O princípio da Indução Finita e jogos para o ensino de funções

Pós-graduação em Matemática em Rede Nacional - IBILCE

Creating Meaningful Homework and Implementing Homework Presentations to Aid in Mathematics Instruction

In this action research study of sixth grade mathematics, I investigated the use of meaningful homework and the implementation of presentations and its effect on students’ comprehension of mathematical concepts. I collected data to determine whether the creating of meaningful homework and the implementation of homework presentations would have a positive impact on the students’ understanding of the concepts being taught in class and the reasoning behind assigning homework. The homework was based on the lesson taught during class time. It was grade-level appropriate and contained problems similar to those students completed in class. A pre-research and post-research survey based on homework perceptions and my teaching practices was given, student interviews were conducted throughout the research period, weekly teacher journals were kept that pertained to my teaching practices and the involvement of the students that particular week, and homework assignments were collected to gauge the students’ understanding of the mathematics lessons. Most students’ perceptions on homework were positive and most understood the reasoning for homework assignments.

Improving Communication about Mathematics through Vocabulary and Writing

In this action research study, where the subjects were my 6th grade mathematics students, I investigated the impact of direct vocabulary instruction on their communication and achievement. I strategically implemented the addition of vocabulary study into each lesson over a four-month time period. The students practiced using vocabulary in verbal discussions, review activities, and in mathematical problem explanations. I discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data I collected. I also found that in general, students felt that knowing the definition of mathematical words was important and that it increased their achievement when they understood the words. In addition, students were more exact in their communication after receiving vocabulary instruction. As a result of this research, I plan to continue to implement vocabulary into daily lessons and keep vocabulary and communication as a focus of my 6th grade mathematics class.

Here is the Plan: So What is the Question?

In this action research study of my classroom of 5th grade mathematics students, I investigated their understanding of the mathematical operations by having them write problems to match given equations. I discovered that writing a story to match an equation does provide insight into a student’s understanding of mathematical concepts, however, reading comprehension is a factor in the understanding. Readers who struggle with comprehension do struggle with understanding and writing math story problems. The discussion that follows the writing of a math story problem and the solving of the written problems helps to strengthen the students’ mathematical abilities as well as their communication skills and confidence levels. Through my study, students learned that it was alright to make mistakes because the learning from those mistakes is what is important. As a result of this research, I plan to continue to have students write stories to match given equations as a source of information about student understanding. I will continue to give opportunities to revisit those written problems as a tool to increase students’ comprehension and communication skills, as well as their confidence.

Understanding the Mathematical Language

In this action research study of my calculus classroom consisting of only 12th grade students, I investigated activities that would affect a student’s understanding of mathematical language. The goal in examining these activities in a systematic way was to see if a student’s deeper understanding of math terms and symbols resulted in a better understanding of the mathematical concepts being taught. I discovered that some students will rise to the challenge of understanding mathematics more deeply, and some will not. In the process of expecting more from students, the frustration level of both the students and the teacher increased. As a result of this research, I plan to see what other activities will enhance the understanding of mathematical language.

Food Handling Practices, Knowledge and Beliefs of Families with Young Children Based on the Health Belief Model

