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Zusammenfassung. Hintergrund: Die Subjektwissenschaftliche Lerntheorie betrachtet Lernprozesse vom Standpunkt des Subjektes. Dabei wird ein besonderer Fokus auf Begründungsstrukturen für gelingende oder nicht gelingende Lernhandlungen gelegt. Die subjektwissenschaftliche Perspektive scheint gerade für die Betrachtung von Lernprozessen in der Alphabetisierung und Grundbildung gewinnbringend, da bisherige (negative) Lernerfahrungen, unterschiedlich zusammengesetzte Kompetenzen sowie spezifische Bildungsziele (wie z.B. gesellschaftliche Teilhabe) auf besondere Weise das Lernen beeinflussen können. Grundbildungszentren (GBZen) können als regionale Anlaufstellen für unterschiedliche Fragestellungen bezüglich der Grundbildung und Alphabetisierung Erwachsener Lernenden gelten. Dabei halten GBZen sowohl niedrigschwellige Lernangebote für Menschen mit Alphabetisierungs- und Grundbildungsbedarfen vor, als auch regionale Netzwerk- und Kooperationsstrukturen, um das Umfeld der Lernenden zu sensibilisieren. Methoden: Anhand von zwölf Interviews und vier Selbstberichten, die im Rahmen einer Evaluationsstudie generiert wurden, wurde folgende Fragestellung sekundäranalytisch beantwortet: Welches Potential haben die GBZen Lernprozesse subjektorientiert zu gestalten? Ergebnisse und Diskussion: Die Ergebnisdarstellung erfolgt anhand einer institutionellen, interaktionellen sowie individuellen Ebene. Die Ergebnisse zeigen, dass die Struktur der GBZen eine wesentliche Vorbedingung darstellt, Lernenden subjektorientiert zu unterstützen, sich das Potenzial in vollem Umfang aber nur durch das Zusammenwirken aller drei Ebenen entfalten kann.

Background Endoscopic and laparoscopic electrosurgical devices (ED) are of great importance in modern medicine but can cause adverse events such as tissue injuries and burns from residual heat. While laparoscopic tools are well investigated, detailed insights about the temperature profile of endoscopic knives are lacking. Our aim is to investigate the temperature and the residual heat of laparoscopic and endoscopic monopolar instruments to increase the safety in handling ED. Methods An infrared camera was used to measure the temperature of laparoscopic and endoscopic instruments during energy application and to determine the cooling time to below 50 °C at a porcine stomach. Different power levels and cutting intervals were studied to investigate their impact on the temperature profile. Results During activation, the laparoscopic hook exceeded 120 °C regularly for an up to 10 mm shaft length. With regards to endoknives, only the Dual Tip Knife showed a shaft temperature of above 50 °C. The residual heat of the laparoscopic hook remained above 50 °C for at least 15 s after activation. Endoknives cooled to below 50 °C in 4 s. A higher power level and longer cutting duration significantly increased the shaft temperature and prolonged the cooling time (p Conclusion Residual heat and maximum temperature during energy application depend strongly on the chosen effect and cutting duration. To avoid potential injuries, the user should not touch any tissue with the laparoscopic hook for at least 15 s and with the endoknives for at least 4 s after energy application. As the shaft also heats up to over 120 °C, the user should be careful to avoid tissue contact during activation with the shaft. These results should be strongly considered for safety reasons when handling monopolar ED.

