GeoPlexo: um material manipulável para o ensino dos números complexos

This study aims to develop a manipulative material to assist the teaching and learning of Complex Numbers. Primarily, It tries to define the status of the current teaching of Complex Numbers, having as guide the bias of the research produced in dissertations and published on the website of Capes and the Virtual Library of Profmat from 2004 to 2014. It presents historical aspects of the theme, a mathematical foundation and a discussion of the use of manipulative materials as teaching resources for the teaching of mathematics. It introduces the manipulative material called GeoPlexo and a sequence of activities of potentiation and settling of complex numbers, explaining its use. It concludes with the importance of manipulative materials as a teaching resource for the teaching of Complex Numbers, especially regarding the geometric visualization of this mathematical object.

Educação financeira no ensino médio: uma abordagem por meio da análise de produtos financeiros com ênfase em consórcios

This paper presents a differential approach of financial mathematics developed in high school, focusing on financial education. We seek through the insertion of texts, analysis of some financial products and by the interpretation of problems to contribute to the financial training of students. Aiming to make financial mathematics more attractive and accessible to the day-today, there are available for studies some practical tools like the citizen calculator which are available for computers and mobile phones. As well as spreadsheets and software Geogebra, that allow you to compare and analyze the financial costs of consortia, financing and financial applications,in addition to being allied in the preparation and control of personal and family budget. By applying the teaching sequence proposed in a nocturnal class of high school, we realized some difficulties that have limited the financial learning of math concepts.Yet identified progress regarding the financial education of students. These observations were made through qualitative and quantitative analysis from notes in the field diary and also answers given by students in specific form.

Proposta de ensino de geometria euclidiana plana para o sexto ano do ensino fundamental sob a ótica do raciocínio lógico-dedutivo

This study will introduce a brief history of the Geometry development, focused in the appearing of the organization in the logical deductive structure achieved by Euclid. Following will be discussed the situation of the learning and teaching of geometry topics since antiquity until the present day, where we will notice that it does not happen with the logical-deductive perspective. After this contextualization, we will propose the realization of a geometry workshop for students of the sixth grade of elementary school, focusing to the development of logical-deductive reasoning. Applied to workshop, changes were observed in the organization of thought of the participating students in the research, furthering the understanding of the concepts and properties of flat euclidean geometry.

Programa Etnomatemática: ponderações da prática pedagógica

The aim of this present work is investigating the interest and motivation for learning, awakened in pupils when the educator practice is guided by the ethnomathematics perspective. The main question is: Can an ethnomathematic approach awaken enthusiasm in pupils, causing it to become more critic and active in building their knowledge? The methodology that guides the investigation is qualitative, based on technical arising of the ethnographic case study. Theoretical contributions that support the investigation are from the scientific methodology and from ethnomathematics. The research material is composed by: researcher’s field diary, audio recording of participant observation, interviews reports of community residents and students parents, highlighting the material produced by students. This study was developed on an 8º year of high school of rural community. During the work were prioritized the ethnomathematics concepts of the Ethnomathematic Program, which establish a link exchange, where the lecturers inserts themselves on the reality of pupils in a way that promote an appreciation of their identity and a commitment to their learning. The educator investigates and values the ideas of pupils throughout dialogues. There are challenges for the application of education with ethno mathematic perspective, pointed out by authors, listed and supplemented in the research. In this context, it is believed that the socio-cultural knowledge must be respect, and as they are understood their specialties, capabilities and characteristics, this can guide teaching practice, making significant process for pupils, providing appropriation of scientific knowledge. Analysis of research practice indicated that students, research subjects, when they decided contextual issues, with their way of life, felt appreciated. The conclusion is that, with continuous action of contextualized of school mathematics, from the recognition of the environment and of cultural identity, the educator has the opportunity of review their own participant condition, and therefore promote an enthusiasm for learning. Because a motivated pupil becomes active, since that the all project is guided in a significant theme.

Metodologia de ensino do conceito de função exponencial à luz da teoria das situações didáticas

This essay presents a proposal on methodology over the mathematical object Exponential Function which enables the development of interpretative and creative skills with potential meaning to the students starting from a didactic sequence structured on the light of The Theory of Didactic Situations from Guy Brousseau and, from the Records of Semiotic Representation of Duval, providing interactions among the students, the teacher and the environment of cooperative learning where the students feel free to express their own ideas as well as to suggest their own approaches. The methodology presented has been developed according to the students first knowledge, valuing their different ways of registering, which have such an important role during the teaching and learning processes. The proposal has been applied to the students from the first year of high school of Colégio Estadual José de Anchieta Ensino Fundamental e Médio, located in a town called Dois Vizinhos –Paraná. In order to the development of the research the methodological tool Didactic Engineering Artigue which consists in a methodology developed only to the research with didactic situations. The main goal has been reached at first, which was to work on the conceptual part of the Exponential Function, the relation of dependence and its main characteristic so that the variable part is in the exponent. Moreover with no imposition but starting from suitable didactic situations, the students were able to realize that they could solve the problems which involve the exponential function and furthermore create new problems (according to their universe) modeled by this kind of function. Its believed that the methodology based on the theory of didactic situations, analysis of students registers, observation on mistakes and obstacles as well as reflections over the aspects of the didactic contract are of fundamental importance to the teaching practice and determinant during the teaching-learning process.

Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.

Pre-Service Teachers’ Mathematics Language and Reflection in the Context of an Early Childhood Mathematics Methods Course

Thesis (Ph.D.)--University of Washington, 2016-06

Playgrounds going wrong: study of the adult style and children's rights during recess in an early childhood and primary education center

Recent perspectives on Pedagogy for Early Childhood Education emphasize children's participation in line with the Children's Rights Convention. The study aimed to analyse how children's rights are dealt with during recess in a school (Early Childhood and Primary Education) in Portugal. The aims were: to characterize the style of the adult (teaching assistants) and the interactions that are established with the children at the playground/recess, and analyse them in terms of children's rights. The qualitative approach was based on the observation during the recess for three weeks. The Adult Style Observation Schedule for Early Childhood Education (ASOS-ECE) was used to register and code the dynamics of six teaching assistants (3 ECE and 3 PE). Critical incidents were also registered. Statistical analysis of the ASOS-ECE levels were complemented with the content analysis of the notes. The playground space was quite limited and affected children's play and well-being. The outdoor playground was never used for the Early Childhood classes, only for Primary Education students but with little supervision. Children were often deprived of playground time by decision of the teaching assistants, as punishment. The results obtained through the Adult Style Observation Schedule for Early Childhood Education (ASOS-ECE) are not satisfactory and are below what would meet the minimum quality value (3,5). For Early Childhood Education, sensibility is the most valued dimension but with very low levels (<2,5). For Primary Education it was autonomy that scored highest (<2,5). The analysis of the notes/critical incidents highlighted articles 12 (expression of own views), 13 (freedom of expression), 19 (protection against violence), 29 (development of personality) and 31 (rest and leisure, play and recreational activities) as being put into question by actions of the adults responsible for the children. Children's rights and well-being need to be put forward in the knowledge base for all adults working with children so that Pedagogy can fulfil its purpose fully.

Mathematical pedagogical content knowledge in early childhood education: A study in initial teacher education in Portugal

The study aims to explore the specificity of mathematics Pedagogical Content Knowledge in Early Childhood Education Pedagogy. The pedagogy of ECE (Siraj-Blatchford, 2010) and the didactics of ECE (Pramling & Pramling-Samuelsson, 2011) suggest dimensions of knowledge that require strong content and PC knowledge of teachers. Recent studies about PCK of ECE teachers highlight similar specific dimensions: organization of educational environment and interactions with children (Lee, 2010, McCray, 2008, Rojas, 2008). The current framework for ECE Teacher Education in Portugal (since 2007) focuses both content knowledge and subject didactics. PCK has been labelled the 'great unknown' in ECE (Rojas, 2008) in traditions where the child's development is considered as the main knowledge base for ECE (Chen & McNamee, 2006, Cullen, 2005, Hedges & Cullen, 2005). We studied the perspectives of 27 initial teacher education students about knowledge for teaching and about ECE Pedagogy. We used one open-ended questionnaire and students' analysis of episodes focusing children's answers or discourse relevant for mathematics (about high numbers and square root). The questionnaire was anonymous and students’ permission to use the answers was obtained. In the questionnaire, interactions with children (62%) and organization of the educational environment (38%) are highlighted as the most important focus for the teacher. Students suggested tasks that were adult planned and oriented to further the situations presented in the episodes. Very few references to children's exploratory actions (Bonawitz et al., 2011) were made. The specificity of ECE (child initiated activities, e.g.) needs to be further developed in initial teacher education.

Genetic origin of the relationship between parental negativity and behavior problems from early childhood to adolescence: A longitudinal genetically sensitive study.

Little is known about how genetic and environmental factors contribute to the association between parental negativity and behavior problems from early childhood to adolescence. The current study fitted a cross-lagged model in a sample consisting of 4,075 twin pairs to explore (a) the role of genetic and environmental factors in the relationship between parental negativity and behavior problems from age 4 to age 12, (b) whether parent-driven and child-driven processes independently explain the association, and (c) whether there are sex differences in this relationship. Both phenotypes showed substantial genetic influence at both ages. The concurrent overlap between them was mainly accounted for by genetic factors. Causal pathways representing stability of the phenotypes and parent-driven and child-driven effects significantly and independently account for the association. Significant but slight differences were found between males and females for parent-driven effects. These results were highly similar when general cognitive ability was added as a covariate. In summary, the longitudinal association between parental negativity and behavior problems seems to be bidirectional and mainly accounted for by genetic factors. Furthermore, child-driven effects were mainly genetically mediated, and parent-driven effects were a function of both genetic and shared-environmental factors.

