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Gustav Theodor Fechner was one of the outstanding German scientists and thinkers. He is well known as the eminent founder of a new science "psychophysics" - the quantitative study of the relations between physical stimuli and sensations. But it seems that first ideas and first solutions of this new science are not the result of hard experimental work but rather of metaphysical speculations. So we found for the first time the important "Fundamentalformel" in the philosophical book "Zend-Avesta", written by Fechner already in 1851. Therefore this formula may not be the result of his later experimental efforts, put down in writing in the important "Elemente der Psychophysik" (1860). In the present paper it was intended to retrace the so-called "indefinite train of thoughts" (Fechner) that lead him to his strictly mathematical formula.

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)

Presents information on mathematical communities, highlighting the Mathematisches Forschungsinstitut at Oberwolfach, Germany. Background information on the development of the institution; Reference to Wilhelm Suss work in the creation of the institution; Functions of the institution; Reference to a report by F. Joachim Weyl.

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)

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.)

Shares Oskar Morgenstern's memories of equilibrium and mathematics in the 1920s. Experience with famines and desolation in Germany; Anti-semitism in Vienna, Austria; Lack of instructions in mathematics and sciences at the University of Vienna.

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]

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.

Predictions about processes linking gender to students' choices of advanced courses were derived from the internal/external frame of reference (I/E) model and expectancy value (EV) theory. The predictions were tested for the domains of mathematics and biology using data from 1,148 students attending academically oriented secondary schools in Germany. Results revealed substantial gender differences on measures gathered in Grade 10. Males outperformed females on the mathematics and biology achievement tests, and reported higher math self-concepts and intrinsic values. Females scored higher on the biology self-concept and intrinsic value scales. Consistent with our expectations, gender differences in Grade 10 mediated the effect of gender on course enrollment in Grade 12. In line with the EV model, self-concepts and intrinsic values had substantial effects on subsequent course choices. As predicted by the I/E model, domain-specific self-concepts and intrinsic values were positively related to course choices in the same domain, but negatively related to choices in the other domain. In addition, results of multigroup structural equation models revealed that the processes underlying course choices were different for males and females. Finally, students' choices of specialized courses were related to their aspired field of college education. [ABSTRACT FROM AUTHOR]

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.

The author reflects on the vulnerability of German Jews who pursued academic careers in mathematics with a focus on the life and works of Adolf Hurwitz. He explains that in writing about Jewish mathematicians in Germany during the Second Empire, it is a difficult issue deciding what should count as Jewish since many Jews were no longer practicing their religion. Hurwitz was considered as one of the most important figures in mathematics in the 19th century. INSET: Two Tributes to Adolf Hurwitz.

