Pensamento estatístico e raciocínio sobre variação: um estudo com professores de matemática - Silva, Claudia Borim da (2007)
Due to student difficulty with understanding standard deviation, this work aimed to identify the reasoning about variation and variability in all parts of the investigation cycle of the statistical thinking. Nine middle and high school Mathematics teachers and two mathematics students of University of São Paulo participated in an action research, 3 hr meetings, lasting in total for 48 hrs. The contents were simple and grouping data frequency distribution, graphics, center and spread measures. The reasoning levels were classified using the general model developed by Garfield (2002). The teachers showed no variaton reasoning during the first week, except for a teacher with idiosyncratic reasoning. During the action research sensibility phase and planning of investigative cycle phase, the teachers developed variability reasoning naturally, but not about variation. However, this experience promoted an upgrade of teachers statistical thinking, that used three (between four) dimensions created by Wild e Pfannkuch (1999). Nevertheless, the statistical thinking upgrade did not implicate a gain in variation reasoning level, observed during the data analysis phase. To compare three discret variable frequency distribution were done using the perception of mode, minimum and maximum values and minimum frequency and use of the distribution chunk with range was organized with existence of the frequency in all groups, understood like verbal until procedural reasoning, respectively. The center measures discussion showed the misconception of mean, which was understood as the mode, and this inhibited necessity perception of a spread measure. The use of correct mean of arithmetic mean induced the teachers use complement measures as the mode and minimum and maximum values, but not the standard deviation. The mean fo standard deviation was predominantely a measure of number of differents observations, signal of homogeneous sample, as many Mathematics textbooks introduced the concept of variation. The comprehension of one standard deviation interval towards mean didn´t develop naturally and the teachers who understood this mean of standard deviation had difficulty to understand what was in the interval, which suposed to develop this integrated reasoning process with the educational softwares created for this intention. In conclusion, the term more variation can cause wastly differing results due to personal interpretation of the phrase ´more variation´ and idiosyncratic reasoning process involved in analysing complex mathematical data: more variation between frequency in only the variable category or variable value in comparing frequency distributions and more variation between sample different observations, both without use of variation from mean