Background Mechanical ventilation with variable tidal volumes (VT) may improve lung function and reduce ventilator-induced lung injury in experimental acute respiratory distress syndrome (ARDS). However, previous investigations were limited to less than 6 h, and control groups did not follow clinical standards. We hypothesised that 24 h of mechanical ventilation with variable VT reduces pulmonary inflammation (as reflected by neutrophil infiltration), compared with standard protective, nonvariable ventilation. Methods Experimental ARDS was induced in 14 anaesthetised pigs with saline lung lavage followed by injurious mechanical ventilation. Pigs (n=7 per group) were randomly assigned to using variable VT or nonvariable VT modes of mechanical ventilation for 24 h. In both groups, ventilator settings including positive end-expiratory pressure and oxygen inspiratory fraction were adjusted according to the ARDS Network protocol. Pulmonary inflammation (primary endpoint) and perfusion were assessed by positron emission tomography using 2-deoxy-2-[18F]fluoro-d-glucose and 68Gallium (68Ga)-labelled microspheres, respectively. Gas exchange, respiratory mechanics, and haemodynamics were quantified. Lung aeration was determined using CT. Results The specific global uptake rate of 18F-FDG increased to a similar extent regardless of mode of mechanical ventilation (median uptake for variable VT=0.016 min−1 [inter-quartile range, 0.012–0.029] compared with median uptake for nonvariable VT=0.037 min−1 [0.008–0.053]; P=0.406). Gas exchange, respiratory mechanics, haemodynamics, and lung aeration and perfusion were similar in both variable and nonvariable VT ventilatory modes. Conclusion In a porcine model of ARDS, 24 h of mechanical ventilation with variable VT did not attenuate pulmonary inflammation compared with standard protective mechanical ventilation with nonvariable VT.

The conceptual development of natural number in preschoolers is well-researched. However, less is known about the conceptual development of zero. Recent studies suggest that children develop an understanding of zero after learning to count. It remains unclear, when a conceptual understanding of “zero” as number word for an empty set emerges. This paper integrates numerical and language theories about how, where and when the concept of zero is formed and is integrated into the class of natural numbers. The counting skills of 107 preschoolers were assessed for the number range between zero and eight as well as for their ordinal understanding of zero. The results show that compared to the natural numbers, zero was substantially more difficult. Children are able to list zero in a number word sequence (0, 1, 2, 3 .... or 3, 2, 1, 0), but were unable to describe a set as having zero numbers. This latter conception contradicts findings regarding natural numbers, in that an empty set is counter intuitive. Zero could be correctly placed when consecutive order was required, but addition and subtraction by counting was more difficult. The results suggest that the conceptual development of zero differs qualitatively from the natural numbers. Based on the results, the ordinal understanding of zero as a predecessor to one, together with its matching linguistic concepts is proposed to be the key to the conceptual development of zero.

Objectives To determine the impact of positive end-expiratory pressure during mechanical ventilation with and without spontaneous breathing activity on regional lung inflammation in experimental nonsevere acute respiratory distress syndrome. Design Laboratory investigation. Setting University hospital research facility. Subjects Twenty-four pigs (28.1-58.2 kg). Interventions In anesthetized animals, intrapleural pressure sensors were placed thoracoscopically in ventral, dorsal, and caudal regions of the left hemithorax. Lung injury was induced with saline lung lavage followed by injurious ventilation in supine position. During airway pressure release ventilation with low tidal volumes, positive end-expiratory pressure was set 4 cm H2O above the level to reach a positive transpulmonary pressure in caudal regions at end-expiration (best-positive end-expiratory pressure). Animals were randomly assigned to one of four groups (n = 6/group; 12 hr): 1) no spontaneous breathing activity and positive end-expiratory pressure = best-positive end-expiratory pressure - 4 cm H2O, 2) no spontaneous breathing activity and positive end-expiratory pressure = best-positive end-expiratory pressure + 4 cm H2O, 3) spontaneous breathing activity and positive end-expiratory pressure = best-positive end-expiratory pressure + 4 cm H2O, 4) spontaneous breathing activity and positive end-expiratory pressure = best-positive end-expiratory pressure - 4 cm H2O. Measurements and main results Global lung inflammation assessed by specific [F]fluorodeoxyglucose uptake rate (median [25-75% percentiles], min) was decreased with higher compared with lower positive end-expiratory pressure both without spontaneous breathing activity (0.029 [0.027-0.030] vs 0.044 [0.041-0.065]; p = 0.004) and with spontaneous breathing activity (0.032 [0.028-0.043] vs 0.057 [0.042-0.075]; p = 0.016). Spontaneous breathing activity did not increase global lung inflammation. Lung inflammation in dorsal regions correlated with transpulmonary driving pressure from spontaneous breathing at lower (r = 0.850; p = 0.032) but not higher positive end-expiratory pressure (r = 0.018; p = 0.972). Higher positive end-expiratory pressure resulted in a more homogeneous distribution of aeration and regional transpulmonary pressures at end-expiration along the ventral-dorsal gradient, as well as a shift of the perfusion center toward dependent zones in the presence of spontaneous breathing activity. Conclusions In experimental mild-to-moderate acute respiratory distress syndrome, positive end-expiratory pressure levels that stabilize dependent lung regions reduce global lung inflammation during mechanical ventilation, independent from spontaneous breathing activity.

