Problem posing based on investigation activities by university students

This paper reports a classroom-based study involving investigation activities in a university numerical analysis course. The study aims to analyse students' mathematical processes and to understand how these activities provide opportunities for problem posing. The investigations were intended to stimulate students in asking questions, to trigger their thinking processes, to promote their ability to investigate and to support them in learning numerical analysis' concepts and procedures. The results show that the investigations provided opportunities for students to experience mathematical processes, including posing questions, formulating and testing conjectures and, to some extent, proving results. They also provide some understanding about the role of problem posing in these processes. Posing questions occurred mainly in an implicit way, in the interpretation of tasks and in identifying regularities, analysing graphs and testing cases. The conjectures were often based on pattern identification or data manipulation, and the students tended to accept them without testing or proving. The students also proposed alternative formulations for the initial questions and posed new problems from their explorations and attempts to refine previous conjectures.     

Social interactions and cognitive effects in contexts of area-comparison problem solving

The paper we present is a case study which has two objectives: the identification of the interactions between pairs of 16 and17-year-old students related to problem solving and the influence of such interactions in their cognitive development. To achieve these aims, we consider problems associated with a definite conceptual structure – problems comparing flat surface areas –, and we focus the analysis of the interactions on the point of view of the thematic and interlocutive dimensions of the discourse. Such analysis has allowed us to identify a wide typology of exchanges, and, from this, to outline four models of interaction -alternative, guided, relaunching, and co-operative. In the cases analysed, these interactions significantly influence the individual development of cognitive and heuristic abilities in the problem solving process. This revised version was published online in July 2006 with corrections to the Cover Date.     

Changes in mechanical properties of sprinting during repeated sprint in elite rugby sevens athletes

This study aimed to analyse fatigue-induced changes in mechanical sprinting properties during a specific repeated-sprint test in elite rugby sevens athletes. Twenty elite rugby sevens players performed ten 40?m sprints on a 30?s cycle with participant’s running back and forth in a marked lane. Radar was used to assess maximal overground sprint performance over each 40?m. Macroscopic mechanical properties (maximal horizontal force (F₀), maximal horizontal power (P_max), maximal ratio of horizontal force (RF_peak), decrease in the ratio of horizontal-to-total force (D_RF), total force and maximal sprinting velocity (v₀)) were drawn from horizontal force velocity relationships, using a validated method applied to the speed–time data. Fatigue-induced changes were analysed comparing the first sprint to an average of 2^nd-4^th, 5^th-7^th and 8^th-10^th. Repeated-sprint ability (RSA) testing induced substantial changes in the maximal velocity component, with a decrease (–15%) in v₀ (effect size (ES)?=?–2.46 to –4.98), and to a lower extent (–5.9%) in the maximal force component F₀ (ES?=?–0.59). D_RF moderately decreased (14%; ES=–0.76–1.11), and RF_peak largely decreased in the later sprints (ES?=?–0.32 to –1.27). Fatigue observed in this RSA test appeared to have a greater effect on the technical ability to produce horizontal force at high velocities, likely due to an alteration in the ability to maintain horizontally oriented force application when velocity increases rather than during the initial acceleration phase, but also the overall force production capacity. The ability to maintain forward-oriented force at high velocities is of central importance for identifying fatigue and monitoring load.     

Statistical biases in Information Retrieval metrics for recommender systems

There is an increasing consensus in the Recommender Systems community that the dominant error-based evaluation metrics are insufficient, and mostly inadequate, to properly assess the practical effectiveness of recommendations. Seeking to evaluate recommendation rankings—which largely determine the effective accuracy in matching user needs—rather than predicted rating values, Information Retrieval metrics have started to be applied for the evaluation of recommender systems. In this paper we analyse the main issues and potential divergences in the application of Information Retrieval methodologies to recommender system evaluation, and provide a systematic characterisation of experimental design alternatives for this adaptation. We lay out an experimental configuration framework upon which we identify and analyse specific statistical biases arising in the adaptation of Information Retrieval metrics to recommendation tasks, namely sparsity and popularity biases. These biases considerably distort the empirical measurements, hindering the interpretation and comparison of results across experiments. We develop a formal characterisation and analysis of the biases upon which we analyse their causes and main factors, as well as their impact on evaluation metrics under different experimental configurations, illustrating the theoretical findings with empirical evidence. We propose two experimental design approaches that effectively neutralise such biases to a large extent. We report experiments validating our proposed experimental variants, and comparing them to alternative approaches and metrics that have been defined in the literature with similar or related purposes.     

Development of an aerobic capacity prediction model from one-mile run/walk performance in adolescents aged 13–16 years

A popular algorithm to predict VO_2Peak from the one-mile run/walk test (1MRW) includes body mass index (BMI), which manifests practical issues in school settings. The purpose of this study was to develop an aerobic capacity model from 1MRW in adolescents independent of BMI. Cardiorespiratory endurance data were collected on 90 adolescents aged 13–16 years. The 1MRW was administered on an outside track and a laboratory VO_2Peak test was conducted using a maximal treadmill protocol. Multiple linear regression was employed to develop the prediction model. Results yielded the following algorithm: VO_2Peak = 7.34 × (1MRW speed in m s^?1) + 0.23 × (age × sex) + 17.75. The New Model displayed a multiple correlation and prediction error of R = 0.81, standard error of the estimate = 4.78 ml kg^?1·min^?1, with measured VO_2Peak and good criterion-referenced (CR) agreement into FITNESSGRAM’s Healthy Fitness Zone (Kappa = 0.62; percentage agreement = 84.4%; Φ = 0.62). The New Model was validated using k-fold cross-validation and showed homoscedastic residuals across the range of predicted scores. The omission of BMI did not compromise accuracy of the model. In conclusion, the New Model displayed good predictive accuracy and good CR agreement with measured VO_2Peak in adolescents aged 13–16 years.