Objective: To determine current food handling practices, knowledge and beliefs of primary food handlers with children 10 years old and the relationship between these components. Design: Surveys were developed based on FightBac!™ concepts and the Health Belief Model (HBM) construct. Participants: The majority of participants (n= 503) were females (67%), Caucasians (80%), aged between 30 to 49 years old (83%), had one or two children (83%), prepared meals all or most of the time (76%) and consumed meals away from home three times or less per week (66%). Analysis: Descriptive statistics and inferential statistics using Spearman’s rank correlation coefficient (rho) (p<0.05 and one-tail) and Chi-square were used to examine frequency and correlations. Results: Few participants reached the food safety objectives of Healthy People 2010 for safe food handling practices (79%). Mixed results were reported for perceived susceptibility. Only half of the participants (53-54%) reported high perceived severity for their children if they contracted food borne illness. Most participants were confident of their food handling practices for their children (91%) and would change their food handling practices if they or their family members previously experienced food poisoning (79%). Participants’ reasons for high self-efficacy were learning from their family and independently acquiring knowledge and skills from the media, internet or job. The three main barriers to safe food handling were insufficient time, lots of distractions and lack of control of the food handling practices of other people in the household. Participants preferred to use food safety information that is easy to understand, has scientific facts, causes feelings of health-threat and has lots of pictures or visuals. Participants demonstrate high levels of knowledge in certain areas of the FightBac!TM concepts but lacked knowledge in other areas. Knowledge and cues to action were most supportive of the HBM construct, while perceived susceptibility was least supportive of the HBM construct. Conclusion: Most participants demonstrate many areas to improve in their food handling practices, knowledge and beliefs. Adviser: Julie A. Albrecht

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Architectures and design patterns for functional design of logic control and diagnostics in industrial automation

