A Thematic Review on the Combination of Statistical Tools and Measuring Instruments for Analyzing Knowledge and Students’ Achievement in Science

Abstract

To overcome difficulties encountered in the analyses of some factors related to the students’ knowledge and for avoiding expensive or difficult to realize tests, we have combined herein particular features of instruments used for measuring the knowledge and for controlling the quality of the testing, with some statistical tools. Initially we propose to extend the metrics of the standard instruments used for measuring knowledge and testing reliability, as the Rashc model and indexes theory. In this framework, the features of indexes of a certified Concept Inventory test are recognized as responses to specific factors, including latent ones, which affect the overall knowledge state. Specifically, by such a straightforward analysis we estimate the quality of the teaching efficacy in physics, which is not a directly measurable quantity by standard tools. Similarly, some results of the Rash analysis for those certified tests, such as the misfitted occurrences and guessing behavior, are treated as auxiliary indicators of knowledge state and are used for analyzing the cause factors which affect it. Also, the threshold parameter appearing on the polytomous Rasch procedure is considered for evaluating the effort needed to improve the tests’ difficulty perceived by students, and next as a measure of the possible academic achievements and proficiency that can be attained through an appropriate improvement of the learning conditions. This idea is advanced by employing the features of the histograms and distributions of students’ abilities calculated by the Rasch technique. We used for those purposes several certified CI tests in certain groups and circumstances to mimic different initial condition of cause factors, and analyzed similarities and dissimilarities of the outcomes of the Rasch analysis’ seen as the system’s responses. By comparing their results, we achieved a better evidencing of problems on the efficiency of teaching and learning fundamental sciences. Also, the combination of different tools is seen useful to improve the resolution of standard instruments of knowledge measurement. Even though the illustrations of those ideas consist of some particular case -studies, the technique proposed herein is believed to be of a more general nature and can be used for analyses in similar circumstances.