A thesis submitted to the Faculty of Engineering and the Built Environment in fulfilment of the requirement for the degree Doctor of Philosophy, University of the Witwatersrand, Johannesburg, 2019 / The design of feedback stabilizing controllers is an essential component of control engineering theory and practice. A large part of the modern literature in control theory is devoted to coming up with new methods of designing feedback stabilizing controllers. This sustained interest in answering the question \how to design a feedback stabilizing controller" has not been accompanied by equal interest in the more existential and fundamental problem of \when is a system stabilizable by feedback". As such the theory of control Lyapunov functions still remains the most general framework that characterizes stabilizability as a system property. This approach however simply replaces one elusive and di cult concept (i.e stabilizability) with an equally diffcult concept, the existence of control Lyapunov functions. In this thesis we analyse control system stabilizability from the perspective of control system quotients which are generalized control system reductions, the focus being on the propagation of the stabilizability property from the lower order quotient system to the original system. For the case where the quotient system is a linear controllable system we prove that propagation of the stabilizability property to the original system is possible if the zero dynamics of the original system are stable. A novel way of constructing the zero dynamics which does not involve the solution of a system of partial differential equations is devised. More generally for analytic non-linear systems given a stabilizable quotient system, we develop a new method of constructing a control Lyapunov function for the original system, this construction involves the solution of a system of partial di erential equations. By studying the integrability conditions of this associated system of partial differential equations we are able to characterize obstructions to our proposed method of constructing control Lyapunov functions in terms of the structure of the original control system. / PH2020

Det finns olika aspekter för att förstå multiplikation och resultat från tidigare forskning visar att många av dagens elever använder formler och uträkningar de egentligen inte förstår. Syftet med denna studie är att exemplifiera olika sätt lärare kan ge stöttning för att eleverna ska utveckla sin förståelse för multiplikation. I studien genomfördes fyra observationer med efterföljande intervjuer i olika mellanstadieklasser. Resultatet visar att lärare ofta ger feedback innehållandes en hög grad av stöttning till eleverna. Det vanligaste matematiska innehållet i den feedback lärarna gav till eleverna var procedurellt inriktad mot den aktuella uppgiften eleverna arbetade med. Stöttningen gavs generellt för att eleverna skulle klara uppgiften snarare än att de skulle få en ökad förståelse för multiplikation. Tidigare forskning visar att lärare upplever det tidskrävande att arbeta med formativ feedback. Detta kan vara en av orsakerna till att vi i denna studie inte kunde identifiera något exempel på formativ feedback från lärare till elev. Resultatet av vår studie skulle kunna användas av yrkesverksamma lärare till att förstå hur formuleringen av deras feedback kan påverka elevernas möjlighet till productive struggle och den konceptuella förståelsen i ett matematiskt område, likt multiplikation.

Purpose: To refute the alleged practice of "pseudoscience" by P. Finn, A. K. Bothe, and R. E. Bramlett (2005) and to illustrate their experimental and systematic bias when evaluating the SpeechEasy, an altered auditory feedback device used in the management of stuttering. Method: We challenged the experimental design that led to the seemingly predetermined outcome of pseudoscience rather than science: Limited preselected literature was submitted to a purposely sampled panel of judges (i.e., their own students). Each criterion deemed pseudoscientific was contested with published peer-reviewed data illustrating the importance of good rhetoric, testability, and logical outcomes from decades of scientific research. Conclusions: Stuttering is an involuntary disorder that is highly resistant to therapy. Altered auditory feedback is a derivation of choral speech (nature's most powerful stuttering "inhibitor") that can be synergistically combined with other methods for optimal stuttering inhibition. This approach is logical considering that in stuttering no single treatment is universally helpful. Also, caution is suggested when attempting to differentiate science from pseudoscience in stuttering treatments using the criteria employed by Finn et al. For example, evaluating behavioral therapy outcomes implements a post hoc or untestable system. Speech outcome (i.e., stuttered or fluent speech) determines success or failure of technique use, placing responsibility for failure on those who stutter.