Recently in most of the industrial automation process an ever increasing degree of automation has been observed. This increasing is motivated by the higher requirement of systems with great performance in terms of quality of products/services generated, productivity, efficiency and low costs in the design, realization and maintenance. This trend in the growth of complex automation systems is rapidly spreading over automated manufacturing systems (AMS), where the integration of the mechanical and electronic technology, typical of the Mechatronics, is merging with other technologies such as Informatics and the communication networks. An AMS is a very complex system that can be thought constituted by a set of flexible working stations, one or more transportation systems. To understand how this machine are important in our society let considerate that every day most of us use bottles of water or soda, buy product in box like food or cigarets and so on. Another important consideration from its complexity derive from the fact that the the consortium of machine producers has estimated around 350 types of manufacturing machine. A large number of manufacturing machine industry are presented in Italy and notably packaging machine industry,in particular a great concentration of this kind of industry is located in Bologna area; for this reason the Bologna area is called “packaging valley”. Usually, the various parts of the AMS interact among them in a concurrent and asynchronous way, and coordinate the parts of the machine to obtain a desiderated overall behaviour is an hard task. Often, this is the case in large scale systems, organized in a modular and distributed manner. Even if the success of a modern AMS from a functional and behavioural point of view is still to attribute to the design choices operated in the definition of the mechanical structure and electrical electronic architecture, the system that governs the control of the plant is becoming crucial, because of the large number of duties associated to it. Apart from the activity inherent to the automation of themachine cycles, the supervisory system is called to perform other main functions such as: emulating the behaviour of traditional mechanical members thus allowing a drastic constructive simplification of the machine and a crucial functional flexibility; dynamically adapting the control strategies according to the different productive needs and to the different operational scenarios; obtaining a high quality of the final product through the verification of the correctness of the processing; addressing the operator devoted to themachine to promptly and carefully take the actions devoted to establish or restore the optimal operating conditions; managing in real time information on diagnostics, as a support of the maintenance operations of the machine. The kind of facilities that designers can directly find on themarket, in terms of software component libraries provides in fact an adequate support as regard the implementation of either top-level or bottom-level functionalities, typically pertaining to the domains of user-friendly HMIs, closed-loop regulation and motion control, fieldbus-based interconnection of remote smart devices. What is still lacking is a reference framework comprising a comprehensive set of highly reusable logic control components that, focussing on the cross-cutting functionalities characterizing the automation domain, may help the designers in the process of modelling and structuring their applications according to the specific needs. Historically, the design and verification process for complex automated industrial systems is performed in empirical way, without a clear distinction between functional and technological-implementation concepts and without a systematic method to organically deal with the complete system. Traditionally, in the field of analog and digital control design and verification through formal and simulation tools have been adopted since a long time ago, at least for multivariable and/or nonlinear controllers for complex time-driven dynamics as in the fields of vehicles, aircrafts, robots, electric drives and complex power electronics equipments. Moving to the field of logic control, typical for industrial manufacturing automation, the design and verification process is approached in a completely different way, usually very “unstructured”. No clear distinction between functions and implementations, between functional architectures and technological architectures and platforms is considered. Probably this difference is due to the different “dynamical framework”of logic control with respect to analog/digital control. As a matter of facts, in logic control discrete-events dynamics replace time-driven dynamics; hence most of the formal and mathematical tools of analog/digital control cannot be directly migrated to logic control to enlighten the distinction between functions and implementations. In addition, in the common view of application technicians, logic control design is strictly connected to the adopted implementation technology (relays in the past, software nowadays), leading again to a deep confusion among functional view and technological view. In Industrial automation software engineering, concepts as modularity, encapsulation, composability and reusability are strongly emphasized and profitably realized in the so-calledobject-oriented methodologies. Industrial automation is receiving lately this approach, as testified by some IEC standards IEC 611313, IEC 61499 which have been considered in commercial products only recently. On the other hand, in the scientific and technical literature many contributions have been already proposed to establish a suitable modelling framework for industrial automation. During last years it was possible to note a considerable growth in the exploitation of innovative concepts and technologies from ICT world in industrial automation systems. For what concerns the logic control design, Model Based Design (MBD) is being imported in industrial automation from software engineering field. Another key-point in industrial automated systems is the growth of requirements in terms of availability, reliability and safety for technological systems. In other words, the control system should not only deal with the nominal behaviour, but should also deal with other important duties, such as diagnosis and faults isolations, recovery and safety management. Indeed, together with high performance, in complex systems fault occurrences increase. This is a consequence of the fact that, as it typically occurs in reliable mechatronic systems, in complex systems such as AMS, together with reliable mechanical elements, an increasing number of electronic devices are also present, that are more vulnerable by their own nature. The diagnosis problem and the faults isolation in a generic dynamical system consists in the design of an elaboration unit that, appropriately processing the inputs and outputs of the dynamical system, is also capable of detecting incipient faults on the plant devices, reconfiguring the control system so as to guarantee satisfactory performance. The designer should be able to formally verify the product, certifying that, in its final implementation, it will perform itsrequired function guarantying the desired level of reliability and safety; the next step is that of preventing faults and eventually reconfiguring the control system so that faults are tolerated. On this topic an important improvement to formal verification of logic control, fault diagnosis and fault tolerant control results derive from Discrete Event Systems theory. The aimof this work is to define a design pattern and a control architecture to help the designer of control logic in industrial automated systems. The work starts with a brief discussion on main characteristics and description of industrial automated systems on Chapter 1. In Chapter 2 a survey on the state of the software engineering paradigm applied to industrial automation is discussed. Chapter 3 presentes a architecture for industrial automated systems based on the new concept of Generalized Actuator showing its benefits, while in Chapter 4 this architecture is refined using a novel entity, the Generalized Device in order to have a better reusability and modularity of the control logic. In Chapter 5 a new approach will be present based on Discrete Event Systems for the problemof software formal verification and an active fault tolerant control architecture using online diagnostic. Finally conclusive remarks and some ideas on new directions to explore are given. In Appendix A are briefly reported some concepts and results about Discrete Event Systems which should help the reader in understanding some crucial points in chapter 5; while in Appendix B an overview on the experimental testbed of the Laboratory of Automation of University of Bologna, is reported to validated the approach presented in chapter 3, chapter 4 and chapter 5. In Appendix C some components model used in chapter 5 for formal verification are reported.

