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Although the interaction between anxiety and attention is considered crucial for learning and performance in mathematics, few studies have examined these cognitive and affective predictors in a single framework or explored the role of sustained attention in promoting children's arithmetic performance, using traditional linear analyses and latent profile analysis (LPA). In this paper, state anxieties (in a math test and in an attention test situation), general anxiety traits, sustained attention (performance-based test and attention deficit/hyperactivity disorder (ADHD) self-ratings) and math achievement of 403 fourth- and fifth-graders (55.8% girls) were assessed. A negative correlation between state anxiety prior to the math test and arithmetic achievements was identified, even when controlling for other non-math related state anxieties and general anxiety. Sustained attention was a strong predictor of arithmetic achievement and functioned as a moderator in the anxiety-performance link. LPA identified six distinct profiles that revealed a complex relationship with arithmetic fluency. The weakest achievement was found for a specific math anxiety subgroup. The findings highlight the important role of the interaction of anxiety and sustained attention in children's ability to perform math and enable new conclusions about the specific nature of math anxiety. Implications for future research are discussed. (ZPID).

A common theme of models of conceptual growth is to establish the hierarchical structures of abilities that can be interpreted along developmental lines. Integrating the literature on the development of mathematical concepts and skills in children, a comprehensive 6 level model for describing, explaining and predicting the development of key numerical concepts and arithmetic skills from age 4 to 8, is proposed. Two studies will be presented. In the first study, 1095 preschool children completed a mathematics test (MARKO-D0) based on a 5-level model. The test fitted with a one-dimensional Rasch model. The extension of the model to a sixth level was verified in a new study: 312 first-graders took part in a mathematics test based on the six levels (MARKO-D1). In order to check whether the data of both samples adhered to the principle of unidimensionality, the data of MARKO-0 and MARKO-1 were used in a common analysis for comparative purposes. The applicability of these findings for a qualitative diagnostics and an adaptive training will be discussed. (Orig.).

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.

This article presents the translation and adaptation process of a mathematics test for the acquisition of key mathematical (arithmetic) concepts by children from four to eight years of age. The origin of this test was in Germany, whence it was sourced by researchers at the University of Johannesburg. A conceptual model of hierarchical mathematics competence development forms the theoretical foundation of the test. This notion of hierarchical competence was tested in a one-dimensional Rasch analysis, which confirmed the hierarchical structure of the test with five levels of ability. In the translation process, it was imperative to ascertain whether the items of the translation had retained the conceptual content of the original test and had been allocated to the same conceptual levels as in the original test. In a number of pilot studies with a total of 1 600 South African children, we focused on the items that had been allocated to a different level, aiming to find out whether this was the result of translation errors. In analyses of different samples, discussing and reflecting on the model fit, and especially on items that did not fit well, ‘misfitting’ items could mostly be attributed to translation difficulties and differences in the children’s strategies, and not to a generally altered model. The final model was established after the rephrasing of critical items. This model has already been tested with 500 additional South African children. Results are presented and discussed, with the focus on the Sesotho test results.

PurposeDespite an increasing number of fragility fractures of the pelvis (FFP) over the last 2 decades, controversy persists on their therapy with special regard to potential complications. Therefore, the present study compared the complication rates and in-hospital mortality of non-operative therapy, percutaneous treatment and open reduction and internal fixation (ORIF) of pelvic fractures in elderly patients.MethodsAll consecutive patients treated for FFP between January 2013 and December 2017 aged 65 years or older were retrospectively identified from an institutional database. Demographic data and specific patient data were collected with a special focus on pre-existing comorbidities. General and surgical complications, hospital length of stay (LOS) and mortality rates were compared.Results379 patients (81.3 ± 7.5 years; 81% female) were identified, 211 (55.7%) were treated non-operatively, 74 (19.5%) percutaneously and 94 (24.8%) with ORIF. The rate of general complications did not differ between treatment groups (non-operative: 21.8%; percutaneous: 28.4%; ORIF: 33.0%; p = 0.103). Surgery-related complications were twofold more frequent in the ORIF group as than in the percutaneously treated group (18.1% vs. 9.5%). The LOS differed significantly (non-operatively: 8.9 ± 7.1 days; percutaneous: 16.6 ± 8.2 days; ORIF: 19.3 ± 12.8 days; p < 0.001). Hospital mortality rate was higher in patients with ORIF (5.3%) than percutaneous treatment (0%) (p = 0.044).ConclusionsComplication rates and hospital mortality in elderly patients with FFPs are high and associated with long LOS. For surgical treatment of FFPs, the complication rate and mortality can be significantly reduced using percutaneous procedures compared to ORIF. Therefore, percutaneous surgery should be preferred where possible.