In Germany, problem solving has important roots that date back at least to the beginning of the twentieth century. However, problem solving was not primarily an aspect of mathematics education but was particularly influenced by cognitive psychologists. Above all, the Gestalt psychology developed by researchers such as Köhler (Intelligenzprüfungen an Anthropoiden. Verlag der Königlichen Akademie des Wissens, Berlin, 1917; English translation: The mentality of apes. Harcourt, Brace, New York, 1925), Duncker (Zur Psychologie des produktiven Denkens. Springer, Berlin, 1935), Wertheimer (Productive thinking. Harper, New York, 1945), and Metzger (Schöpferische Freiheit. Waldemar Kramer, Frankfurt, 1962) made extensive use of mathematical problems in order to describe their specific problem-solving theories. However, this research had hardly any influence on mathematics education-neither as a scientific discipline nor as a foundation for mathematics instruction. In the German mathematics classroom, problem solving, which is according to Halmos (in Am Math Mon 87:519-524, 1980) the "heart of mathematics," did not attract the interest it deserved as a genuine mathematical topic. There is some evidence that this situation may change. In the past few years, nationwide standards for school mathematics have been introduced in Germany. In these standards, problem solving is specifically addressed as a process-oriented standard that should be part of the mathematics classroom through all grades. This Abstract In Germany, problem solving has important roots that date back at least to the beginning of the twentieth century. However, problem solving was not primarily an aspect of mathematics education but was particularly influenced by cognitive psychologists. Above all, the Gestalt psychology developed by researchers such as Köhler (Intelligenzprüfungen an Anthropoiden. Verlag der Königlichen Akademie des Wissens, Berlin, 1917; English translation: The mentality of apes. Harcourt, Brace, New York, 1925), Duncker (Zur Psychologie des produktiven Denkens. Springer, Berlin, 1935), Wertheimer (Productive thinking. Harper, New York, 1945), and Metzger (Schöpferische Freiheit. Waldemar Kramer, Frankfurt, 1962) made extensive use of mathematical problems in order to describe their specific problem-solving theories. However, this research had hardly any influence on mathematics education-neither as a scientific discipline nor as a foundation for mathematics instruction. In the German mathematics classroom, problem solving, which is according to Halmos (in Am Math Mon 87:519-524, 1980) the "heart of mathematics," did not attract the interest it deserved as a genuine mathematical topic. There is some evidence that this situation may change. In the past few years, nationwide standards for school mathematics have been introduced in Germany. In these standards, problem solving is specifically addressed as a process-oriented standard that should be part of the mathematics classroom through all grades. This article provides an overview on problem solving in Germany with reference to psychology, mathematics, and mathematics education. It starts with a presentation of the historical roots but gives also insights into contemporary developments and the classroom practice. [ABSTRACT FROM AUTHOR]

The paper explores the trend of the early 20th century to consolidate mathematics, natural sciences, medicine and technology under the umbrella of one integrative culture--a tendency which contrasts with the increasing mainstream trend of separating the humanities from the natural sciences. The unifying umbrella was framed by the great encyclopedia Die Kultur der Gegenwart which was published by B. G. Teubner from 1905 to 1925 and was planned to run up to 62 volumes. We analyze the quantitative rate of the parts devoted to the humanities, the natural sciences and technology, respectively, the degree to which these parts were completed in this encyclopedia. In particular, we investigate the role of mathematicians and their reasons to find a classification for the mathematical, natural scientific and engineering parts of culture as well as their reasons, to win Nobel prize winners and other famous scientists to become co-editors and authors. We examine the published volumes in the fields of mathematics, chemistry, physics, astronomy and technology in order to show what type of publication--professional or popular--was intended. Furthermore, we illuminate how the educational reform of mathematics, natural sciences and technology of this period--which included a reform of girls' and women's education--was reflected in the encyclopedia Die Kultur der Gegenwart.

In this article, we discuss the complexity of geometric proofs with respect to a theoretical analysis and empirical results from studies in Taiwan and Germany. Based on these findings in both countries, specific teachings experiments with junior high school students were developed, conducted, and evaluated. According to the different classroom and learning culture in East Asia and Western Europe, the interventions differed in their way of organizing the learning activities during regular mathematics lessons. The statistical analysis of the pre-post-test data indicated that both interventions were successful in fostering students' proof competence. [ABSTRACT FROM AUTHOR]

This article results from the project “Oral History by example of new developments in mathematics at the University of Hamburg”, which was worked out under the leading of Professor Dr. Karin Reich at the Institute for the History of Science, Mathematics and Technology at the University of Hamburg in winter term 2006/2007. [ABSTRACT FROM AUTHOR]

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.

Many empirical investigations concerning the use of computer algebra systems (CAS) and symbolic calculators (SC) are restricted to a period of only a few weeks. They do not show long-term effects on students understanding. Therefore, a long term project (2003-2012) was started to test the use of symbolic calculators in Bavarian "Gymnasien" (grammar schools) in Germany. The project started with an evaluation in grade 10 (see Weigand, 2008). During the 2006/07 and the following school years the project was implemented in the 11th grade. The content taught was calculus: basic properties of functions, limits, continuity, derivatives, and applications of calculus. The evaluation of the project was intended to give answers to the following questions: How did basic mathematical skills (algebraic transformations, solving equations) change? How did students use the SC? How did they evaluate the use of the new tool? The results show that it takes a long time (one year) to get students acquainted with the technology. Moreover, hopes have not been fulfilled that students of these project classes would improve to a greater degree (especially in abilities which might typically be supported by the use of the SC, e. g. interpreting graphs) than students in the control classes. In addition, a relationship between the mathematical abilities of students and their ability in using the SC in problem-solving processes was made. The results of this study raise questions concerning the adequate way to support and foster the - theoretically quite often emphasised - new possibilities of CAS and SC in the class room. [ABSTRACT FROM AUTHOR]