Wie hängen sprachliche und mathematische Entwicklung zusammen? Dieser Frage wird derzeit mit großem Interesse aus unterschiedlichen Perspektiven nachgegangen. Dieser Sammelband vereint Erkenntnisse aus Psychologie, Neurowissenschaften, Mathematikdidaktik, (Psycho-)Linguistik und Mehrsprachigkeitsforschung. Der interdisziplinäre Ansatz bietet einen umfassenden Blick auf den aktuellen Forschungsstand, dargestellt von national und international renommierten Forschenden. Das Buch gliedert sich in drei Teile. Der erste Teil „Modelle und Theorien“ fasst theoretische Überlegungen zusammen und stellt Strukturen für Forschung und Praxis bereit. Dieser Teil dient dazu, den Grundstein für die anderen Teile sowie für zukünftige Forschung zu legen. Der zweite Teil „Kindergartenalter“ sowie der dritte Teil „Grundschulalter“ decken empirische Befunde über die Korrelation zwischen Sprache und mathematischem Lernen in der jeweiligen Altersgruppe ab. Ein besonderer Fokus liegt hierbei auf dem Aspekt der Mehrsprachigkeit. Damit bietet dieser Sammelband eine große Bandbreite fachspezifischen Wissens für Bildungswissenschaftler*innen, Lehramtsstudierende, Psycholog*innen und Forschende zur Mehrsprachigkeit.

Background Continuous external negative pressure (CENP) during positive pressure ventilation can recruit dependent lung regions. We hypothesised that CENP applied regionally to the thorax or the abdomen only, increases the caudal end-expiratory transpulmonary pressure depending on positive end-expiratory pressure (PEEP) in lung-injured pigs. Eight pigs were anesthetised and mechanically ventilated in the supine position. Pressure sensors were placed in the left pleural space, and a lung injury was induced by saline lung lavages. A CENP shell was placed at the abdomen and thorax (randomised order), and animals were ventilated with PEEP 15, 7 and zero cmH2O (15 min each). On each PEEP level, CENP of − 40, − 30, − 20, − 10 and 0 cmH2O was applied (3 min each). Respiratory and haemodynamic variables were recorded. Electrical impedance tomography allowed assessment of centre of ventilation. Results Compared to positive pressure ventilation alone, the caudal transpulmonary pressure was significantly increased by CENP of ≤ 20 cmH2O at all PEEP levels. CENP of – 20 cmH2O reduced the mean airway pressure at zero PEEP (P = 0.025). The driving pressure decreased at CENP of ≤ 10 at PEEP of 0 and 7 cmH2O (P < 0.001 each) but increased at CENP of – 30 cmH2O during the highest PEEP (P = 0.001). CENP of – 30 cmH2O reduced the mechanical power during zero PEEP (P < 0.001). Both elastance (P < 0.001) and resistance (P < 0.001) were decreased at CENP ≤ 30 at PEEP of 0 and 7 cmH2O. Oxygenation increased at CENP of ≤ 20 at PEEP of 0 and 7 cmH2O (P < 0.001 each). Applying external negative pressure significantly shifted the centre of aeration towards dorsal lung regions irrespectively of the PEEP level. Cardiac output decreased significantly at CENP -20 cmH2O at all PEEP levels (P < 0.001). Effects on caudal transpulmonary pressure, elastance and cardiac output were more pronounced when CENP was applied to the abdomen compared with the thorax. Conclusions In this lung injury model in pigs, CENP increased the end-expiratory caudal transpulmonary pressure. This lead to a shift of lung aeration towards dependent zones as well as improved respiratory mechanics and oxygenation, especially when CENP was applied to the abdomen as compared to the thorax. CENP values ≤ 20 cmH2O impaired the haemodynamics.

