This mixed methods research design, which was modelled on the constructivist view of schooling, sets out to investigate the effect of developing mathematical problem solving skills of grade 8 learners on their performance and achievement in mathematics. To develop the mathematical problem solving skills of the experimental group, a problem-centred teaching and learning environment was created in which problem posing and solving were the key didactic mathematical activity. The effect of the intervention programme on the experimental group was compared with the control group by assessing learners’ problem solving processes, mathematical problem solving skills, reasoning and cognitive processes, performance and achievement in mathematics. Data were obtained through questionnaires, a mathematical problem solving skills inventory, direct participant observation and questioning, semi-structured interviews, learner journals, mathematical tasks, written work, pre- and post- multiple-choice and word-problem tests. Data analysis was largely done through descriptive analysis and the findings assisted the researcher to make recommendations and suggest areas that could require possible further research. / Mathematics Education / M. Ed. (Mathematical Education)

This study aimed on revealing which metacognitive strategies are constructed by EJA students, in the literacy phase, when solving mathematical problems and in what way the dialogue between these strategies interferes in their school performance. For this, the research was carried out through a pedagogical intervention in a class, whose teaching institution belongs to the S System, composed of eleven participants. The methodological approach of this study consists of the organized research-act with the following stages: observation, interviews, application of questionnaires, application of didactic sequences and preparation of field diary for data collection and analysis. The bibliographical incursion is reported in authors such as Flavell, Miller and Miller (1999); Ludovico et al. (2001); Portilho (2011); Locatelli (2014); Silva (2009); Souza (2009); Charlot (2000, 2005, 2013); Freire (2015); Dante (2010) who subsidized the interpretations of didactic phenomena occurring in the classroom, from the perspective of four categories: Mathematics in EJA, Mathematical Problem Solving, Metacognition and Relation with Knowing. The analysis of the data allowed to dissuade the mutual effects between the concept of Metacognition and the theory of Relation with Knowing, since both concepts approach the subject's gaze on himself and on knowledge. That is, the understanding of metacognitive processes favors students' learning, by being able to perceive what they know and how they learn, both individually and collectively in the classroom. Therefore, it was noticed that the solving of mathematical problems presents itself as a favorable methodology to this process, instigating the subjects to think about their own reasoning while they are working the activities proposed in the classes. It was also noted that the social and identity dimensions of the subjects studied, in their relationship with knowledge, permeate the whole conjuncture of the looking at oneself and other colleagues during the resolution of the proposed tasks: to think about the reason for their difficulties and / or Skills; To be admitted as a singular and social subject; Making comparisons with yourself and other colleagues; Dealing with their individuality and, at the same time, allowing the exchange of knowledge. / Este estudo objetivou desvelar quais estratégias metacognitivas são construídas por estudantes da EJA, em fase de letramento, ao resolver problemas matemáticos e de que maneira o diálogo entre essas estratégias interfere no seu desempenho escolar. Para tanto, a pesquisa foi realizada por meio de uma intervenção pedagógica em uma turma, cuja instituição de ensino pertence ao Sistema S, compondo-se de onze participantes. A abordagem metodológica deste estudo consiste no tipo pesquisa-ação organizada nas seguintes etapas: observação, entrevistas, aplicação de questionários, aplicação de sequências didáticas e elaboração de diário de campo para coleta e análise dos dados obtidos. A incursão bibliográfica reporta-se em autores como Flavell, Miller e Miller (1999); Ludovico et al (2001); Portilho (2011); Locatelli (2014); Silva (2009); Souza (2009); Charlot (2000, 2005, 2013); Freire (2015); Dante (2010) que subsidiaram as interpretações dos fenômenos didáticos ocorridos em sala de aula, sob a ótica de quatro categorias: Matemática na EJA, Resolução de Problemas Matemáticos, Metacognição e Relação com o Saber. A análise dos dados permitiu dessumir incidências mútuas entre o conceito de Metacognição e a teoria da Relação com o Saber, uma vez que ambos conceitos abordam o olhar do sujeito sobre si próprio e sobre o saber. Ou seja, a compreensão dos processos metacognitivos favorece a aprendizagem dos alunos, ao se sentirem capazes de perceber o que sabem e como aprendem, tanto de forma individual como coletiva em sala de aula. Para tanto, percebeu-se que a resolução de problemas matemáticos apresenta-se como metodologia favorável a esse processo, instigando os sujeitos a pensarem sobre seu próprio raciocínio enquanto estão trabalhando as atividades propostas nas aulas. Notou-se também que as dimensões social e identitária dos sujeitos pesquisados, na sua relação com o saber, permeiam toda a conjuntura do olhar para si e para os demais colegas durante a resolução das tarefas propostas: pensar no porquê de suas dificuldades e/ou habilidades; admitir-se enquanto sujeito singular e social; fazer comparativos consigo e com os demais colegas; lidar com sua individualidade e, ao mesmo tempo, permitir a troca de conhecimentos.