The aim of this study is to investigate how teachers in Sweden and Vietnam provides formative feedback to their pupils. It is our ambition to find out what differences and similarities there are in how and why teachers work with formative feedback, in both countries. Moreover, the last aim is to look at how Swedish teachers and Vietnamese teachers can learn from each other. We will interview two teachers from Sweden and two from Vietnam to see how they work with formative feedback. All interviewees are English teachers and work in primary school. We found that formative feedback is something all four teachers work with, more or less. However, they all express that oral formative feedback occur more often than written. Of course there are a lot of differences of the implementation of feedback but we can find multiple similarities as well. Furthermore, differences are many in the two countries, for example, the amount of pupils in classes. Another example is that the teachers in Vietnam had no knowledge about formative feedback before our interviews. Still, they manage to implement formative feedback in different ways, without the proper terms.

Application of clearly defined feedback types, which have been correlated with improved student performance, has great potential for maximizing instructor use of feedback and its effect on a learner's self-regulatory learning (SRL) for optimized learning. Within SRL, where learner performance is influenced by a recursive internal process, instructional feedback plays a critical role. Yet, the characteristics of external feedback that influence SRL to improve performance are unclear in the literature. Within a theoretical framework where feedback catalyzes self-regulation, this quantitative study sought to integrate feedback type research to expand the SRL model. Data were graded assignments from 23 undergraduate level and 8 graduate level online university courses randomly selected from a pool of 86 possible courses. Applying non-experimental logistic regression and using descriptive statistics, feedback was categorized to determine the quantity of each of the 5 feedback types [task correctness (FC), task elaboration (TE), task process (FP), self-regulation (FR), and personal or self-related (FS)], as well as how they correlated with improved performance. The results indicate that the feedback types were not normally distributed, FS was statistically not present and FE was most used, and the logistical regression indicated that the presence of FC and FR was minimally associated with improved performance. Additional experimentation is needed to normalize the type distribution and test the strength of the FC and FR effect. This study initiated a clarification in understanding the external component of feedback in the SRL model, which is necessary to harness feedback to create positive change in the self-regulatory processes of learners.

Recent research has shown that summative feedback has a negative effect on pupils’ learning, because the feedback given lacks information sufficient to pupils. This compared to formative feedback which has shown positive results on pupils learning (William 2019). Despite the positive research results, it is problematic to implement the method in to practical teaching (Grevholm 2012). The purpose of this study is to analyze how formative feedback is used in mathematical teaching for grades 4-6 in Swedish schools. The study aims to answer the following questions: How is formative- and summative feedback in mathematics given? How is verbal feedback in mathematics used? This study has used the qualitative methods observation and interview to get a deeper insight of individual choices made by teachers. To analyze the collected materials, the theory of formative feedback in different levels have been used. The results show that the most common used formative feedback was in a verbal form. Verbal formative feedback was preferred since it involves direct communication, seldomly misunderstood. The results also show that written formative feedback was rarely given because it was considered time-consuming. Verbal formative feedback was mostly given to the pupils on a self-regulation level.

Abstract This study investigates the effectiveness of using Oral Corrective Feedback (OCF) as a way of promoting young learners' language acquisition from an EFL (English As a Foreign Language) perspective. Furthermore, this study also looks at learners' and teachers' thoughts about oral corrective feedback and whether it serves its intended purpose in the classroom towards learners' language learning. My method is based on scientific articles and sets out previous studies to investigate how oral corrective feedback may be beneficial for young learners' EFL and L2 language development. Previous experimental research indicates that the use of oral corrective feedback has a positive effect on learners' L2 development and language acquisition. In this current study I provide an overview of the possible advantages and disadvantages of using oral corrective feedback in young learners' L2 development in an educational context which also includes an insight into teachers' attitude. The results show that OCF is beneficial for young learners’ L2 development if the learners are aware of the OCF that is being provided. The results also indicate that OCF is affected by the teachers' attitude towards OCF. Key terms: OCF, EFL, L2, corrective oral feedback, oral feedback types, teacher’s attitude OCF, learners' attitude OCF, teacher OCF and uptake.

