A avaliação da aprendizagem na licenciatura em matemática: o que dizem documentos, professores e alunos?

Tese (doutorado) - Pontifícia Universidade Católica de São Paulo, Programa de Estudos Pós-Graduados em Educação Matemática, São Paulo, 2017.Este estudo investiga como vem sendo abordada a avaliação da aprendizagem em cursos de licenciatura, tanto como prática quanto como elemento curricular constituinte da formação docente. A pesquisa buscou investigar o que dizem documentos, professores e alunos sobre a avaliação da aprendizagem na licenciatura em matemática. A relevância do estudo reside na importância da avaliação como elemento central nos processos de ensino e de aprendizagem e no reduzido número de pesquisas sobre o tema. Os referenciais teóricos foram buscados em Fernandes, em Lopes e Silva e em Arredondo e Diago e complementados por Hoffmann e Luckesi. Numa abordagem qualitativa de pesquisa, foram analisados os projetos político-pedagógicos de cursos de licenciatura em matemática de cinco universidades federais, uma de cada região geográfica do país, bem como os planos de ensino dos componentes curriculares dessas licenciaturas, limitados aos disponibilizados pelas instituições. Foram também realizadas entrevistas semiestruturadas com 10 professores e 10 alunos de cada um desses cursos e com dois pesquisadores da área de avaliação da aprendizagem, num total de 102 participantes. Para tratamento dos dados, utilizaram-se elementos da análise de conteúdo, conforme descrita por Bardin. A análise dos dados evidenciou que: na organização de quatro das licenciaturas pesquisadas não há espaço reservado à avaliação da aprendizagem como componente curricular; o tema é tratado de forma superficial, tanto pelos professores formadores (o que também foi apontado pelos licenciandos entrevistados) quanto nos documentos consultados; um número inexpressivo de referências bibliográficas listadas nos documentos analisados versa sobre avaliação da aprendizagem; o desempenho dos licenciandos é avaliado quase sempre por meio de provas, listas de exercícios, trabalhos e seminários, revelando uma concepção de avaliação como mera verificação da aprendizagem; são os professores da área de Educação, de modo geral, que concebem e praticam uma avaliação da aprendizagem com características de avaliação formativa. Assim, este estudo levantou importantes elementos para reflexão e para eventuais mudanças das práticas de avaliação de professores formadores, visando dar maior destaque à avaliação da aprendizagem como elemento curricular constituinte da formação inicial do futuro professor de matemática da educação básica.Abstract : This study investigated how the assessment of learning is being focused in teaching certification programs, both as a practice and curricular element of teacher training. Content derived from documents and teachers and students interviewed on the assessment of learning in teaching certification in mathematics was investigated. The relevance of the study lies in the importance of assessment as a central element in the teaching and learning processes and in the current dearth of studies on the subject. The theoretical approaches for the study were based on Fernandes, Lopes and Silva, and Arredondo and Diago and complemented by Hoffmann and Luckesi. This qualitative study analyzed the political-pedagogic projects of teaching certification courses in mathematics of five federal universities, one from each geographic region of Brazil, along with the teaching plans for curriculum components of these courses, as provided by the institutions. Semi-structured interviews were also conducted involving 10 teachers and 10 students from each of the courses plus two researchers from the learning assessment area, giving a total of 102 participants. Data treatment was performed using elements of content analysis, as per Bardin, revealing that no space was dedicated to the assessment of learning as a curricular component in the structure of four of the teaching certification courses studied; the subject was only touched upon, both by teacher trainers (also cited by students interviewed) and in the documents consulted; scant bibliographic references listed in the documents analyzed addressed the assessment of learning; the performance of trainee teachers was only assessed based on exams, lists of exercises, studies, and seminars, evidencing a concept of assessment of mere checking of learning; generally, teachers from the education area conceive and practice the assessment of learning based on formative assessment. Therefore, this study yielded important elements for reflection and change in student assessment practices among trainee teachers, with a focus on the assessment of learning as a constituent element of the curriculum in the training of future teachers of mathematics in basic education

Anéis singulares e anéis não singulares

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas. Programa de Pós-Graduação em Matemática e Computação Científic

False signs and the non-specificity of theoryof mind: Evidence that preschoolers have general difficulties in understanding representations

The discoveryt hat 3-year-old children have difficulties understanding false belief has fuelled twod ecades of research directeda tu nderstanding whyc hildren have this problem. One unresolved question is whether false belief problems ared ue to difficulties with mental or representational aspects of mental states. This question has implications for current arguments about the domain specificity of theoryo fm ind in typically developing children and in populations with autism and brain damage.W e revisit this question, presenting evidence that preschoolers' difficulty with false belief is not ad omain-specific problem with mental states but am ore general difficulty with understanding representations. The question of whether theoryofmind is eitheradomain-specific or adomain-general capacity has been debated formore than two decades. Theorists taking adomain-specific approach have argued that there is adedicated theoryofmind system with specialized mechanisms that process mentalr epresentations about one'so wn and other people's beliefs and other mentalstates. On the domain-general side of the debate, theorists have proposed that children'sa bilityt ou nderstandm entalr epresentations such as beliefs reflectst heir conceptual understanding of representations more generally.P erner (1991), fore xample, argues that understanding of false belief is based on the ability to metarepresent, that is, to understand representations as representations. Support forthe domain-general view was initially provided by evidence of changes in preschool children'su nderstanding not only of mentalr epresentations uch as beliefs, but also of external, non-mental representation such as photographs. In the false belief task, ap rotagonist observes as tateo fa ffairs (e.g.o bject in location 1) which then unexpectedly changes in their absence (object movedt ol ocation 2) leaving the protagonist with afalse belief. Evidence from numerous studies suggests that adistinct changeoccursinunderstanding of mental representations between the ageof3and 5 years old (seeW ellman, Cross, &W atson, 2001 forr eview). While task factors ma