Abstracts - Earli

Students’ understanding about the dense structure of rational numbersXanthi (Xenia) Vamvakoussi, University of Athens, GreeceStella Vosniadou, University of Athens, GreeceIn this paper we present preliminary results of an empirical study that investigated students’understanding of the dense structure of the rational numbers set, from a conceptual changeperspective. According to the conceptual change approach, students’ initial explanatoryframeworks for number are tied around natural numbers and it is predicted that learning aboutproperties of rational numbers that are different than those of natural numbers will be difficult andaccompanied by misconceptions. One such property is density: While natural numbers are discrete(between two successive natural numbers there is no other natural number), the rational numbersare dense (i.e. between any two non equal rational numbers there are infinitely many rationalnumbers). We hypothesized that students’ responses to tasks related to density would beconstrained a) by the idea of discreteness, and b) by the kind of numbers defining the givenintervals (e.g. natural numbers, decimals, fractions). The participants of the study were 181 7thgraders, 166 9th graders, 202 11th graders and 197 upper secondary school graduates. Weadministered forced choice questionnaires, consisting of 14 items. The results of the study showedthat the idea of discreteness remained strong up to the last grades of the upper secondary schooland also for graduates. We also found that students gave more sophisticated answers in the case ofnatural numbers than in all other cases, and that they showed a strong tendency to answer thatthere are fractions between fractions and decimals between decimals. In addition, some studentsattributed the property of discreteness to fractions, but not to decimals, or vice versa. These resultssupport our hypotheses.Constructing conceptual development scales by using IRT modelsErzsébet Korom, University of Szeged, HungaryGyöngyvér Molnár, University of Szeged, HungaryThis paper presents a study aiming to assess the development of students’ conceptual change in thefield of structure of matter. To put the results into developmental context and to break thecorrespondence between category labels and score levels, the models of Item Response Theory(IRT) were used, which permit items to have any number of categories assigned to the same scorelevel, while the categories are still modeled separately. The aim of the study was to define theability level necessary to abandon the different types of conceptual understanding of simplephysical phenomena (nañve beliefs or partially correct, but qualitatively different misconceptions)and to reach the level of scientific understanding. Samples were drawn form the 8th, 10th and 12thgrades, with ca. 240 students in each cohort. A pencil and paper test was used. The first part of thetest contained 18 items about the features of different states of matter in multiple-choice format.The remaining 35 items used free-response format for students to express their understanding ofthe particle model and to apply their knowledge to explain physical phenomena. Two procedureswere used to quantify the results: (1) responses were scored 0 for not acceptable and 1 foracceptable; (2) in the second part of the test, 4- to 6-point scales were also used. The results showthat students with average ability levels have a high probability (78%) of solving items on thefeatures of the structure of matter in a school-like disciplinary manner. The item difficulty levelsof items that require knowledge application are in the middle or the upper third of the ability scale.Item thresholds indicate the ability level for each of the categories. These change by items withdifferent content and by items with the same content but different task type.– 540 –