Copyright of European Early Childhood Education Research Journal is the property of Routledge and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

There is still a lack of quantitative information concerning optimal blood flow in the aorta and in the carotid arteries during extracorporeal circulation (ECC). Problems are not only based on the location of the aortic cannula, they are furthermore associated with the cannula design itself and the effects on blood cells and aortic wall shear stresses. We simulated a two-phase fluid flow induced by different cannulas in the ascending aorta during ECC. Three commercially available cannulas were examined according to their influence on red blood cells (RBC). Additionally, mass flow in the carotid vessels and wall shear stresses acting on the aortic wall were evaluated. A constant volume flow of blood (3.4 L/min) was applied. Numerical results demonstrate a strong relation between the mass flow rate in the carotid vessels and the geometry of the aortic outflow cannula. RBC distributions both in the aorta and the carotid vessels changed depending on cannula geometry. Maximum blood velocities, shear stresses on the aortic wall, and the fluid mechanical load acting on RBCs varied depending on each cannula design. This numerical approach demonstrates the significant influence of the cannula design on the distribution of RBCs in the carotid vessels during ECC. [ABSTRACT FROM AUTHOR]

In a data set of 291 spontaneous utterances from German 5-year-olds, 7-year-olds and adults, nuclear pitch contours were labeled manually using the GToBI annotation system. Ten different contour types were identified.The fundamental frequency (F0) of these contours was modeled using third-order orthogonal polynomials, following an approach similar to the one Grabe, Kochanski, and Coleman (2007) used for English. Statistical analyses showed that all but one contour pair differed significantly from each other in at least one of the four coefficients. This demonstrates that polynomial modeling can provide quantitative empirical support for phonological labels in unscripted speech, and for languages other than English. Furthermore, polynomial expressions can be used to derive the alignment of tonal targets relative to the syllable structure, making polynomial modeling more accessible to the phonological research community. Finally, within-contour comparisons of the three age groups showed that for children, the magnitude of the higher coefficients is lower, suggesting that they are not yet able to modulate their pitch as fast as adults. [ABSTRACT FROM PUBLISHER]

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.)

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.

Copyright of Lithuanian Journal of Statistics / Lietuvos Statistikos Darbai is the property of Lithuanian Statistical Association and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This study reported the specific findings of a larger comparative study concerning Turkish and German mathematics teachers' values. The main focus was on the teaching experience of the mathematics teachers. Interactions related to nationality were also of interest. The research methodology employed in this study was a descriptive study. The teachers involved in the study were 27 German and 33 Turkish mathematics teachers. A five-point Likert-type questionnaire was used as the data collection instrument. The data were subjected to descriptive and inferential statistics for analysis. Effect size coefficients were also calculated. The results showed that: (a) the teaching experience between the countries has a significant effect on the values and (b) both Turkish and German math teachers' level of experience does not have a significant impact on their values. [ABSTRACT FROM AUTHOR]