Numerous studies have revealed that the majority of South African learners lack basic numeracy knowledge. As arithmetic content builds on previous content, a sound foundation for future mathematical learning is crucial for children at the beginning of school. However, many South African children starting school do not have the pre-knowledge to follow the lessons and instructions, so that a knowledge gap opens right from the beginning of school. In this chapter, we present a programme that provides pre-service or in-service teachers with a guideline on how to structure early numeracy pedagogy according to the individual child’s developmental level. The maths training programme presented, ‘Meerkat Maths’, is based on a validated model of the development of arithmetic concepts. It is divided into three modules that take into account how mathematical, language, and general cognitive skills build upon one another. The content is mediated by stories, music, games, and dramatisation to increase learner motivation and promote positive attitudes towards mathematics. The programme thus combines theoretical knowledge with practical classroom activities, thereby enabling teachers to apply theory to practice, with the ultimate aim of providing preschool learners with the knowledge required to be able to follow the Grade 1 maths curriculum.

Summary Against the background of the low mathematical performance of South African learners in international panel studies, there is an urgent need to improve mathematical education. In particular, the curriculum and its structure raise questions. It is logical that the prescribed curricula should align with learners’ developmental trajectories. Given the hierarchical structure of mathematics, the curricular requirements should pay attention to learners’ current knowledge of mathematical concepts. The aim of this study was to compare the curricular requirements as defined by the CAPS with the conceptual current knowledge of South African learners. South African Grade 1 learners (N = 602) were assessed on a test of numeracy concepts, based on a theoretically informed and empirically validated model of developing mathematical proficiency. The content of the CAPS for Grade 1 was aligned to the model levels by two experts (Cohen’s κ = .753, p&thinsp

Research has shown that a profound place value understanding is crucial for success in learning mathematics. At the same time, a substantial number of students struggles with developing a sustainable place value understanding. In this regard, two aspects of the place value system appear especially relevant: First, the knowledge of the decimal structure of numbers, and second, the relation between the bundling units. To support teaching place value understanding, a developmental model of place value understanding focusing on both aspects has been constructed and validated in Germany. The model comprises five levels of place value understanding that build upon each other hierarchically. This study aims at validating the level hierarchy in Turkey to prepare the usage of the developmental model as learning trajectory for Turkish primary schools. N=437 Turkish students from Grades 2 through 4 completed a translated version of the item collection of the German validation study as well as a Turkish place value test that is not based on a developmental model. In a Rasch analysis, most items of the translated item collection showed item difficulties as predicted by the model. In a regression analysis, item difficulties were well predicted by their allocation within the level hierarchy, while other item characteristics did not inform about the item difficulties. Substantial correlations between the translated item collection and the Turkish test underpin the claim that the model is appropriate to assess Turkish students’ place value understanding as well as structuring place value instruction in Turkish primary schools.

