying mathematics at German universities. Sections on mathematics in German secondary schools, reasons for the decline in numbers, and issues related to reversing the trend are included. The article also highlights the German "Diplom" and mathematics departments in Baden-Wurttemberg. (MM)

Argues that the paradox of mathematical knowledge--that mathematics cannot be separated from empirical experience and yet cannot be explained by empiricist epistemology--can only be resolved if the causal interactions between knower and environment are accepted. Contains 26 references. (DDR)

Classroom management is an emotionally demanding task for mathematics teachers, especially if students exhibit frequent discipline problems. Intense classroom conflicts can result in persistent latent emotional dispositions, such as fear or anger, that teachers are not directly aware of but that have a strong influence on their classroom management. However, little is known about the relationship between mathematics teachers' latent emotions and their classroom management strategies. This paper reports on findings from an exploratory, video-based single case study in an urban secondary school in Germany. One mathematics double lesson (95 minutes in total) was videotaped to conduct a depth-hermeneutical analysis of identified classroom management strategies and the corresponding latent teacher emotions. The results suggest that mathematics teachers use classroom management strategies not only to establish orderly lessons but also to regulate intense latent emotions that arise during classroom teaching. [ABSTRACT FROM AUTHOR]

Background: Although research on mathematics learning programs has taken off in recent years, little is known about how different person characteristics are related to practice behaviour with such programs. When implementing a mathematics learning program in the classroom, it might be important to know whether students with specific characteristics need more encouragement to make use of this learning opportunity. Objectives: Using a supply‐use model, we analysed the predictive power of students' cognitive characteristics (prior mathematics knowledge), personality traits (conscientiousness), motivational‐affective characteristics (mathematics self‐concept and mathematics anxiety), and family background characteristics (socioeconomic status and migration background) for practising with an adaptive arithmetic learning program. Methods: We used longitudinal data from 203 fifth graders from seven non‐academic‐track schools in Germany. Practice behaviour, measured by completed tasks in the learning program, was recorded weekly for every student over a period of 22 weeks. Results and Conclusions: The results of our multilevel analyses showed that mathematics anxious students practised less with the program. We did not find any relationship with the other characteristics. Takeaways: Our results suggest that mathematics anxious students need more encouragement when practising with a mathematics learning program; otherwise, they do not get the chance to benefit from the use. Lay Description: What is already known about this topic: The use of mathematics learning programmes in mathematics education has recently intensified.It is important that students practice with such learning programmes regularly over a longer period of time in order for them to achieve learning success.Students differ in their mathematics learning behaviour. What this paper adds: Little is known about how person characteristics are related to practice behaviour with mathematics learning programmes.Students may differ in their use of a mathematics learning programme, which is why cognitive characteristics, personality traits, motivational‐affective characteristics, and family background characteristics may affect students' practice behaviour. Implications for practice: Mathematics anxious students practiced less with a mathematics learning program, and need more encouragement to benefit equally from the implementation in school.Teachers should keep in mind that after the initial enthusiasm, practice with a programme may decrease over time, especially after school holidays. [ABSTRACT FROM AUTHOR]

