This study is concerned with how children interpret the slope of a line graph. Today with the vast accumulations of data which are available from computers, people are being faced with an ever increasing amount of pictorial representation of this data. Therefore it is of the utmost importance that children understand pictorial representation. Yet in spite of the popularity of graphs as tools of communication, studies show that many adults experience difficulty in reading information presented in a graphical form. The slope of the graph was chosen for this investigation because it is in this aspect of graphing (as shown by the results of the 1981 B.C. Assessment) that children in British Columbia seem to have the greatest difficulty when they reach Grade 8. The study dealt with positive, negative, zero and infinite slopes, combinations of these slopes, curvilinear graphs and qualitative graphs, that is, graphs that have no numerical data shown on the axes. The researcher chose to use a structured individual interview as a means of collecting data about how the students interpreted the slope of a line graph. Graphs used in the interviews dealt with temperature, height, weight and distance. Twenty-two students were chosen for this study. The students were found to have problems mainly with graphs dealing with distance related to time. This problem may be due to the fact that many students read only one axis and when interpreting distance seem to include direction as an added dimension of the graph. Infinite slope graphs were misinterpreted by every student, which may be due to the fact that they ignore the time axis. In general students used two methods of interpreting graphs. In some cases they observed the direction of the graph from left to right, that is, whether the slope went up or down from left to right. In other cases they examined the end points on the graph and drew their conclusions from them. The choice of method varied with the contextual material shown on the graph, which may be due to the children's concept of the parameter in the physical world and whether they see the parameter as being able to increase and decrease over time. From the study the investigator feels that more discussion of graphing by teachers and students is needed if the misconceptions are to be cleared up. Discussion of the parameters of both axes by teachers might help clear up the misconceptions students have about distance travelled over a period of time when this is expressed as a graph. There would be less chance of a graph being read as a map if the relationships between the two axes were demonstrated to students. Teachers also need to be aware of both methods used by students in interpreting graphs. / Education, Faculty of / Graduate

O presente trabalho tem por objetivo divulgar e explorar as Provas sem Palavras no âmbito do Ensino Fundamental e Médio para, posteriormente, servir de possível material de consulta por parte de professores, na busca de melhores métodos de explicação sobre importantes assuntos desenvolvidos em sala. Dessa forma, imagina-se que a compreensão dos alunos através da visualização fortalecerá de maneira significativa a aquisição do conhecimento. Para tanto, são sugeridos diversos temas onde a visualização é desenvolvida e explicada, seja através de relato, seja através de demonstrações matemáticas. / The aim of the present work is to disseminate and explore the Proof Without Words in the scope of elementary and high school to be used later as a possible reference material for teachers in the search for better methods of explanation on important subjects developed in the classroom. In this way, it is imagined that students’ comprehension through visualization will significantly strengthen the acquisition of knowledge. In order to do so, several themes are suggested where the visualization is developed and explained, either through storytelling or through mathematical demonstrations.