Obstáculos superados pelos matemáticos no passado e vivenciados pelos alunos na atualidade : a polêmica multiplicação de números inteiros

In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning

Polinômios algébricos e trigonométricos com zeros reais

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Regra de Sinais de Descartes para polinômios ortogonais

Pós-graduação em Matematica Aplicada e Computacional - FCT

Ensino e aprendizagem de matemática: o uso de recursos manipulativos em sala de aula

In this work, we understand the importance of the use of manipulative resources for learning mathematics. For both we developed a qualitative phenomenological approach. Performing a case study with nine 7th grade students of the Elementary School, we used the abacus of the integers to examine in what way the use of Abacus contributes to students learning. The choice of material was made according to the focus of research, understanding the signs rule. In the analysis and interpretation of data, highlight lines of students, subject of the research, units of meaning that allow us to say that the material using awakened interest in students Who actively participated in the research and enabled them to understand the rule of signs, to operate with integers enabled them to understand the rule of signs, to operate with integers

Ensino e aprendizagem de matemática: o uso de recursos manipulativos em sala de aula

In this work, we understand the importance of the use of manipulative resources for learning mathematics. For both we developed a qualitative phenomenological approach. Performing a case study with nine 7th grade students of the Elementary School, we used the abacus of the integers to examine in what way the use of Abacus contributes to students learning. The choice of material was made according to the focus of research, understanding the signs rule. In the analysis and interpretation of data, highlight lines of students, subject of the research, units of meaning that allow us to say that the material using awakened interest in students Who actively participated in the research and enabled them to understand the rule of signs, to operate with integers enabled them to understand the rule of signs, to operate with integers

A resource for signs and Feynman diagrams of the standart model

When performing a full calculation within the standard model (SM) or its extensions, it is crucial that one utilizes a consistent set of signs for the gauge couplings and gauge fields. Unfortunately, the literature is plagued with differing signs and notations. We present all SM Feynman rules, including ghosts, in a convention-independent notation, and we table the conventions in close to 40 books and reviews.

Caution, children crossing: Heterogeneity of victim's cost of care and negligence rule

The paper deals with a bilateral accident situation in which victims haveheterogeneous costs of care. With perfect information,efficient care bythe injurer raises with the victim's cost. When the injurer cannot observeat all the victim's type, and this fact can be verified by Courts, first-bestcannot be implemented with the use of a negligence rule based on thefirst-best levels of care. Second-best leads the injurer to intermediate care,and the two types of victims to choose the best response to it. This second-bestsolution can be easily implemented by a negligence rule with second-best as duecare. We explore imperfect observation of the victim's type, characterizing theoptimal solution and examining the different legal alternatives when Courts cannotverify the injurers' statements. Counterintuitively, we show that there is nodifference at all between the use by Courts of a rule of complete trust and arule of complete distrust towards the injurers' statements. We then relate thefindings of the model to existing rules and doctrines in Common Law and Civil Lawlegal systems.

Addendum to Perception and Interpretation of Advance Warning Signs on County Roads, HR-256, 1985

This contract extension was granted to analyze data obtained in the original contract period at a level of detail not called for in the original contract nor permitted by the time constraints of the original contract schedule. These further analyses focused on two primary questions: I. What sources of variation can be isolated within the overall pattern of driver recognition errors reported previously for the 16 signs tested in Project HR-256? 2. Were there systematic relations among data on the placement of signs in a simulated signing exercise and data on the respondents' ability to detect the presence of a sign in a visual field or their ability to recognize quickly and correctly a sign shown them or the speed with which these same persons can respond to a sign for a driver decision?

Design and evaluation of web interface signs to improve web usability : a semiotic framework