This study examined the effect of two forms of feedback (qualitatitive and quantitative) on the development of the spoken fluency of English language learners. Sixty-five intermediate- high students from 22 countries and 11 native languages enrolled in an intensive English language program at the English Language Center, Brigham Young University in Provo, Utah, participated.Throughout the 11-week course, the treatment group (consisting of 33 participants) received feedback on a weekly basis during speaking assessment tasks. The first form of feedback consisted of a quantitative analysis of their spoken fluency. This analysis, performed by PRAAT acoustic analysis software, measured several key features: speech rate (syllables per minute), pause frequency and duration, fillers, false starts, and connectedness of speech (mean length of run). In addition to measurements of their own performance, participants were presented with data on the average performance of their peers, as well as measurements of how closely their performance approximated the fluency measurements of a native speaker.The second form of feedback was qualitative, consisting of written descriptions of the participants` dysfluencies including fillers, high pause frequency and duration, low speech rate and false starts. Participants also received qualitative feedback in the form of self-assessment where they analyzed their own previously made recordings.Following the completion of the treatment, participants completed a survey eliciting their perceptions of the forms and effectiveness of feedback they had received over the course of the treatment. Though participants reported that the feedback (especially the qualitative variety) was useful, through statistical analysis of test and task scores it was found that other than for filler and false starts, feedback was not a significant factor in influencing the students' improvement over the course of the semester, and it is probable that other factors (task repetition) played a larger role.

Optimal delivery of instruction is both critical and challenging in dynamic, scenario-based training (SBT) computer simulations such as those used by the military. Tasks that human instructors must perform during these sorts of simulated training exercises can impose a heavy burden on them. Partially due to advances in the state-of-the-art in training technology and partially due to the military's desire to reduce the number of personnel required, it may be possible to support functions that overburdened instructors perform by automating much of the SBT process in a computer simulation. Unfortunately though, after more than 50 years of literature documenting research conducted in the area of training interventions, few empirically-supported guidelines have emerged to direct the choice and implementation of effective, automated training interventions. The current study sought to provide empirical guidance for the optimal timing of feedback delivery (i.e., immediate vs. delayed) in a dynamic, SBT computer simulation. The premise of the investigation was that the demand for overall cognitive resources during the training exercise would prescribe the proper timing of feedback delivery. To test the hypotheses, 120 volunteers were randomly assigned to 10 experimental conditions. After familiarization on the experimental testbed, participants completed a total of seven, 10-minute scenarios, which were divided across two training phases. During each training phase participants would receive either immediate or delayed feedback and would perform either high or low cognitive load scenarios. Four subtask measures were recorded during test scenarios as well as subjective reports of mental demand, temporal demand and frustration. Instructional efficiency ratios were computed using both objective performance data and subjective reports of mental demand. A series of planned comparisons were conducted to investigate the training effectiveness of differing scenario cognitive loads (low vs. high), timing of feedback delivery (immediate vs. delayed), and sequencing the timing of feedback delivery and the cognitive load of the scenario. In fact, the data did not support the hypotheses. Therefore, post hoc, exploratory data analyses were performed to determine if there were trends in the data that would inform future investigations. The results for these analyses are discussed with suggested directions for future research.

To determine if learned helplessness results from lack of control over negative events or simply the number of negative events experienced, 60 university students were assigned to one of five treatments: controllable low negative, uncontrollable low negative, controllable high negative, uncontrollable high negative, and no treatment. Backward digit and letter span tasks served as test tasks. The generally nonsignificant results were discussed as possibly due to a procedural error. Further research on this question is needed.