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 study presents serogroup 6 isolates from invasive pneumococcal disease (IPD) before and after the recommendation for childhood pneumococcal conjugate vaccination in Germany (July 2006). A total of 19,299 (children: 3508, adults: 15,791) isolates were serotyped. Serogroup 6 isolates accounted for 9.5% (children) and 6.7% (adults), respectively. 548 isolates had serotype 6A, 558 had serotype 6B, 285 had serotype 6C, and 4 had serotype 6D. Among children, serotype 6B was most prevalent (7.5% of isolates) before vaccination, followed by 6A and 6C. After the 7-valent pneumococcal conjugate vaccine (PCV7), the prevalence of serotype 6B significantly decreased (p = 0.040), a pattern which continued in the higher-valent PCV period (PCV10, PCV13). Serotype 6A prevalence showed a slight increase directly after the start of PCV7 vaccination, followed by a decrease which continued throughout the PCV10/13 period. Serotype 6C prevalence remained low. Serotype 6D was not found among IPD isolates from children. Among adults, prevalence of both 6A and 6B decreased, with 6B reaching statistical significance (p = 0.045) and 6A showing a small increase in 2011–2012. Serotype 6C prevalence was 1.5% or lower before vaccination, but increased post-vaccination to 3.6% in 2011/12 (p = 0.031). Four serotype 6D isolates were found post-PCV7 childhood vaccination, and two post-PCV10/13. Antibiotic resistance was found mainly in serotype 6B; serotype 6A showed lower resistance rates. Serotype 6C isolates only showed resistance among adults; serotype 6D isolates showed no resistance. Multilocus sequence typing showed that sequence type (ST) 1692 was the most prevalent serotype 6C clone. Thirty-two other STs were found among serotype 6C isolates, of which 12 have not been previously reported. The four serotype 6D isolates had ST 948, ST 2185 and two new STs: 8422 and 8442. Two serogroup 6 isolates could not be assigned to a serotype, but had STs common to serogroup 6. [ABSTRACT FROM AUTHOR]

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 enrolled in upper-secondary school are systematically graded better. [ABSTRACT FROM AUTHOR]

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.

Objective: To examine, whether overweight in adolescents can be predicted from the body mass index (BMI) category, at the age of 6, the mother's education level and mother's obesity and to quantify the proportion of overweight at the age of 14 that can be explained by these predictors. Method: Pooled data from three German cohorts providing anthropometric and other relevant data to a total of 1 287 children. We used a classification and regression tree (CART) approach to identify the contribution of BMI category at the age of 6 (obese: BMI>97th percentile (P97); overweight: P90P90) at the age of 14. Results: While 4.8% [95%CI: 3.2;7.0] of 651 boys and 4.1% [95%CI: 2.6;6.2] of 636 girls with a BMIP97 (similar results for girls). BMI≥P75 at the age of 6 explained 63.5% [95%CI: 51.1;74.5]) and 72.0% [95%CI: 60.4;81.8] of overweight/obesity at the age of 14 in boys and girls, respectively. Conclusions: Overweight/obesity in adolescence can be predicted by BMI category at the age of 6 allowing for parent counselling or risk guided interventions in children with BMI≥P75, who accounted for >2/3 of overweight/obesity in adolescents. [ABSTRACT FROM AUTHOR]

Background: There is growing evidence that air pollutants are associated with the risk of type 2 diabetes. Subclinical inflammation may be a mechanism linking air pollution with diabetes. Information is lacking whether air pollution also contributes to worse metabolic control in newly diagnosed type 2 diabetes. We examined the hypothesis that residential particulate matter (PM10) is associated with HbA1c concentration in newly diagnosed type 2 diabetes. Methods: Nationwide regional levels of particulate matter with a diameter of ≤10 µm (PM10) were obtained in 2009 from background monitoring stations in Germany (Federal Environmental Agency) and assigned to place of residency of 9,102 newly diagnosed diabetes patients registered in the DPV database throughout Germany (age 65.5±13.5 yrs; males: 52.1%). Mean HbA1c (%) levels stratified for air pollution quartiles (PM10 in µg/m3) were estimated using linear regression models adjusting for age, sex, BMI, diabetes duration, geographic region, year of ascertainment, and social indicators. Findings: In both men and women, adjusted HbA1c was significantly lower in the lowest quartile of PM10 exposure in comparison to quartiles Q2–Q4. Largest differences in adjusted HbA1c (95% CI) were seen comparing lowest quartiles of exposure with highest quartiles (men %: −0.42 (−0.62; −0.23)/mmol/mol: −28.11 (−30.30; −26.04), women, %: −0.28 (−0.47; −0.09)/mmol/mol: −0.28 (−0.47; −0.09)). Interpretation: Air pollution may be associated with higher HbA1c levels in newly diagnosed type 2 diabetes patients. Further studies are warranted to examine this association. [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]