Technological innovations, the development of the internet, and globalization have increased the number and complexity of web applications. As a result, keeping web user interfaces understandable and usable (in terms of ease-of-use, effectiveness, and satisfaction) is a challenge. As part of this, designing userintuitive interface signs (i.e., the small elements of web user interface, e.g., navigational link, command buttons, icons, small images, thumbnails, etc.) is an issue for designers. Interface signs are key elements of web user interfaces because ‘interface signs’ act as a communication artefact to convey web content and system functionality, and because users interact with systems by means of interface signs. In the light of the above, applying semiotic (i.e., the study of signs) concepts on web interface signs will contribute to discover new and important perspectives on web user interface design and evaluation. The thesis mainly focuses on web interface signs and uses the theory of semiotic as a background theory. The underlying aim of this thesis is to provide valuable insights to design and evaluate web user interfaces from a semiotic perspective in order to improve overall web usability. The fundamental research question is formulated as What do practitioners and researchers need to be aware of from a semiotic perspective when designing or evaluating web user interfaces to improve web usability? From a methodological perspective, the thesis follows a design science research (DSR) approach. A systematic literature review and six empirical studies are carried out in this thesis. The empirical studies are carried out with a total of 74 participants in Finland. The steps of a design science research process are followed while the studies were designed and conducted; that includes (a) problem identification and motivation, (b) definition of objectives of a solution, (c) design and development, (d) demonstration, (e) evaluation, and (f) communication. The data is collected using observations in a usability testing lab, by analytical (expert) inspection, with questionnaires, and in structured and semi-structured interviews. User behaviour analysis, qualitative analysis and statistics are used to analyze the study data. The results are summarized as follows and have lead to the following contributions. Firstly, the results present the current status of semiotic research in UI design and evaluation and highlight the importance of considering semiotic concepts in UI design and evaluation. Secondly, the thesis explores interface sign ontologies (i.e., sets of concepts and skills that a user should know to interpret the meaning of interface signs) by providing a set of ontologies used to interpret the meaning of interface signs, and by providing a set of features related to ontology mapping in interpreting the meaning of interface signs. Thirdly, the thesis explores the value of integrating semiotic concepts in usability testing. Fourthly, the thesis proposes a semiotic framework (Semiotic Interface sign Design and Evaluation – SIDE) for interface sign design and evaluation in order to make them intuitive for end users and to improve web usability. The SIDE framework includes a set of determinants and attributes of user-intuitive interface signs, and a set of semiotic heuristics to design and evaluate interface signs. Finally, the thesis assesses (a) the quality of the SIDE framework in terms of performance metrics (e.g., thoroughness, validity, effectiveness, reliability, etc.) and (b) the contributions of the SIDE framework from the evaluators’ perspective.

Signs and Symptoms of Temporomandibular Dysfunction in Fibromyalgic Patients

Objective: The objective of this study was to determine the frequency of signs and symptoms of temporomandibular disorder (TMD) in fibromyalgic patients. Methods: Sixty subjects of both sexes (mean age, 49.2 +/- 13.8 years) with fibromyalgia (FM) diagnosis were included in this study. All patients were examined by a calibrated investigator to identify the presence of TMD using the Research Diagnostic Criteria for TMD. Results: The most common signs (A) and symptoms (B) reported by FM patients were (A) pain in the masticatory muscles (masseter, 80%; posterior digastric, 76.7%), pain in the temporomandibular joint (83.3%), and 33.3% and 28.3%, respectively, presented joint sounds when opening and closing the mouth; (B) headache (97%) and facial pain (81.7%). In regard to the classic triad for the diagnosis of the TMD, it was found that 35% of the FM patients presented, at the same time, pain, joint sounds, and alteration of the mandibular movements. It was verified that myofascial pain without limitation of mouth opening was the most prevalent diagnosis (47%) for the RDC subgroup I. For the subgroup II, the disk displacement with reduction was the most prevalent diagnosis (21.6%). For the subgroup III, 36.7% of the subjects presented osteoarthritis. Conclusions: Thus, there is a high prevalence of signs and symptoms of TMD in FM patients, indicating the need for an integrated diagnosis and treatment of these patients, which suggest that the FM could be a medium- or long-term risk factor for the development of TMD.

Design, development and field evaluation of a Spanish into sign language translation system

This paper describes the design, development and field evaluation of a machine translation system from Spanish to Spanish Sign Language (LSE: Lengua de Signos Española). The developed system focuses on helping Deaf people when they want to renew their Driver’s License. The system is made up of a speech recognizer (for decoding the spoken utterance into a word sequence), a natural language translator (for converting a word sequence into a sequence of signs belonging to the sign language), and a 3D avatar animation module (for playing back the signs). For the natural language translator, three technological approaches have been implemented and evaluated: an example-based strategy, a rule-based translation method and a statistical translator. For the final version, the implemented language translator combines all the alternatives into a hierarchical structure. This paper includes a detailed description of the field evaluation. This evaluation was carried out in the Local Traffic Office in Toledo involving real government employees and Deaf people. The evaluation includes objective measurements from the system and subjective information from questionnaires. The paper details the main problems found and a discussion on how to solve them (some of them specific for LSE).

