My thesis, An investigation into how low achieving secondary students learn fractions through visual representations, developed at the University of Nottingham and funded by the university and CAPES, is finally available online for download:
The abstract is:
The gap between low and high achievers is a worldwide concern in Education, especially when it comes to mathematics. One way of facing this issue is by investigating the learning processes of those disadvantaged students at a classroom level. Bearing this in mind, I started my research by observing lessons for low achieving students in an underperforming school in England. After getting acquainted with the context, I designed lesson plans to teach fraction addition and subtraction following three design principles: lessons should enable students to build their knowledge about fractions on visual representations, students should have opportunities to solve tasks without being told how to do it beforehand and lesson plans should maintain some coherence with participant teachers’ current practices. The first principle is the most relevant for my findings, and its choice was based on the growing evidence pointing out the relevance of visual representations for mathematical learning and as a potential pathway to overcome some difficulties faced by low achieving students. Three teachers enacted the lesson plans with a different low achieving group each. Data was collected of the pupils’ working out, as registered in the worksheets, and also in the form of audio recordings, taken during the lessons, of my interactions with students about their thinking while solving the tasks. The data analysis revealed aspects of students’ learning through visual representations that were grouped into two major findings. Firstly, the lessons were successful in promoting reasoning anchored in visual representations, and enabled students to extend their knowledge beyond what was explicitly taught to them. Secondly, an apparent lack of visual skills and prior knowledge on multiplication restricted their engagement with some tasks. The final discussion focuses on the role of visual representations in the learning of mathematics in general, but mainly for low achieving students, and how this can be implemented in classrooms.