A goal in many countries is to institute state-wide exams to base student assessment more firmly on norms for all classes. This raises the question as to the extent to which greater standardization of grading practice can be reached by implementing state-wide exit exams. Since there is a lack of longitudinal studies, we analyzed the effect of the implementation of state-wide exit exams in all 19 academic upper secondary schools (N= 19) in the German state of Bremen over 5 years. We used a standardized achievement test in mathematics and students’ exit exam and semester grades. For the advanced courses, the results show a standardization effect at the school level and for semester grades. No standardization effect is found for the exit exams on the individual level. For the basic courses, the results show positive effects for semester and exit exams grades. Theoretical and practical implications as well as the robustness of the findings are discussed. [ABSTRACT FROM PUBLISHER]

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]

Activities of daily living (ADL) of children are widely assessed with the Pediatric Evaluation Disability Inventory (PEDI). This study examined test–retest and inter-rater reliability of the German PEDI (PEDI-G). During the adaptation of the PEDI nine items were added. In total, 117 parents of 53 children without and 64 children with a diagnosed physical disability from Austria, Germany, and Switzerland participated. Reliability was examined by intraclass correlation coefficient (ICC), standard error of measurement (SEM) and smallest detectable difference (SDD) for the Functional Skill Scale with and without added items and the Caregiver Assistance Scale. Cohen`s Kappa was used to calculate the reliability of the Modification Scale. All ICC's for test–retest and inter-rater reliability were above 0.75, indicating good to very good reliability. The SDD varied from 0.83–5.58 across PEDI domains and scales. For the Modification Scale, Cohen's weighted kappa varied from 0.25 to 1.00 indicating sufficient reliability for some but not all items. Our findings indicate that the Functional Skill Scale and the Caregiver Assistance Scale of the PEDI-G are reliable scales that can be used to evaluate ADLs of children with and without physical disability. [ABSTRACT FROM PUBLISHER]

Objective: To examine whether intra- and intergenerational caregiving affect subjective well-being (SWB) of the caregivers longitudinally. Methods: Data were drawn from the German Ageing Survey (DEAS), which is a population-based longitudinal study of individuals living in Germany aged 40 and over. The waves in 2002, 2008 and 2011 were used (with 10,434 observations). SWB was examined in a broad sense, covering affective (AWB) and cognitive well-being (CWB), positive (PA) and negative affect (NA) as well as functional and mental health. While intragenerational caregiving was defined as providing care for spouse/partner, intergenerational caregiving was defined as providing care for mother, father, mother-in-law, father-in-law, partner’s mother or partner’s father. Results: Fixed effects regressions adjusting for sociodemographic factors, social network, self-efficacy and morbidity showed that intergenerational informal care did not affect the various SWB outcome measures. Intragenerational caregiving affected CWB (women) and mental health (total sample and men), whereas it did not affect the other outcome variables. Conclusion: Our findings highlight the importance of intragenerational caregiving for mental health (men) and cognitive well-being (women). Consequently, interventions to avoid mental illness due to intragenerational caregiving are urgently needed. [ABSTRACT FROM AUTHOR]

Interference Frisian (IF) is a variety of Frisian, spoken by mostly younger speakers, which is heavily influenced by Dutch. IF exhibits all six logically possible word orders in a cluster of three verbs. This phenomenon has been researched by Koeneman and Postma (2006), who argue for a parameter theory, which leaves frequency differences between various orders unexplained. Rejecting Koeneman and Postma’s parameter theory, but accepting their conclusion that Dutch (and Frisian) data are input for the grammar of IF, we will argue that the word order preferences of speakers of IF are determined by frequency and similarity. More specifically, three-verb clusters in IF are sensitive to: their linear left-to-right similarity to two-verb clusters and three-verb clusters in Frisian and in Dutch; the (estimated) frequency of two- and three-verb clusters in Frisian and Dutch. The model will be shown to work best if Dutch and Frisian, and two- and three-verb clusters, have equal impact factors. If different impact factors are taken, the model’s predictions do not change substantially, testifying to its robustness. This analysis is in line with recent ideas that the sequential nature of human speech is more important to syntactic processes than commonly assumed, and that less burden need be put on the hierarchical dimension of syntactic structure. [ABSTRACT FROM AUTHOR]