A maximum density rule for surfaces of quasicrystals

Motivated by Bravais' rule, of wide validity for crystals, we introduce a maximum density rule for the surfaces of quasicrystals and use it to determine the 5-, 2- and 3-fold bulk terminations in a geometric icosahedral model of i-AlPdMn and i-AlCuFe that represent surfaces.

Visual signs and symptoms of multiple system atrophy

Multiple system atrophy (MSA) is a rare movement disorder and a member of the 'parkinsonian syndromes', which also include Parkinson's disease (PD), progressive supranuclear palsy (PSP), dementia with Lewy bodies (DLB) and corticobasal degeneration (CBD). Multiple system atrophy is a complex syndrome, in which patients exhibit a variety of signs and symptoms, including parkinsonism, ataxia and autonomic dysfunction. It can be difficult to separate MSA from the other parkinsonian syndromes but if ocular signs and symptoms are present, they may aid differential diagnosis. Typical ocular features of MSA include blepharospasm, excessive square-wave jerks, mild to moderate hypometria of saccades, impaired vestibular-ocular reflex (VOR), nystagmus and impaired event-related evoked potentials. Less typical features include slowing of saccadic eye movements, the presence of vertical gaze palsy, visual hallucinations and an impaired electroretinogram (ERG). Aspects of primary vision such as visual acuity, colour vision or visual fields are usually unaffected. Management of the disease to deal with problems of walking, movement, daily tasks and speech problems is important in MSA. Optometrists can work in collaboration with the patient and health-care providers to identify and manage the patient's visual deficits. A more specific role for the optometrist is to correct vision to prevent falls and to monitor the anterior eye to prevent dry eye and control blepharospasm.

Supercritical CO2 recovery of caffeine from green coffee oil: new experimental solubility data and modeling

The caffeine solubility in supercritical CO2 was studied by assessing the effects of pressure and temperature on the extraction of green coffee oil (GCO). The Peng-Robinson¹ equation of state was used to correlate the solubility of caffeine with a thermodynamic model and two mixing rules were evaluated: the classical mixing rule of van der Waals with two adjustable parameters (PR-VDW) and a density dependent one, proposed by Mohamed and Holder² with two (PR-MH, two parameters adjusted to the attractive term) and three (PR-MH3 two parameters adjusted to the attractive and one to the repulsive term) adjustable parameters. The best results were obtained with the mixing rule of Mohamed and Holder² with three parameters.

Comparative study of intermaxillary relationships of manual and swallowing methods

This study compared the mandibular displacement from three methods of centric relation record using an anterior jig associated with (A) chin point guidance, (B) swallowing (control group) and (C) bimanual manipulation. Ten patients aged 25-39 years were selected if they met the following inclusion criteria: complete dentition (up to the second molars), Angle class I and absence of signs and symptoms of temporomandibular disorders and diagnostic casts showing stability in the maximum intercuspation (MI) position. Impressions of maxillary and mandibular arches were made with an irreversible hydrocolloid impression material. Master casts of each patient were obtained, mounted on a microscope table in MI as a reference position and 5 records of each method were made per patient. The mandibular casts were then repositioned with records interposed and new measurements were obtained. The difference between the two readings allowed measuring the displacement of the mandible in the anteroposterior and lateral axes. Data were analyzed statistically by ANOVA and Tukey's test at 5% significance level. There was no statistically significant differences (p>0.05) among the three methods for measuring lateral displacement (A=0.38 ± 0.26, B=0.32 ± 0.25 and C=0.32 ± 0.23). For the anteroposterior displacement (A=2.76 ± 1.43, B=2.46 ± 1.48 and C=2.97 ± 1.51), the swallowing method (B) differed significantly from the others (p<0.05), but no significant difference (p>0.05) was found between chin point guidance (A) and bimanual manipulation (C). In conclusion, the swallowing method produced smaller mandibular posterior displacement than the other methods.