Students' conclusions from measurement data: The more decimal places, the better?

Abstract

In this study with 153 middle school students, we investigate the influence of the number of decimal places from the reading of a measurement device on students' decisions to change or keep an initial hypothesis about falling objects. Participants were divided into three groups, introduced to two experiments - the time it takes a free falling object with a zero, and a nonzero initial horizontal velocity to fall a certain distance - and asked to state a hypothesis that compares the falling times of the two experiments. We asked the participants whether they wanted to change or keep their initial hypothesis after they were provided with data sets. Members of each group were given the same number of measurements but with a different number of decimal places. Results show that for an increase in the number of decimal places, the number of participants switching from a false to a correct hypothesis decreases, and at the same time the number of students switching from a correct to a false hypothesis increases. These results indicate that showing more exact data to students - given through different resolutions of the measurement device - may hinder students' ability to compare data sets and may lead them to incorrect conclusions. We argue that this is due to students' lack of knowledge about measurement uncertainties and the concept of variance.