Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning

Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations.

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.

How gender fair are German schoolbooks in the twenty-first century? An analysis of language and illustrations in schoolbooks for mathematics and German

Schoolbooks convey not only school-relevant knowledge; they also influence the development of stereotypes about different social groups. Particularly during the 1970s and 1980s, many studies analysed schoolbooks and criticised the overall predominance of male persons and of traditional role allocations. Since that time, women’s and men’s occupations and social functions have changed considerably. The present research investigated gender portrayals in schoolbooks for German and mathematics that were recently published in Germany. We examined the proportions of female and male persons in pictures and texts and categorized their activities, occupational and parental roles. Going beyond previous studies, we added two criteria: the use of gender-fair language and the spatial arrangements of persons in pictures. Our results show that schoolbooks for German contained almost balanced depictions of girls and boys, whereas women were less frequently shown than men. In mathematics books, males outnumbered females in general. Across both types of books, female and male persons were engaged in many different activities, not only gendertyped ones; however, male persons were more often described via their profession than females. Use of gender-fair language has found its way into schoolbooks but is not used consistently. Books for German were more gender fair in terms of linguistic forms than books for mathematics. For spatial arrangements, we found no indication for gender biases. The results are discussed with a focus on how schoolbooks can be optimized to contribute to gender equality.

Nest choice in laying hens: Effects of nest partitions and social status.

Nest choice in loose-housed laying hens is influenced by nest characteristics, position and social factors. We examined the relative preference of laying hens for two group-nests differing in the presence or absence of a partition in the middle of the nest and whether this was influenced by social status. We hypothesized that hens would prefer the partitioned nest as it provides more enclosure, and that social status would affect nest choice. Relative preference for the nests was assessed in a free choice preference test conducted in two consecutive trials each with eight groups of 20 hens from 18 to 31 weeks of age. The hens were individually marked and had access to two commercial group-nests (49 × 114 cm), one of which contained an internal wooden partition (30 × 10 cm) which divided the nest in two halves. At 28 weeks of age, the position of the nests was switched. The number of eggs laid was recorded daily. On one day each at 24 and 28 weeks of age (after the nest switch) video recordings were made of the first 5 h of daylight. From these videos we recorded the number of nest visits per egg per nest and the number of nest visits for individual hens. On one day each at 24 and 27 weeks of age we also recorded videos from within the nests to assess individual nest choice for egg-laying. In addition, we recorded aggressive interactions between individual hens during the first hour of light on one day each at 18, 24 and 27 weeks of age to establish social status. We found a relative preference for the partition nest with a greater proportion of eggs laid in these nests as well as fewer nest visits per egg. The hens were also consistent in their egg-laying location over the two days of observation. After the nest switch, however, the hens did not switch egg laying location and the number of visits per egg no longer differed between nests suggesting that the preference for the partitioned nest was only important at the beginning of lay. In addition, although social rank had no impact on preference of nest type, lower ranking hens performed more nest visits and laid their eggs slightly later on the second observation day (week 27 of age) compared with higher ranking hens. Therefore, the use of partitions could improve the attractiveness of group-nests.