Background: Computer‐based assessment allows for the monitoring of reader behaviour. The identification of patterns in this behaviour can provide insights that may be useful in informing educational interventions. Objectives: Our study aims to explore what different patterns of reading activity exist, and investigates their interpretation and consistency across different task sets (units), countries, and languages. Three patterns were expected: on‐task, exploring and disengaged. Methods: Using log data from the PISA 2012 digital reading assessment (9226 students from seven countries), we conducted hierarchical cluster analyses with typical process indicators of digital reading assessments. We identified different patterns and explored whether they remained consistent across different units. To validate the interpretation of the identified patterns, we examined their relationship to performance and student characteristics (gender, socio‐economic status, print reading skills). Results and Conclusions: The results indicate a small number of transnational clusters, with unit‐specific differences. Cluster interpretation is supported by associations with student characteristics—for example, students with low print reading skills were more likely to show a disengaged pattern than proficient readers. Exploring behaviour tended to be exhibited only once across the three units: It occurred in the first unit for proficient readers and in later units for less skilled readers. Major Takeaways: Behavioural patterns can be identified in digital reading tasks that may prove useful for educational monitoring and intervention. Although task situations are designed to evoke certain behaviours, the interpretation of observed behavioural patterns requires validation based on task requirements, assessment context and relationships to other available information. Lay Description: What is already known about the subject matter?: Students differ in how they read, comprehend and use digital information.Indicators from process data provide insight about how students engage with digital reading tasks. What does this paper add to the subject matter?: Based on multiple process indicators, a small number of clusters indicating different behavioural activity can be distinguished.These clusters can be described as on‐task, passive, hasty, exploring, disengaged, persistent and lost interest.A meaningful interpretation of the clusters must consider the requirements of the underlying tasks. Implications for practice and/or policy: Knowledge of how students engage with digital resources may provide useful feedback for teachers to guide students' learning or intervene when they struggle.Educational monitoring: The high comparability of country‐specific results suggests an invariant set of solution strategies in the digital reading assessment. [ABSTRACT FROM AUTHOR]

Background: Students often show unfavourable attribution: they attribute poor school performance to stable factors such as lack of ability and good school performance to variable factors such as effort. However, attribution can be influenced by individualized digital re‐attributional feedback leading to positive motivational effects and higher learning outcomes. This is very promising, but it still is unclear, whether this digital re‐attributional feedback can also be successfully integrated in everyday classroom activities. Objectives: The present field experiment investigated how integrating digital re‐attributional feedback into classroom instruction affects student attribution, motivation and learning outcomes. Methods: In the experiment, 8th–10th grade high school students (N = 322) worked with a digital mathematics learning program which was integrated in a three‐week teaching unit. Half the students in each classroom received only standard feedback after each practice task (SF group); the other half received additionally an individual re‐attributional feedback (RF group) after every third task. Attribution, mathematics self‐concept, and self‐efficacy were measured by an online questionnaire twice a week; learning outcomes in mathematics were measured weekly. Results and Conclusion: Hierarchical analyses showed that re‐attributional feedback led to a more favourable attribution in case of success on stable factors. Especially low‐performing students benefited from this feedback. No effects on attribution in case of failure, self‐efficacy or learning outcomes could be found. Further research could investigate if certain adaptations to the digital re‐attributional feedback is more effective in a real classroom setting and has a broader impact on different students. Lay Description: What is already known about this topic: Working with computers in the classroom and at home is becoming more common.Re‐attributional feedback can increase student's motivation when given directly after solving a task and at a high density.Digital re‐attributive feedback can be given in a high density.Re‐attributional training sessions have been shown to be effective in individual training sessions or outside the students' classroom. What this paper adds: The study took place within a real teaching environment during mathematics class for 4 weeks.Digital re‐attributional feedback sessions were directly integrated into the students' online learning which was part of the teaching plan. The implications of study findings for practitioners: Computer‐based re‐attributional training show some limited effects in regular classroom instruction and could be well integrated in student online learning—when adapted accordingly.Low‐performing students show less favourable attribution than better‐performing students in case of success and benefit the most from re‐attributional training. [ABSTRACT FROM AUTHOR]

Facilitators of professional development (PD) for mathematics teachers currently gain increasing attention, as their practices are crucial for the success of spreading mathematics educational ideas and innovations into schools and strengthening the professional expertise of teachers. So far, mainly two components of facilitation have been empirically researched: facilitators' knowledge resources and facilitation moves. In this paper, we propose to develop a more comprehensive conceptual framework in order to explain facilitators' practices and underlying decisions. For this purpose, we lift Schoenfeld's ROG framework for teachers' decision-making (comprising resources, orientations, and goals) to the facilitator level, and add identity as a fourth component to obtain what we call the ROGI framework. We draw on data collected simultaneously in two PD projects for mathematics teachers in Germany and in Israel. Through three cases of facilitation, we illustrate how the adapted ROGI framework helps to understand processes of decision-making made by facilitators during mathematics professional development sessions. [ABSTRACT FROM AUTHOR]

Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers' professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions. [ABSTRACT FROM AUTHOR]

In Germany, the Abitur is the highest qualification granted at the end of secondary education after 12 or 13 years of schooling; it provides a general university entrance qualification. Traditionally, written and oral examinations are required to obtain the Abitur. Until 1990, there were mainly decentralized examinations in mathematics in West Germany (Federal Republic of Germany [FRG]), which were taken after 13 school years, and a centralized examination that students took after 12 years of school in East Germany (German Democratic Republic [GDR]). In the unified Germany, examinations are now increasingly set by the 16 individual federal states. This paper has a special focus on changes and permanent features in the written Abitur examination in mathematics in Germany in the context of the social changes caused by the German reunification in 1990. These changes since 1990 are described with regard to the initial situation and framing conditions for the written Abitur examination. Two time periods are considered: (1) the examination situation in the FRG and GDR before 1990 and (2) the changes in the five eastern German federal states (former GDR) under the system change and accession to the FRG after 1990 but before the PISA shock. [ABSTRACT FROM AUTHOR]

This paper focuses on commonalities and differences of three approaches to large-scale professional development (PD) in mathematics education, based on two studies from Germany and one from the United States of America. All three initiatives break new ground in improving PD targeted at educating 'multipliers,' and in all three cases specific design principles for successful PD are defined, implemented, and discussed. All three teams systematically investigate the success of their PD activity and thereby discuss their theoretical assumptions, research questions, methods, and results. Given the goal of scaling up, the initiatives are pilot projects due to the relatively small number of participants. The paper highlights the diversity of approaches, each including various specific strengths but also some limitations. This is done by analyzing the three studies regarding the features 'large-scale PD and scientific knowledge on it', 'goals and design of PD', 'research design and methods', and 'research results and implications'. Overall, the studies help to understand the enormous challenges of the field when aiming at large-scale PD and systematically investigating and reflecting its impact. One prominent challenge is teacher educators' double role of intervening and investigating. All three studies recommend a continued or even stronger focus on participants' practice and its challenges. It makes sense to assume that the focus on participants' practice and strengths is even more important when starting further cascades. [ABSTRACT FROM AUTHOR]

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Understanding the students' perception of STACK tasks is vital for optimizing the students' learning. Questionnaires are a common method to learn about their experiences, but they are time-consuming for teachers and students. Plus, they are usually answered with a certain delay after students have completed the task. To solve these problems, we developed STACKrate, a JavaScript-based tool that allows teachers to easily integrate a collection of evaluation questions directly into STACK questions. Thus, the evaluation is done directly after the students completed their work on the tasks. The tool uses a star rating principle and is designed to be intuitive and easy to use for students. In this paper, we describe the features and benefits of STACKrate and tell about the use of the tool in a course at Ruhr-Universität Bochum, Germany. We then discuss the added value of STACKrate in evaluation over the use of questionnaires alone. [ABSTRACT FROM AUTHOR]

The study presented in the paper has the following goals. The first is to review and compare teacher competence frameworks developed in Eastern (Chinese) and Western (German) contexts, exemplified for the domain of mathematics. Major similarities of the two contexts could be reconstructed in the conceptualization of teacher competence as a multidimensional construct comprising knowledge, teaching-related skills and beliefs. Distinct differences could be identified as well, with the Chinese frameworks including a wider range of teacher-competence facets and emphasizing more teaching-related competencies than the Western (German) frameworks. The second purpose is to adapt and validate a German framework of the measurement of mathematics teacher competence in a Chinese context. This adaptation and validation uses exemplarily mathematics teacher, in detail follow-up-studies of the international Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M). With the integration of a qualitative approach (e.g. elemental validity) and a quantitative approach (e.g. construct validity) to validate the framework, the results of both approaches suggest a satisfactory validity for the adaptation. Overall, the results point out that the examined teacher competence framework and its instruments can be used for comparative analyses in Germany and China. [ABSTRACT FROM AUTHOR]

