Considering that geometry is taught according to certain principles that do not encourage creativity, I have decided to employ the mixed methods philosophical framework applying the concurrent transformative design in the form of an exploratory case study. The case study to (i) explore and design a model that influences learning using polygon pieces and mathematics dictionary in the teaching and learning of geometry to grade 8 learners; (ii) investigate if the measurement of angles and sides of polygons using polygon pieces assisted by mathematics dictionary promote learners’ comprehension of geometry and (iii) investigate how mathematics teachers should use polygon pieces along with mathematics dictionary to teach properties of triangles in order to promote learners’ conceptual understanding. Drawing from my research findings a model has been developed from the use of polygon pieces and mathematics dictionary. The model use of mathematics dictionary in teaching and learning geometry is to develop learners’ mathematics vocabulary and terminology proficiency. Polygon pieces are to enhance the comprehension of geometric concepts. The quantitative data emerged from marked scripts of the diagnostic and post-intervention tests, the daily reflective tests and intervention activities were analysed as percentages and presented in line and bar graphs. Qualitative data obtained from observation notes and transcribed interviews were analysed in three forms: thematically, constant comparison and keywords in context. These findings support other research regarding the importance of using physical manipulatives with mathematics dictionary in teaching and learning geometry. They align with other findings that stress that manipulatives are critical facilitating tools for the development of mathematics concepts. The investigations led into the designing of a teaching model for the topic under study for the benefit of the mathematics community in the teaching and learning of geometry, focusing on properties of triangles. The model developed during this study adds to the relatively sparse teaching models but growing theoretical foundation of the field of mathematics. / Mathematics Education / Ph. D. (Mathematics Education)

CAPES / Apresentamos neste trabalho alguns paradoxos lógico-matemáticos, como o paradoxo de Galileu, e também alguns paradoxos geométricos, como os paradoxos de Curry, de Hooper e de Banach-Tarski. Empregamos os paradoxos de Curry e de Hooper para motivar o estudo de conceitos de Geometria e de Teoria dos Números, tais como área, semelhança de triângulos, o Teorema de Pitágoras, razões trigonométricas no triângulo retângulo, o coeficiente angular da reta e a sequência de Fibonacci, e organizamos atividades lúdicas para a sala de aula no Ensino Fundamental e no Ensino Médio. / We present in this work some logical-mathematical paradoxes, as Galileo's paradox, and also some geometric paradoxes, such as Curry's paradox, Hooper's paradox and the Banach-Tarski paradox. We employ the Curry and Hooper paradoxes to motivate the study of concepts of Geometry and Number Theory, such as area, triangle similarity, Pythagorean Theorem, trigonometric ratios in the right triangle, angular coefficient of the line, and Fibonacci sequence, and we organize recreation activities for the classroom in Elementary and High School.