Closed-loop investigation of the dynamical properties of cardiomyocyte electrophysiology by means of Dynamic clamp and Mathematical modelling

The research field of my PhD concerns mathematical modeling and numerical simulation, applied to the cardiac electrophysiology analysis at a single cell level. This is possible thanks to the development of mathematical descriptions of single cellular components, ionic channels, pumps, exchangers and subcellular compartments. Due to the difficulties of vivo experiments on human cells, most of the measurements are acquired in vitro using animal models (e.g. guinea pig, dog, rabbit). Moreover, to study the cardiac action potential and all its features, it is necessary to acquire more specific knowledge about single ionic currents that contribute to the cardiac activity. Electrophysiological models of the heart have become very accurate in recent years giving rise to extremely complicated systems of differential equations. Although describing the behavior of cardiac cells quite well, the models are computationally demanding for numerical simulations and are very difficult to analyze from a mathematical (dynamical-systems) viewpoint. Simplified mathematical models that capture the underlying dynamics to a certain extent are therefore frequently used. The results presented in this thesis have confirmed that a close integration of computational modeling and experimental recordings in real myocytes, as performed by dynamic clamp, is a useful tool in enhancing our understanding of various components of normal cardiac electrophysiology, but also arrhythmogenic mechanisms in a pathological condition, especially when fully integrated with experimental data.

Executive functions in 5- to 8-year olds: Developmental changes and relationship to academic achievement

Pronounced improvements in executive functions (EF) during preschool years have been documented in cross-sectional studies. However, longitudinal evidence on EF development during the transition to school and predictive associations between early EF and later school achievement are still scarce. This study examined developmental changes in EF across three time-points, the predictive value of EF for mathematical, reading and spelling skills and explored children's specific academic attainment as a function of early EF. Participants were 323 children following regular education; 160 children were enrolled in prekindergarten (younger cohort: 69 months) and 163 children in kindergarten (older cohort: 78.4 months) at the first assessment. Various tasks of EF were administered three times with an interval of one year each. Mathematical, reading and spelling skills were measured at the last assessment. Individual background characteristics such as vocabulary, non-verbal intelligence and socioeconomic status were included as control variables. In both cohorts, changes in EF were substantial; improvements in EF, however, were larger in preschoolers than school-aged children. EF assessed in preschool accounted for substantial variability in mathematical, reading and spelling achievement two years later, with low EF being especially associated with significant academic disadvantages in early school years. Given that EF continue to develop from preschool into primary school years and that starting with low EF is associated with lower school achievement, EF may be considered as a marker or risk for academic disabilities.

Skills training and social influences for violence prevention in middle schools: A curriculum evaluation

This pilot study evaluated the effect of skills training and of social influences on self-reported aggressive behavior in a sample of 239 sixth-grade students. The effect of two intervention groups and one control group were compared. In the first intervention group, a 15-session, violence-prevention curriculum was taught by the teacher. In the second intervention group, the same curriculum was taught by the teacher with the assistance of peer leaders trained to modify social norms about violence. The control group was evaluated but did not receive any training. The design included four schools. In two schools, three classes were assigned to one of the two interventions or to the control group. In the other two schools, two classes were assigned to either intervention (teacher only) or control. Students were evaluated before and after the implementation of the curriculum using a standardized questionnaire.^ The primary outcome was the effect of the curriculum and peer leaders on self-reported aggressive behaviors. The secondary outcome was their impact on intervening variables: knowledge about violence, conflict-resolution skills, self-efficacy, and attitudes.^ The intervention had a moderate effect on reducing self-reported aggressive behaviors among boys in two of the six classes that received the curriculum. Both classes with peer leaders reduced their aggressive behavior, but this reduction was significant in only one. A peer leader selection problem could probably explain this lack of effect.^ In three of the four schools, both interventions had an overall significant effect on increasing knowledge about violence and skills to reduce violence. Students also developed a more negative attitude toward violence after the intervention. As hypothesized, attitude change was stronger among students from the teacher plus peer leader group. No intervention effect was observed on self-efficacy nor on attitudes toward skills to reduce violence. Limitations of the study and implications for violence prevention in schools are discussed. ^

Complexity and non-linearity in earth surface processes - concepts, methods and applications

Complexity has long been recognized and is increasingly becoming mainstream in geomorphology. However, the relative novelty of various concepts and techniques associated to it means that ambiguity continues to surround complexity. In this commentary, we present and discuss a variety of recent contributions that have the potential to help clarify issues and advance the use of complexity in geomorphology.