Children with mathematical difficulties need to spend more time than typically achieving children on solving even simple equations. Since these tasks already require a larger share of their cognitive resources, additional demands imposed by the need to switch between tasks may lead to a greater decline of performance in children with mathematical difficulties. We explored differential task switch costs with respect to switching between addition versus subtraction with a tablet-based arithmetic verification task and additional standardized tests in German elementary school children in Grades 1 to 4. Two independent studies were conducted. In Study 1, we assessed the validity of a newly constructed tablet-based arithmetic verification task in a controlled classroom-setting (n = 165). Then, effects of switching between different types of arithmetic operations on accuracy and response latency were analyzed through generalized linear mixed models in an online-based testing (Study 2; n = 3,409). Children with mathematical difficulties needed more time and worked less accurately overall. They also exhibited a stronger performance decline when working in a task-switching condition, when working on subtraction (vs. addition) items and in operations with two-digit (vs. one-digit) operations. These results underline the value of process data in the context of assessing mathematical difficulties. [ABSTRACT FROM AUTHOR]

The registered report was targeted at identifying latent profiles of competence development in reading and mathematics among N = 15,012 German students in upper secondary education sampled in a multi-stage stratified cluster design across German schools. These students were initially assessed in grade 9 and provided competence assessments on three measurement occasions across six years using tests especially developed for the German National Educational Panel Study (NEPS). Using Latent Growth Mixture Models, Using Latent Growth Mixture Models, we aimed at identifying multiple profiles of competence development. Specifically, we expected to find at least one generalized (i.e., reading and mathematical competence develop similarly) and two specialized profiles (i.e., one of the domains develops faster) of competence development and that these profiles are explained by the specialization of interest and of vocational education of students. Contrary to our expectations, we did not find multiple latent profiles of competence development. The model describing our data best was a single-group latent growth model confirming a competence development profile, which can be described as specializing in mathematical competences, indicating a higher increase in mathematical competences as compared to reading competences in upper secondary school. Since only one latent profile was identified, potential predictors (specialization of vocational education and interest) for different profiles of competence development were not examined. [ABSTRACT FROM AUTHOR]

This study presents a small part of a larger study investigating Turkish and German mathematics teachers' and their students' values (Values in Mathematics Teaching in Turkey and Germany). The main focus of the study was school levels of the teachers working at primary and secondary schools. The interactions related to nationality were also of interest. The methodology employed in this paper was a descriptive study. The participants were 27 German and 33 Turkish teachers. A five-point Likert-type questionnaire was used as data collection instrument. The data were subjected to descriptive and inferential statistics for analysis. Effect size coefficients were also calculated. The results indicated that school levels of the teachers within and between the two nations had a significant effect on the mathematics teachers' education values. It is thought that these findings may help to show interesting differences in systems in Germany and Turkey. [ABSTRACT FROM AUTHOR]

Gender disparities persist in the field of mathematics in German science and academia. From one scientific career level to the next, the proportion of female scientists decreases and women are still underrepresented in the top positions in science/academia. Gatekeeping is assumed to be one reason for the persistence of this disparity. Gatekeepers influence access to and advancement in the science system: They recruit researchers and provide support in the form of knowledge relevant for career advancement and open the way for further career steps, i.e., they hold an important decision-making position regarding the future of prospective female scientists. The study investigates if and if so, how gender disparities are reinforced in recruitment and support processes by gatekeepers in a mathematical cluster of excellence in Germany. Qualitative semi-structured interviews were conducted with 44 scientific gatekeepers in leadership positions. The results show how recruitment and support practices, perceptions, and criteria of scientific potential are interwoven with gender stereotypes, thereby creating potential barriers for female PhD students and postdocs. [ABSTRACT FROM AUTHOR]