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. 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.

This article presents the translation and adaptation process of a mathematics test for the acquisition of key mathematical (arithmetic) concepts by children from four to eight years of age. The origin of this test was in Germany, whence it was sourced by researchers at the University of Johannesburg. A conceptual model of hierarchical mathematics competence development forms the theoretical foundation of the test. This notion of hierarchical competence was tested in a one-dimensional Rasch analysis, which confirmed the hierarchical structure of the test with five levels of ability. In the translation process, it was imperative to ascertain whether the items of the translation had retained the conceptual content of the original test and had been allocated to the same conceptual levels as in the original test. In a number of pilot studies with a total of 1 600 South African children, we focused on the items that had been allocated to a different level, aiming to find out whether this was the result of translation errors. In analyses of different samples, discussing and reflecting on the model fit, and especially on items that did not fit well, 'misfitting' items could mostly be attributed to translation difficulties and differences in the children's strategies, and not to a generally altered model. The final model was established after the rephrasing of critical items. This model has already been tested with 500 additional South African children. Results are presented and discussed, with the focus on the Sesotho test results.

This paper argues for teaching pre-service teachers about remediation strategies for learners who encounter problems in mathematics in the early grades. The premise is that all teachers should be equipped with theory-based practical knowledge to support learning. A few teaching sessions to develop the concepts that underlie the mathematical operations of addition and subtraction are introduced in this paper. An empirically validated, comprehensive model of cumulative arithmetic competence development from the ages of four to eight years forms the basis for the construction of the suggested teaching unit. The model distinguishes five competence levels of arithmetical conceptual development, and proposes that concepts build on one another hierarchically. A ‘part plus part is equivalent to whole’ model was constructed based on this hierarchical structure and the understanding that the concept of addition is a dynamic process. The teaching examples include exercises for all children, not only ones who struggle. Possibilities for adapting the exercises to the individual development level of slower or faster learners are also included. All exercises are accompanied by a reflection on the procedure and strategies applied in order to support meaningful and sustainable learning and to give student teachers the opportunity to use knowledge of mathematical cognition theory during their pre-service years.

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.

In the German school system, children are seen as educationally impaired when they are more than two grades behind in their performance in several areas of learning, and this has been the case for several years. A special problem is the fact that support measures are often effective only to a limited extent, or only for a short period.The study at hand focuses on the question of whether educationally impaired children with large deficits in mathematics can be supported successfully by means of a highly adaptive support measure (MARKO-T), and whether the effects of this support can be maintained over a certain period. For this, 32 educationally impaired third-graders with math deficits were supported individually with MARKO-T twice a week, over a period of ten weeks. As control group, 32 similarly impaired third-graders were paralleled according to the mathematical and cognitive achievements of the training group. Two further control groups, each with 32 unimpaired first-graders, were paralleled according to their mathematical and cognitive achievements, respectively. The results showed that the very poor mathematical performance of the educationally impaired children could be significantly improved with this support programme. Four months after the end of the training, significant support effects could still be established when compared to the educationally impaired control group. The comparison with the two control groups demonstrated that the developmental curve of the children with learning difficulties increased in a way that was comparable to that of the unimpaired first-graders.