About half of the students that are declared engineering majors end up leaving engineering within their first two years at the university. This happens following the required math and science courses that these students must take before getting into the technical engineering coursework. There are two systems that students must be a part of at the university to feel comfortable and have the desire to continue on in their degree. These include the academic system and the social system. The experiences engineering students have during their first required math course, Calculus I, is likely not promoting integration into these two systems. This study analyzed student grade data from Calculus I for trends about student persistence in engineering, along with interviewing students about their experience in Calculus I. These analyses revealed that students do not integrate into the social system of engineering during this course and only persisting students show some positive signs of integration into the academic system. This indicates that there are many gaps in the engineering student experience during their early career that can help these students feel like they belong in engineering and want to stay. Fortunately, there are many areas that can easily be remedied to provide a better social and academic experience in Calculus I to help increase the number of students that remain in engineering until graduation.

[pt] A análise dos erros dos alunos pode e deve ser utilizada como ferramentas para aumentar a eficiência do processo de ensino e aprendizagem da Matemática. Esta pesquisa objetivou coletar e analisar os principais erros cometidos pelos alunos ingressantes no curso de Engenharia da Universidade Cândido Mendes, na disciplina de Cálculo I. A partir dessa análise foram feitas sugestões de mudanças em metodologias e abordagens do ensino específico da disciplina Cálculo I. / [en] The analysis of errors can and should be used as tools to increase the efficiency of the process of teaching and learning of mathematics. This survey aimed to collect and analyze the main mistakes made by students entering the course of engineering at Universidade Cândido Mendes, in the discipline of Calculus I. From this analysis suggestions were made for changes in methodologies and approaches of Calculus I specific teaching.

This dissertation follows the analysis of communication processes established in the discipline Calculus Differential and Integral I of course degree in mathematics at the Center for Distance Higher Studies, Federal University of Sergipe, partner institution of the program Open University of Brazil. This is a qualitative research, case study with a phenomenological approach, with the use of elements ethnographic. The subjects were students, tutors and teacher discipline coordinator bound to Calculus I course in the school period 2010/2 of that institution. The dissertation focused on the following problem: how were established communication processes between the group tutor-student- teacher discipline coordinator in the context of the Calculus I discipline and how it interfered in the process of teaching and learning of this group. We tried to build a clash of ideas from studies of Vygotsky (1991, 1996), Morin (2005, 2009, 2010) and Peters (2003, 2004) regarding communication and interrelationships with the teaching and learning. In view of the aspects analyzed the study pointed out that the processes of communication between subjects occurred in a discontinuous manner and in the case of student-tutor occurred via e-mail or individual messages, and that the guidelines were articulated from written language only, so you could see that some of the difficulties with regard to learning content was related to the difficulties presented in the displacement of a teaching-learning developed from language "spoken " trampled to another predominantly written language. Due to this fact, some students have resorted to private tutors not linked to the UAB program. Another point worth mentioning is that the efficiency in relation to communication processes established between students-teachers- cut across the responsibilities of persons involved and into the limits of the tasks of a number of professionals who advised. / Esta dissertação decorre da análise dos processos de comunicação estabelecidos na disciplina Cálculo Diferencial e Integral I do curso de licenciatura em matemática do Centro de Estudos Superior a Distância da Universidade Federal de Sergipe, instituição parceira do programa Universidade Aberta do Brasil. Trata-se de uma pesquisa qualitativa, estudo de caso com uma abordagem fenomenológica, com a utilização de elementos de natureza etnográfica. Os sujeitos foram os alunos, tutores e professor coordenador de disciplina vinculado a disciplina Cálculo I no período letivo 2010/2 da referida instituição. A investigação centrou-se no seguinte problema: de que maneira foram estabelecidos os processos de comunicação entre o grupo aluno-tutor- professor coordenador de disciplina no contexto da disciplina Cálculo I e como isso interferiu no processo de ensino-aprendizagem deste grupo. Buscou-se construir um embate de idéias a partir dos estudos de Vygotsky (1991, 1996), Morin (2005, 2009, 2010) e Peters (2003, 2004) no que concerne comunicação e as inter-relações com o ensino-aprendizagem. Diante dos aspectos analisados o estudo apontou que os processos de comunicação entre os sujeitos ocorreram de forma pontual, sendo que no caso de aluno-tutor ocorreu por meio de mensagens individuais. Os orientações foram articuladas a partir de linguagem exclusivamente escrita, sendo possível constatar que parte das dificuldades no que concerne a aprendizagem de conteúdos estava relacionada às dificuldades apresentadas no deslocamento de um ensinoaprendizagem desenvolvido a partir de linguagem oralizada para um outro calcado em linguagem predominantemente escrita. Em decorrência desse fato, alguns alunos recorreram a professores particulares não vinculados ao programa Universidade Aberta do Brasil. Outro ponto que vale destacar é que a eficiência em relação aos processos de comunicação estabelecidos entre alunos-tutores-professor coordenador de disciplina perpassam as responsabilidades dos sujeitos envolvidos e adentra os limites das incumbências de uma série de profissionais que os assessoraram.

The purpose of this dissertation was to investigate the relationship between the Advanced Placement Calculus AB exam and student achievement in college level Math 1710-Calculus I. The review of literature shows that this possible relationship is based on Alexander Astin's longitudinal input-environment-outcome (I-E-O) model. The I-E-O model was used to analyze the relationship between the input and outcome of the two variables. In addition, this quantitative study determined the relationship between a score of 3 or lower on the Advanced Placement Calculus AB exam and student achievement in college level Math 1710-Calculus I. The sample population of this study contained 91 students from various high schools in Texas. Spearman's rank correlation revealed there was a statistically significant relationship between Advanced Placement Calculus AB exam scores and final grades in Math 1710-Calculus I.