The present study investigated direct as well as indirect relations between children's emotion regulation (anger- and avoidant-oriented strategies), behavior regulation, and mathematics achievement in a longitudinal study during the transition from primary to secondary school in Germany. Participants were 76 primary school students attending grade four at Time 1, of whom 51 participated again as secondary school students attending grade five at Time 2, as well as children's mothers and teachers. Anger- and avoidant-oriented emotion regulation strategies at Time 1 were negatively associated to behavior regulation at Time 2. Behavior regulation at Time 2 was positively related to mathematics achievement at Time 2. There were no direct relations between emotion regulation (anger- and avoidant-oriented strategies) at Time 1 and mathematics achievement at Time 2. However, we found significant indirect negative effects between emotion regulation (anger- and avoidant-oriented strategies) at Time 1 and mathematics achievement at Time 2 via behavior regulation at Time 1. Thus, anger- and avoidant-oriented emotion regulation at Time 1 indirectly affected mathematics achievement negatively at Time 2 via behavior regulation at Time 2. This study confirms the complex structure of self-regulatory processes and underlines the importance of specific emotion regulation strategies for mathematics achievement. [ABSTRACT FROM AUTHOR]

In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics (Grassmann/Du Bois), on the possibility of quantitative psychology (Fechner/Kries, Wundt/Zeller), and on the meaning of temperature measurement (Maxwell,Mach.). Late nineteenth-century scrutinisers of the foundations of mathematics (Dedekind, Cantor, Frege, Russell) made little of Helmholtz's essay. Yet it inspired two mathematicians with an eye on physics (Poincaré and Hölder), and a few philosopher-physicists (Mach, Duhem,Campbell). The aim of the present paper is to situate Helmholtz's contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement., (2003 Published by Elsevier Ltd.)

The article discusses the life, works and contribution of Alexander Grothendieck in mathematics. Grothendieck is a man who changed mathematics within 20 years of work in functional analysis and algebraic geometry. He was born in Berlin, Germany in 1928 and became a political activist in all major European revolutions. He worked in functional analysis between 1950 and 1955, and posed many questions on the structure of topological linear locally convex spaces. Among his contributions to functional analysis include nuclear spaces, topological tensor products and Grothendieck inequality.

This large‐scale and longitudinal study examines early home support for learning, formal/informal home mathematics activities, and their associations with children's mathematical development between age two and six. Data were collected in Germany between 2012 and 2018, N = 1184 (49% girls, 51% boys), and 15% of children had parents with a migration history. Linguistically and mathematically stimulating, attentive, and responsive parent–child engagement at age two predicted children's mathematical skills at age four and six (small‐to‐medium effect size). Both formal and informal home mathematical activities at age five predicted children's mathematical skills at age six (small effect size), and were associated with children's prior mathematics attainment. This study also provides indicators where individual differences and social circumstances are relevant to understanding different early mathematics outcomes. [ABSTRACT FROM AUTHOR]

Against the growing demand for the STEM labour force, the study examines labour market returns to STEM qualifications among immigrants who arrived in Germany since the 1980s. Analysing the German microcensus data for years 2015 and 2016, we demonstrate that skilled immigrants with STEM qualifications largely attain better labour market outcomes in Germany compared to immigrants without STEM qualifications, thus narrowing the gap to their native-born counterparts. Male immigrants succeed in utilizing their STEM capital better than female immigrants, but all immigrants face difficulties in translating their STEM qualifications into STEM employment. Our analyses further focus on returns to various STEM qualifications, attesting that medical qualifications are especially beneficial for Germany's female immigrants. The analysis of heterogeneous effects of STEM qualifications across major migrant groups reveals that Eastern European male immigrants make the best of their STEM qualifications, whereas among women, STEM qualified from Turkey or MENA countries are the most successful. These and other findings are discussed both from the supply and demand sides of the labour market. [ABSTRACT FROM AUTHOR]

