Dificuldades encontradas por discentes da educação básica na construção e interpretação de gráficos de barras, setores e box-plot

Abstract

The work aims to investigate the difficulties encountered by basic education students in the construction and interpretation of bar, sector and box-plot graphs in a high school class regarding the reading, interpretation and construction of sector and box-plot graphs.The research is qualitative in nature and, to collect data, we developed and applied a sequence of activities with a high school class from a state school in Alagoas, in which the students had to calculate their Body Mass Index (BMI). The class was divided into four groups with a total of 29 students, in which they shared their weight and height data. Based on this information, they calculated measures of central tendency, such as arithmetic mean, mode and median. They also calculated the first, second and third quartiles. At the end of the activity, the students produced bar graphs, pie charts and box-plots. This process allowed them to understand, in practice, fundamental statistical concepts. However, we found that, although pie charts are the most well-known, students do not associate the percentage of the parts with the correct measurement of the angle, and are somewhat easy to read and interpret, but have many difficulties in constructing them. Specifically, we observed that students were able to identify the proportions represented in pie charts, but faced challenges when trying to construct these charts from raw data, especially with regard to converting percentages into angles. This suggests a gap in understanding the relationship between the part and the whole, as well as in the practical application of basic mathematical concepts, such as the rule of three, to construct the charts. On the other hand, in situations that addressed the box-plot, possibly because it is not a common chart for the group, students demonstrated greater care with the scales and calculation of the measurements. The box-plot, by its nature, requires a more detailed understanding of the measures of dispersion, such as quartiles and outliers, which seems to have encouraged students to pay more attention to the mathematical details involved. Despite being a less familiar graph, the students' careful approach suggests that the complexity of the box-plot may have served as a motivator for a more rigorous analysis of the data. In addition, the hands-on activity of calculating BMI and working with real data from the students themselves appears to have increased the group's engagement and motivation. Contextualizing statistical concepts with an everyday application, such as health and the human body, facilitated the understanding of abstract concepts. However, we observed that some students still had difficulty interpreting measures of dispersion, such as the interquartile range, and relating these measures to the graphical representation in the box-plot. In summary, the research showed that, although students demonstrated progress in understanding basic statistical concepts, such as measures of central tendency and reading graphs, there are still significant challenges in constructing and interpreting more complex graphs, such as the box- plot, and in the practical application of mathematical concepts to construct pie charts. This reinforces the need for pedagogical approaches that integrate theory and practice more consistently, as well as emphasizing the importance of contextualized activities that promote statistical literacy in a meaningful way for students.