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.

Stratification of high-risk prostate cancer into prognostic categories: a European multi-institutional study

BACKGROUND High-risk prostate cancer (PCa) is an extremely heterogeneous disease. A clear definition of prognostic subgroups is mandatory. OBJECTIVE To develop a pretreatment prognostic model for PCa-specific survival (PCSS) in high-risk PCa based on combinations of unfavorable risk factors. DESIGN, SETTING, AND PARTICIPANTS We conducted a retrospective multicenter cohort study including 1360 consecutive patients with high-risk PCa treated at eight European high-volume centers. INTERVENTION Retropubic radical prostatectomy with pelvic lymphadenectomy. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS Two Cox multivariable regression models were constructed to predict PCSS as a function of dichotomization of clinical stage (< cT3 vs cT3-4), Gleason score (GS) (2-7 vs 8-10), and prostate-specific antigen (PSA; ≤ 20 ng/ml vs > 20 ng/ml). The first "extended" model includes all seven possible combinations; the second "simplified" model includes three subgroups: a good prognosis subgroup (one single high-risk factor); an intermediate prognosis subgroup (PSA >20 ng/ml and stage cT3-4); and a poor prognosis subgroup (GS 8-10 in combination with at least one other high-risk factor). The predictive accuracy of the models was summarized and compared. Survival estimates and clinical and pathologic outcomes were compared between the three subgroups. RESULTS AND LIMITATIONS The simplified model yielded an R(2) of 33% with a 5-yr area under the curve (AUC) of 0.70 with no significant loss of predictive accuracy compared with the extended model (R(2): 34%; AUC: 0.71). The 5- and 10-yr PCSS rates were 98.7% and 95.4%, 96.5% and 88.3%, 88.8% and 79.7%, for the good, intermediate, and poor prognosis subgroups, respectively (p = 0.0003). Overall survival, clinical progression-free survival, and histopathologic outcomes significantly worsened in a stepwise fashion from the good to the poor prognosis subgroups. Limitations of the study are the retrospective design and the long study period. CONCLUSIONS This study presents an intuitive and easy-to-use stratification of high-risk PCa into three prognostic subgroups. The model is useful for counseling and decision making in the pretreatment setting.

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.