Germany has been officially free of bovine tuberculosis since 1996. However, in the last years there has been an increase of bovine tuberculosis cases, particularly in the southern part of Germany, in the Allgäu region. As a consequence a one-time tuberculosis surveillance program was revisited with different premortal and postmortal tests. The aim of this paper was to estimate diagnostic sensitivities and specificities of the different tests used within this surveillance program. In the absence of a perfect test with 100% sensitivity and 100% specificity, thus in the absence of a gold standard, a Bayesian latent class approach with two different datasets was performed. The first dataset included 389 animals, tested with single intra-dermal comparative cervical tuberculin (SICCT) test, PCR and pathology; the second dataset contained 175 animals, tested with single intra-dermal cervical tuberculin (SICT) test, Bovigam® assay, pathology and culture. Two-way conditional dependencies were considered within the models. Additionally, inter-laboratory agreement (five officially approved laboratories) of the Bovigam® assay was assessed with Cohen's kappa test (21 blood samples). The results are given in posterior means and 95% credibility intervals. The specificities of the SICT test, SICCT test, PCR and pathology ranged between 75.8% [68.8–82.2%] and 99.0% [96.8–100%]. The Bovigam® assay stood out with a very low specificity (6.9% [3.6–11.1%]), though it had the highest sensitivity (95.7% [91.3–99.2%]). The sensitivities of the SICCT test, PCR, SICT test, pathology and culture varied from 57.8% [48.0–67.6%] to 88.9% [65.5–99.7%]. The prevalences were 19.8% [14.6–26.5%] (three-test dataset) and 7.7% [4.2–12.3%] (four-test dataset). Among all pairwise comparisons the highest agreement was 0.62 [0.15–1]). In conclusion, the specificity of the Bovigam® assay and the inter-laboratory agreement were lower than expected. [ABSTRACT FROM AUTHOR]

The importance of learning technologies for mathematics education is increasing as new opportunities arise for mathematics education for all students, in school and at home. These so-called technology-enhanced learning environments (TELEs) incorporating technology with mathematical content are useful for developing mathematical knowledge and can simultaneously foster self-regulated learning (SRL) and motivational learning in mathematics. However, how do primary students' differences in their SRL and motivation affect their rating of the quality of mathematical TELEs? To answer this research question, we asked third and fourth-grade primary students (n = 115) to evaluate both their SRL, including metacognition and motivation, and the quality characteristics of the ANTON application, a frequently and intensively used TELE in Germany. Using a person-centered research approach by conducting a cluster analysis, we identified three SRL profiles of primary students--motivated self-learners, non-motivated self-learners, and average motivated non-self-learners--who differ in their ratings of the quality characteristics of the TELE (output variables). Our results highlight that motivated self-learners and non-motivated self-learners vary significantly in their rating of the adequacy of the TELE to their mathematical learning and highly but not significantly concerning the TELE's reward system. Moreover, differences existed between the motivated self-learners and the average motivated non-self-learners regarding their rating of the characteristic differentiation. Based on these findings, we assume that technical elements associated with adequacy, differentiation, and rewards of mathematical TELEs should be tailorable to the needs of individuals and groups of primary schoolchildren. [ABSTRACT FROM AUTHOR]

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Supporting students with difficulties in learning mathematics is a challenge for teachers and educational administrators. Formative assessment is considered to play a successful role in supporting at-risk students as well as students without difficulties in mathematics. There is a need for intervention programs, including formative assessment techniques, that (a) are easy to implement in the regular classroom without requiring radical changes in teachers' individual teaching style, and (b) are effective in supporting at-risk students at the earliest stage possible in their school careers. This article analyzes an effectiveness trial of a formative assessment program developed to meet these goals and conducted in the first two years of elementary school. The examination of the longitudinal dataset from Grades 1–3 (N = 2,330) revealed an effect after the implementation, which was maintained at nearly the same effect size one year after completion of the program. The findings imply that formative assessment can foster the arithmetic achievement of students at risk as well as that of the entire class without changing the curriculum or teachers' individual teaching style. [ABSTRACT FROM AUTHOR]