Regional odontodysplasia in early childhood: A clinical and histological study

Regional odontodysplasia (RO) is a rare disorder of dental development. The affected teeth are clinically hypoplastic and hypocalcified, presenting a ghost-like appearance radiographically. The aim of this work was to report a clinical case of a child with both primary and permanent dentition affected by RO. The conducted therapy was based on a conservative approach, which consisted of follow-up clinical evaluations of the anomalous teeth. However, the endodontic treatment of the primary incisors failed. Then, the chosen option for patient rehabilitation became extraction followed by removable of prosthesis confection. The extracted teeth were processed for histological analysis. In spite of the uncertain prognosis, but taking into account the psychological aspects of the patient, a conservative approach in an attempt to maintain those viable teeth in the oral cavity should be established.

A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

A summative evaluation of a HIV/AIDS Early Childhood Care, Education and Development Teacher Training Workshop in Mongu, Zambia

Objective. To conduct a summative evaluation of an Early Childhood Care, Education and Development (ECCED) Teacher Training Workshop in Mongu, Zambia by assessing changes in knowledge, attitudes and intent to use the information. ^ Study design. A matched cohort survey design was used with additional qualitative data collected by structured observation of workshop sessions, daily facilitator and participant debriefs and participant interviews. ^ Results. Matching pre and post tests were completed by 27 individuals in addition to daily debriefs, structured workshop observation and participant interviews with 22% of the group. The participant population was predominantly female individuals aged 15-44 years old that had completed high school and additional post-secondary training, been teaching children aged 0 – 8 years for 2-5 years in the Western Province and received other HIV/AIDS and ECCED education. Pre-tests indicated a strong understanding of ECCED principles and misconceptions regarding HIV transmission, prevention and the disease's impact on early childhood development. The workshop was found to significantly increase the participants' knowledge of topics covered by the curriculum (paired t-test, N=27, p = 0.004, 95% CI 1.8, 8.6). Participants began with a more limited understanding of HIV/AIDS than ECCED, but the mean gain was much greater at 7.4 +/- 12.3 points. Significantly more participants believed at post-test that HIV/AIDS education should increase for future educators. The 77.8% of participants that increased their knowledge scores at post-test expressed significantly less fear of having a child with HIV/AIDS in the classroom (Independent Samples t-test, N= 27, p = 0.011). Overall participant fear decreased 15.5%. 92.6% and 88.9% of participants planned at post-test to respectively use and share the taught information in their daily professional lives and reported on innovative strategies to communicate with the community. ^ Conclusions. Teacher training workshops can significantly increase HIV/AIDS awareness and promote positive attitudes in educators working with children affected by HIV/AIDS. Using participant suggested teaching techniques such as poems and songs and translating the materials to the local language could assist future facilitators to both culturally and professionally relate to the workshop audience as well as increase participant capacity to share the information with the local community. ^

MEETING THE NEEDS OF HANDICAPPED CHILDREN: A STUDY OF EDUCATIONAL AND HEALTH CARE SERVICES PROVIDED TO PRE-KINDERGARTEN CHILDREN IN THE HOUSTON INDEPENDENT SCHOOL DISTRICT EARLY CHILDHOOD PROGRAM FOR THE HANDICAPPED (PARENT SATISFACTION, FUNCTIONAL STATUS, PSYCHOSOCIAL DEVELOPMENT)

The Education for All Handicapped Children Act of 1975, P.L. 94-142, created a new challenge for the nation's public school systems. During 1982-1983, a national study, called the "Collaborative Study of Children with Special Needs", was conducted in 5 metropolitan school districts to evaluate the effectiveness of education and health care services of children in kindergarten to 6th grade being provided under P.L. 94-142 programs. This dissertation (the Substudy) was undertaken to augment the findings of the Collaborative Study. The purpose of this study was to develop a database to provide descriptive information on the demographic, service and health characteristics of a small group of 3 and 4 year old handicapped children served by the Houston Independent School District (HISD) during 1982-1983.^ The study involved a stratified sample of 105 three and four year old children divided into 3 groups according to type of handicapping condition.^ The results of the study gave a clearer picture of the demographic characteristics of these Pre-K children. Specifically, sex ratio was approximately one, lower than the national norm. Family and socioeconomic characteristics were assessed.^ The study used an independence/dependence index composed of 11 items on the parent questionnaire to assess the level of functional independence of each child. An association was found between index scores and parent-reported effects of the child on family activity. Parents who said that their child's condition had affected the family's job situation, housing accomodations, vacation plans, marriage, choice of friends and social activities were also more likely to report less independence in the child. In addition, many of the Substudy children had extensive care-taking needs reflected in specific components of the index such as dressing, feeding, toileting or moving about the house.^ In general the results of the Pre-K Substudy indicate that at the early childhood level, the HISD special education program is functioning well in most areas and that parents are very satisfied with the program. (Abstract shortened with permission of author.)^