Purpose: Preliminary iodine concentration (UIC) measurements in spot urines of the representative German adult study DEGS indicated a severe worsening of iodine status compared to previous results in German children (KiGGS study). Therefore, we aimed to evaluate adult iodine status in detail and to investigate the impact of hydration status on UIC. Methods: UIC and creatinine concentrations were measured in 6978 spot urines from the German nationwide DEGS study (2008-2011). Twenty-four-hour iodine excretions (24-h UIE) were estimated by relating iodine/creatinine ratios to age- and sex-specific 24-h creatinine reference values. Urine osmolality was measured in two subsamples of spot urines ( n = 100 each) to determine the impact of hydration status on UIC. Results: In DEGS, median UIC was 69 µg/L in men and 54 µg/L in women, lying clearly below the WHO cutoff for iodine sufficiency (100 µg/L). Estimated median 24-h UIE was 113 µg/day, accompanied by 32 % of DEGS adults, lying below the estimated average requirement (EAR) for iodine. Comparative analysis with the KiGGS data (>14,000 spot urines of children; median UIC 117 µg/L) revealed a comparable percentage

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.

The (German) market for law professors fulfils the conditions for a hog cycle: In the short run, supply cannot be extended or limited; future law professors must be hired soon after they first present themselves, or leave the market; demand is inelastic. Using a comprehensive German dataset, we show that the number of market entries today is negatively correlated with the number of market entries eight years ago. This suggests short-sighted behavior of young scholars at the time when they decide to prepare for the market. Using our statistical model, we make out-of-sample predictions for the German academic market in law until 2020. [ABSTRACT FROM AUTHOR]

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth-grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers. [ABSTRACT FROM AUTHOR]

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 Scale of Positive and Negative Experience (SPANE) measures the frequency of positive and negative affect. It consists of two subscales, one for positive and one for negative affect with six adjectives each and assesses a broad range of emotions. In this study, the psychometric properties of the German version of the scale were explored with reliability and confirmatory factorial analysis by using a German sample of N = 498. To examine the convergent validity of the SPANE we correlated its subscales with other well-being and happiness measures. Retest-reliabilities were tested after four weeks, taking into account the occurrence of emotionally significant life events. The scale was also applied to evaluate a training of subjective well-being and in a study on text comprehensibility. The results confirmed the postulated two-factor structure of the SPANE and showed good psychometric properties and convergent validity. In conclusion, the German version of the scale behaves in accordance with the original scale and may be used in future studies of well-being. [ABSTRACT FROM AUTHOR]

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.

Sex differences in mathematical performance have frequently been examined over the last decades indicating an advantage for males especially when numerical problems cannot be solved by (classroom-)learnt strategies and/or estimation. Even in basic numerical tasks such as number line estimation, males were found to outperform females - with sex differences argued to emerge from different solution strategies applied by males and females. We evaluated the latter using two versions of the number line estimation task: a bounded and an unbounded task version. Assuming that women tend more strongly to apply known procedures, we expected them to be at a particular disadvantage in the unbounded number line estimation task, which is less prone to be solved by specific strategies such as proportion judgement but requires numerical estimation. Results confirmed more pronounced sex differences for unbounded number line estimation with males performing significantly more accurately in this task version. This further adds to recent evidence suggesting that estimation performance in the bounded task version may reflect solution strategies rather than numerical estimation. Additionally, it indicates that sex differences regarding the spatial representation of number magnitude may not be universal, but associated with spatial-numerical estimations in particular. [ABSTRACT FROM AUTHOR]