Seit einigen Jahren werden kombinatorische Aufgaben als eigenstandiges Thema im Mathematikunterricht der Grundschule behandelt, das diverse Lerngelegenheiten bereithalt. Dies wirft Fragen zur Bearbeitungsweise sowie zu den Reprasentationen der Schulerinnen und Schuler auf. In einer empirischen Studie (N = 548) wurden anhand von sechs Kombinatorikaufgaben Leistungen und Bearbeitungsweisen von Lernenden in der dritten Klasse erhoben. Besonderes Augenmerk wurde auf die verwendeten Darstellungen und den Abstraktionsgrad sowie den Einsatz von Makrostrategien gerichtet. Diese drei Faktoren wurden hinsichtlich ihres Einflusses auf die Losungsgute untersucht. Die Ergebnisse zeigen, dass nicht alle Schulerinnen und Schuler ohne Anleitung geeignete Losungsansatze zu kombinatorischen Problemen fanden. Die Darstellungsweise hatte einen vergleichsweise geringen Einfluss auf die Losungsquote. Im Gegensatz dazu konnten unterschiedlich starke positive Zusammenhange zwischen Abstraktionsgrad bzw. Strategieeinsatz und Losungserfolg nachgewiesen werden. Aus den Ergebnissen der Studie lassen sich Schlusse uber die Vermittlung und didaktische Aufbereitung des Themenfeldes Kombinatorik in der Grundschulmathematik ziehen.

Background Electrical impedance tomography (EIT) with indicator dilution may be clinically useful to measure relative lung perfusion, but there is limited information on the performance of this technique. Methods Thirteen pigs (50–66 kg) were anaesthetised and mechanically ventilated. Sequential changes in ventilation were made: (i) right-lung ventilation with left-lung collapse, (ii) two-lung ventilation with optimised PEEP, (iii) two-lung ventilation with zero PEEP after saline lung lavage, (iv) two-lung ventilation with maximum PEEP (20/25 cm H2O to achieve peak airway pressure 45 cm H2O), and (v) two-lung ventilation under unilateral pulmonary artery occlusion. Relative lung perfusion was assessed with EIT and central venous injection of saline 3%, 5%, and 10% (10 ml) during breath holds. Relative perfusion was determined by positron emission tomography (PET) using 68Gallium-labelled microspheres. EIT and PET were compared in eight regions of equal ventro-dorsal height (right, left, ventral, mid-ventral, mid-dorsal, and dorsal), and directional changes in regional perfusion were determined. Results Differences between methods were relatively small (95% of values differed by less than 8.7%, 8.9%, and 9.5% for saline 10%, 5%, and 3%, respectively). Compared with PET, EIT underestimated relative perfusion in dependent, and overestimated it in non-dependent, regions. EIT and PET detected the same direction of change in relative lung perfusion in 68.9–95.9% of measurements. Conclusions The agreement between EIT and PET for measuring and tracking changes of relative lung perfusion was satisfactory for clinical purposes. Indicator-based EIT may prove useful for measuring pulmonary perfusion at bedside.

This study investigates math anxiety (MA) by comparing trait-components of MA with realtime assessments of situational anxiety responses (state-components) in children. The research to date on MA in children is somewhat disparate in regard to methodology, and firm conclusions regarding the relation of MA to intelligence, math achievement and learning motivation are not readily drawn. Typically, the measures used in the MA research have differed by operationalizing either trait-MA and/or state- (or statelike)-MA, but have failed to compare the implications of their respective assumptions and the significance of their findings. Trait-MA and state-MA, self-ratings of math skills, attitudes towards mathematics, math achievement, the social anxiety, test anxiety, learning motivation and intelligence of 1,179 students (48.1% girls) from grades 4 and 5, were assessed. The findings yield evidence of a pronounced state-trait discrepancy. A negative correlation between state-MA and math achievement was observed for all intelligence levels, even when controlling for test- and social-anxiety traits, while there was no negative relation between trait-MA and achievement. State-MA was associated with lower intelligence, lower self-ratings, more negative attitudes, higher performance avoidance and work avoidance goals. In contrast, trait-MA was slightly related to higher mastery approach goals. The failure to adequately differentiate between state- and trait-based research into MA appears to be one reason for key inconsistencies between research findings and warrants further investigations., Preprint of: Orbach, L., Herzog, M., & Fritz, A. (2019). Relation of state- and trait-math anxiety to intelligence, math achievement and learning motivation. Journal of Numerical Cognition, 5(3), 371–399. https://doi.org/10.5964/jnc.v5i3.204

