This diploma thesis outlines a set of three complex geographical tasks with different thematic focus inspired by the PISA research of scientific literacy. Using these tasks selected skills and knowledge of students are verified. The research examines how different are levels of mastery of selected skills and knowledge of primary school students and eight-year gymnasium students, and among the boys and girls thereof. This research is complemented by a questionnaire survey among teachers of tested students. In the testing there were involved 196 students from seven primary schools and 202 students of eight-year schools.

Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes.

<p>Surface electromyography (sEMG) has been used to monitor muscle activity and predict fatigue in the workplaces. However, objectively measuring fatigue is challenging in complex work with unpredictable work cycles, where sEMG may be influenced by the dynamically changing posture demands. The sEMG is affected by various variables and substantial change in mean power frequencies (MPF), and a decline over 8-9% is primarily considered musculoskeletal fatigue. These MPF thresholds have been frequently used, and there were limited efforts to test their appropriateness in determining musculoskeletal fatigue in live workplaces (which predominantly consist of complex tasks). In addition, the techniques that consider both muscular and postural measurements that incorporate dynamic posture changes observed in complex work have not yet been explored. The overall objective of this work is to leverage both postural and muscular cues to identify musculoskeletal fatigue in complex tasks/jobs (i.e., tasks involving different levels of exertions, durations, and postures). The work was completed in two studies.</p> The first study aimed to (1) predict subjective fatigue using objective measurements in non-repetitive tasks, (2) determine whether the musculoskeletal fatigue thresholds in non-repetitive tasks differed from the previously reported threshold, and (3) utilize the empirically calculated thresholds to test their appropriateness in determining musculoskeletal fatigue in live surgical workplaces. The findings showed that the multi-modal measurements indicate better sensitivity than single-modality (sEMG) measurements in detecting decreases in MPF, a predictor of fatigue. In addition, the results showed that the thresholds in dynamic non-repetitive tasks, like surgery, are different than the previously reported 8% threshold. Additionally, implementing muscle-specific thresholds increased the likelihood of more accurately reporting subjective fatigue. The second study aimed to develop a multi-modal fatigue index to detect musculoskeletal fatigue. A controlled laboratory study was performed to simulate the non-repetitive physical demands at different postures. A series of experiments were conducted to test the effectiveness of various metrics/models to identify subjective fatigue in complex tasks. Next, the composite fatigue index (CFI) function was developed using the time-synced integration of both muscular signals (measured with sEMG sensors) and postural signals (measured with Inertial Measurement Unit (IMU) sensors). The variables from sEMG (amplitude, frequency, and the number of muscles showing signs of fatigue) and IMU (the prevalence of static and demanding postures and the number of shoulders in static/demanding posture) sensors were integrated to generate the CFI function. The prevalence of static/demanding postures was developed using the cumulative exposures to static/demanding postures based on the material fatigue failure theory. The single value fatigue index was obtained using the resultant CFI function, which incorporates both muscular and postural variables, to quantify the muscular fatigue in dynamic non-repetitive tasks. The findings suggested that the propagation of musculoskeletal fatigue can be detected using the multi-modal composite fatigue index in complex tasks. The resultant CFI function was then applied to surgery tasks to differentiate the fatigued and non-fatigued groups. The findings showed that the multi-modal fatigue assessment techniques could be utilized to incorporate the muscular and postural measurements to identify fatigue in complex tasks beyond single-modality assessment approaches.