Developmental Coordination Disorder (DCD) and Attention Deficit Hyperactivity Disorder (ADHD) often co-occur and are associated with specific learning difficulties. Robust prevalence estimations do not yet exist. We studied how symptoms of DCD and/or ADHD are related to difficulties in reading, writing, and mathematics. Using the data from a large online study with a sample of 3,170 3rd and 4th grade children in Germany, including parent-reported DCD- and ADHD symptoms, we followed two approaches. In the categorical approach, we divided the children into groups with and without DCD and/or ADHD on the basis of cut-offs. The results showed that children without DCD/ADHD have fewer difficulties in all learning domains. Children with only DCD showed less learning difficulties than children with ADHD and the comorbid group. In the continuous approach, we performed a latent profile analysis on the basis of symptoms of fine and gross motor problems, inattention, hyperactivity, impulsivity, and intelligence. This yielded four disability profiles of children with (1) no DCD- or ADHD-symptoms, (2) clinical ADHD-scores and above-average DCD, (3) above-average DCD and inattention, and (4) above-average ADHD. Profiles 2 and 3 appeared related to the lowest learning achievement. Theoretical implications are discussed. [ABSTRACT FROM AUTHOR]

A frequent observation in the school context is that opportunities to learn from errors are often missed. However, a positive error climate may support learning from errors. For the school subject of mathematics, some findings about characteristics of the error climate already exist. But, a comparison of the error climate between different school subjects is still pending. In the present study, it is analyzed whether the error climate differs in different school subjects and whether the same interrelations between the ways in which individuals deal with errors can be found in these different school subjects. In a study with 937 students from 48 classrooms from grades 5 to 7, in different secondary schools in Germany and Austria, we assessed the error climate and individual reactions following errors in mathematics, German, and English. Small mean differences between mathematics and the two language subjects were yielded. In addition, we found medium-sized correlations between the error climate measures in the three school subjects. However, the same pattern of interrelations between error climate and the way individuals deal with errors for all three school subjects could be shown. The results suggest that the perception of the error climate is rather similar in different school subjects. This has implications, for instance, for interventions that aim at fostering the error climate. [ABSTRACT FROM AUTHOR]

As mathematical competence is linked to educational success, professional achievement, and even a country's economic growth, researchers have been interested in early predictors for quite some time. Although there have been numerous studies on domain‐specific numerical abilities predicting later mathematical competence in preschool children, research in toddlers is scarce, especially regarding additional influential aspects, such as domain‐general cognitive abilities and the children's social background. Using a large‐scale dataset, the present study examined predictive effects of numeracy skills in 17‐month‐olds for later mathematical achievement. We found small, positive effects, even when controlling for child‐related variables (i.e., age and sex) and the children's social background (i.e., maternal education and household language). Additionally, we compared results with a domain‐general categorization task and found no distinct effect on mathematical competence. The present results are discussed with regard to the specificities of the dataset, as well as implications for future studies on predictors of mathematical competence. [ABSTRACT FROM AUTHOR]

The present paper offers an exploration of the role achievement values play in the generation of mathematical achievement as measured in school grades and test scores. Based on a comparative study of 1665 German, Israeli, and Canadian 14-year-olds two hypotheses are tested. First, it is assumed that achievement value preferences have a dual role in the generation of high academic performance. On the one hand, they are assumed to facilitate a high achievement-related self-esteem, which itself is a strong covariate of good academic performance. On the other hand, they are expected to sensitize for achievement pressure from parents, which in turn increases anxiety, and henceforth lowers the achievement-related self-esteem. Secondly, it is assumed that one will find cross-cultural variation in the strength of the two postulated effects. The "positive" role of achievement values is assumed to be stronger in cultures with a more positive view on achievement (Canada, Israel), whereas the "negative" role is assumed to be stronger in cultures with a less positive view on achievement (Germany). Hypotheses were tested in a structural equation modeling frame, and are essentially confirmed. Effect sizes are, however, low, and confirmation pertains almost exclusively to grades, not to test scores as measures of mathematical abilities. [ABSTRACT FROM AUTHOR]