This study investigated trait-math anxiety during the transition from primary to secondary school. Currently, very disparate findings exist for primary school and early secondary school students, which can be explained by inconsistent definitions and different operationalizations of math anxiety, amongst other reasons. This study is aimed at contributing to the definition of terms. For this purpose, a questionnaire based on the psychological state-trait anxiety model was examined. Trait-math anxiety, self-ratings of math skills, attitudes towards mathematics, math achievement and intelligence of 1289 students (48.6% girls) from grades 4 and 5 were assessed. A characteristic distribution of trait-math anxiety and different types of trait-math anxiety were found. It was found that 1.3% of children were maximal trait-math anxious, 4% were high trait-math anxious and 12% were low trait-math anxious. In comparison to children without trait-math anxiety, the trait-math anxiety group had a significantly higher IQ and poorer self-ratings and attitudes, and only in secondary school did they show significantly better math performances. Furthermore, a similar tendency exists for math achievement in primary school. The data underline the complexity of the relationship between trait-math anxiety and math performance. As in previous surveys on trait-math anxiety, no negative correlation was found. In secondary school a positive correlation existed for boys. Although our study proved a clear gender difference for trait-math anxiety in general, no gender differences were found in higher trait-math anxiety expressions. As the extent of trait-math anxiety decreased, gender differences were increasingly manifested. The self-rating of math skills was examined as a key factor for the development of trait-math anxiety. Students who perceive their math skills as low have a greater risk for trait-math anxiety. When comparing different types of schools, more students from Gymnasium, a school type with higher requirements, showed trait-math anxiety. These findings highlight the role of school expectations and peers’ abilities to prevent and alleviate math anxiety in class.

A resilient understanding of the decimal place value system is a crucial element of primary mathematical education that has a deep impact on further arithmetical development. Place value understanding has been identified as a good predictor of math performances as well as math difficulties. Difficulties in understanding the place value system affect children in different grades in countries all over the world.

Although research has provided evidence for a clear association of core executive function (CEF) to math performance, fewer studies have been carried out on arithmetic fact retrieval in relation to the symptoms of attention deficit hyperactivity disorder (ADHD). The present study assessed mathematical achievement on a basic number skill test and on an arithmetic fact retrieval task. Besides math achievement, self-ratings of ADHD symptoms (attention deficits, hyperactivity, impulsivity), core executive functions (inhibition, cognitive flexibility, working memory capacity, global index) and state anxiety in 646 fourth and fifth grade students (48.1 % girls) were measured. CEF was evaluated by means of a tablet-based test. Regression analysis showed different predictors for both math abilities. While all CEF measures, inattention and impulsivity self-ratings predicted basic number skills, only inhibition, WMC and inattention self-rating were predictors of arithmetic fact retrieval. On the basis of a cluster analysis of ADHD self-ratings and CEF performance, three different groups were identified: 1: low ADHD, average CEF; 2: high ADHD, low CEF; 3: moderate ADHD, high CEF. Cluster 2 showed scores below the mean in both math scores, whereas cluster 3 exhibited performances above the mean in both math scores. No math differences were found between cluster 1 and 3. The data yield evidence that the association between CEF and math achievement depends on the specific math skill and test type. The results underline the importance of differentiating between CEF components and specific math abilities. Implications for future research on the associations between mathematics, ADHD and CEF are discussed.