Encouragement to Increase the Use of Psychosocial Skills in the Diagnosis and Therapy of Patients With Functional Dysphonia.

Clinicians believe that psychosocial factors play a causal role in the etiology of many forms of functional dysphonia (FD). But for decades, all attempts to confirm such causation have failed. This paper aims to show the logic of this failure, to discuss the possibilities of employing psychology in therapy nonetheless, and to encourage clinicians to use their psychosocial knowledge and skills. The failure to confirm psychic and social factors as causal in the etiology of FD is basically a consequence of a principal shortcoming of evidence-based medicine (EBM). As the gold standard for validity, reliability, and objectivity in medical research, EBM is based on calculability and hence the processing of quantitative data. But life paths and life situations are best or sometimes only expressible in qualitative, experiential, and idiographic terms. Thus EBM-guided evaluation undervalues most psychosocial studies. This report of an experienced multidisciplinary voice team proposes alternative pathways for integrating psychosocial knowledge into the diagnosis and the treatment of FD. The difference between the fields of activity of psychotherapists and speech-language pathologists is discussed, and the latter group is shown the potential benefits of using more of their psychosocial knowledge and skills.

A project to improve the information seeking skills and increase the use of evidence-based research in public health practice

The ability of public health practitioners (PHPs) to work efficiently and effectively is negatively impacted by their lack of knowledge of the broad range of evidence-based practice information resources and tools that can be utilized to guide them in their development of health policies and programs. This project, a three-hour continuing education hands-on workshop with supporting resources, was designed to increase knowledge and skills of these resources. The workshop was presented as a pre-conference continuing education program for the Texas Public Health Association (TPHA) 2008 Annual Conference. Topics included: identification of evidence-based practice resources to aid in the development of policies and programs; identification of sources of publicly available data; utilization of data for community assessments; and accessing and searching the literature through a collection of databases available to all citizens of Texas. Supplemental resources included a blog that served as a gateway to the resources explored during the presentation, a community assessment workbook that incorporates both Healthy People 2010 objectives and links to reliable sources of data, and handouts providing additional instruction on the use of the resources covered during the workshop.^ Before- and after-workshop surveys based on Kirkpatrick's 4-level model of evaluation and the Theory of Planned Behavior were administered. Of the questions related to the trainer, the workshop, and the usefulness of the workshop, participants gave "Good" to "Excellent" responses to all one question. Confidence levels overall increased a statistically significant amount; measurements of attitude, social norms, and control showed no significant differences before and after the workshop. Lastly, participants indicated they were likely to use resources shown during the workshop within a one to three month time period on average. ^ The workshop and creation of supplemental resources served as a pilot for a funded project that will be continued with the development and delivery of four 4-week long webinar-based training sessions to be completed by December 2008. ^

Measuring global value chains and regional economic integration : an international input-output approach

Firms that are expanding their cross-border activities, such as vertical specialization trade, outsourcing, and fragmentation productions, have brought dramatic changes to the global economy during the last two decades. In an attempt to understand the evolution of the interaction among countries or country groups, many trade-statistics-based indicators have been developed. However, most of these statistics focus on showing the direct trade-specific-relationship among countries, rather than considering the roles that intercountry and interindustrial production networks play in a global economy. This paper uses the concepts of trade in value added as measured by the input–output tables of OECD and IDE-JETRO to provide alternative indicators that show the evolution of regional economic integration and global value chains for more than 50 economies. In addition, this paper provides thoughts on how to evaluate comparative advantages on the basis of value added using an international input–output model.