We present a deterministic (1+o(1))-approximation O(n1/2+o(1) + D1+o(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here n is the number of nodes in the network and D is its (hop) diameter. This is the first non-trivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+o(1))-approximation Õ(√n1/2D1/4+D)-time algorithm of Nanongkai [STOC 2014] by a factor of as large as n1/8, and (ii) the O(є-1logє-1)-approximation factor of Lenzen and Patt-Shamir's Õ(n1/2+є+D)-time algorithm [STOC 2013, pp. 381-390] within the same running time. (Throughout, we use Õ(.) to hide polylogarithmic factors in n.) Our running time matches the known time lower bound of Ω(√n/log n + D) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433-456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40-57]. It also implies a (2+o(1))-approximation O(n1/2+o(1)+D1+o(1))-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in Proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the "hitting set argument" commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic construction of an (no(1), o(1))-hop set of size n1+o(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988), pp. 434-446], source detection [C. Lenzen and D. Peleg, in Proceedings of PODC, 2013, pp. 375-382], and partial distance estimation [C. Lenzen and B. Patt-Shamir, in Proceedings of PODC, 2015, pp. 153-162]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+o(1))-approximation no(1)-time algorithm on congested cliques, and (ii) a (1+o(1))-approximation no(1)-pass n1+o(1)-space streaming algorithm. The first result answers an open problem in [D. Nanongkai, in Proceedings of STOC, 2014, pp. 565-573]. The second result partially answers an open problem raised by McGregor in 2006 [List of Open Problems in Sublinear Algorithms: Problem 14]. [ABSTRACT FROM AUTHOR]

Results of international comparison studies show substantially better mathematics performance of the investigated Asian than European students from the early years on. A Taiwanese-German Research Program (TaiGer) engages in exploring differences and similarities in the educational system, in teachers' knowledge and beliefs and in teaching or learning practice in Taiwan and Germany. Embedded in this Research Program, this contribution focuses on early mathematics education. As mathematics is often seen as an internationally more or less homogeneous discipline, it could be assumed that differences in the educational outcomes could be explained by, e.g. cultural-societal factors, curriculum or instruction practice. This contribution gives an overview about results of studies analyzing the differences between children's mathematical performance in Asia and Europe or America with a focus on early childhood education. For a sound comparison between countries aiming to analyze if cultural differences or other aspects (e.g. teaching practice or structural differences) are responsible for differences, basic conditions concerning teaching and learning should be controlled. At first sight, it could be recognized that, next to the cultural background, Germany and Taiwan differ extremely in basic frame conditions (e.g. preservice training) concerning early mathematics education. For this reason, this contribution analyzed if, with a third well-considered European country, a comparative design for ongoing research could be possible, where pairwise similarities allow to clarify relations between differences in early mathematics education and the cultural background on the one hand and early mathematics education and institutional frame conditions or the teachers' professional knowledge on the other hand. [ABSTRACT FROM AUTHOR]

• First study investigating causal inference of a math remedial program in Germany. • Microanalysis of a math remedial program with detailed information of the sample. • Semester-long remedial courses can be helpful compensating missing math skills. Almost all German universities complain that the math skills of students entering the higher education system do not meet the level demanded by universities. This is a major problem, particularly in math-related study programs such as economics, engineering or science. To bridge the gap, almost all universities offer some remedial math courses. However, there is only weak empirical evidence for the effectiveness of these courses in Germany. This paper aims to fill this gap by evaluating a remedial math course given within the Economics Department of a German university. A key finding: taking a math remedial course on a regular basis will enhance students' math skills and increase the probability of passing the final math exam by 35 percent. [ABSTRACT FROM AUTHOR]

We analyze the empirical content of the Roy model, stripped down to sector-specific unobserved heterogeneity and self-selection on the basis of potential outcomes. We characterize sharp bounds on the joint distribution of potential outcomes and testable implications of the Roy model. We apply these bounds to derive a measure of departure from Roy self-selection, so as to identify prime targets for intervention. Special emphasis is put on the case of binary outcomes. We analyze a Roy model of college major choice in Canada and Germany and take a new look at the underrepresentation of women in science, technology, engineering, and mathematics. [ABSTRACT FROM AUTHOR]