This study examines the interplay of state- and trait-math anxiety (MA) and core executive functions (CEF) on math achievement in children. According to attention control theory, MA affects the CEF by triggering the inhibition function, so that some working memory (WM) is blocked, thus reducing task processing capacity. However, research on the interplay between MA and CEF in children is rare, and the findings in the literature are inconsistent. In this paper, state- and trait-MA, math achievement, CEF (inhibition, cognitive flexibility, working memory capacity, global index of CEF) and self-ratings of ADHD symptoms (attention deficits, hyperactivity, impulsiveness) of 646 fourth and fifth grade students (48.1% girls) are assessed. CEF were evaluated with a tablet-based test. The data revealed negative correlations between state-MA and math achievement for all CEF levels and cognitive processes. However, inhibition control functioned as a moderator of the relation between state-MA and math achievement. Children with higher inhibition abilities showed more pronounced negative relations. No moderation effects were identified for working memory capacity and the CEF global index. The findings highlight the importance of distinguishing between these three CEF and raise questions for future research on the interplay between cognitive and affective factors as predictors of math achievement.

Background: Several studies have shown the influence of mathematical knowledge on both individual opportunities and chances for a self-determined and prosperous life as well as the welfare of nations. Against this background, the contents of maths education in the foundation phase as well as the way in which it is conveyed gain importance. While competence-oriented approaches (e.g. the Curriculum Assessment Policy Statements [CAPS]) state learning goals that all learners should achieve, developmental approaches (e.g. developmental models) describe typical learning trajectories of learners. As both approaches are quite separated, there is a need for bridging the gap between them. Aim: This article aims at revisiting the CAPS critically and comparing contents for early numeracy instruction. A possible alternative to the CAPS is intended. Setting: In this article, we describe a maths learning programme for Grade-R ( Meerkat Maths ) that combines and integrates empirical findings and curricular demands. The presented maths training aims at teaching maths in such a way that it suits children’s development, raises a positive attitude towards maths and also meets educational expectations. Methods: Contents of the training programme and the CAPS are compared against the background of empirical research on numerical development and predictors for arithmetic performance. Results: The results reveal that research based math instruction can be conveyed in a formal training programme. Conclusion: Keeping in mind the qualifications and training of Grade-R teachers, teacher training is necessarily embedded in the programme. Thus, the described programme is a comprehensive application of recent research for maths classes in the early grades.

Electric drives efficiency is determined by the mechanical and magnetic properties of the functional elements stator and rotor. Focus element for this investigation is the rotor including its permanent magnets. Due to several manufacturing influences the properties of those magnets vary considerably. Magnet failures that can occur during manufacture are cracks, blowholes or inclusions, which can lead to commutation problems or to increased noise [1]. Crack propagation is a long-lasting process and cause unintentional failure in field. Currently no automated quality inspection of micro cracks is available in electric drive production. Consequently, the challenge is to develop reliable and safe process concept, to separate bad from good rotors based on magnetic field measurements in order to detect failures at the internal or external assembled magnets. For this purpose, a data analyzing method was developed to identify and characterize micro cracks in already assembled permanent magnets.

Although the general development of mathematical abilities in primary school has been the focus of many researchers, the development of place value understanding has rarely been investigated to date. This is possibly due to the lack of conceptual approaches and empirical studies related to this topic. To fill this gap, a theory-driven and empirically validated model was developed that describes five sequential conceptual levels of place value understanding. The level sequence model gives us the ability to estimate general abilities and difficulties in primary school pupils in the development of a conceptual place value understanding. The level sequence model was tried and tested in Germany, and given that number words are very differently constructed in German and in the languages used in South African classrooms, this study aims to investigate whether this level sequence model can be transferred to South Africa. The findings based on the responses of 198 Grade 2-4 learners show that the English translation of the test items results in the same item level allocation as the original German test items, especially for the three basic levels. Educational implications are provided, in particular concrete suggestions on how place value might be taught according to the model and how to collect specific empirical data related to place value understanding.