How to tell about errors not boringly: methodological analysis of expounding the basis of data processing

Abstract

The authors continue to report about results they have obtained in the process of creating a special introductory one-semester Laboratory Physics course «Search for Physics laws». It is known that the teaching experience and the results of the performed tests show that most students do not acquire the basic skills for conducting an experimental research. This course was built on the basis of the algorithm of systematic construction of students’ skills for carrying out an experimental research. The authors have used Galperin’s stepwise teaching procedure which was developed on the assumption that learning any kind of knowledge involves different kinds of actions. The authors have analysed different ways of how to expound the basic ideas of data analysis, and shown their connection with the point, syncretic and training-interval paradigms. Action diagrams are provided for each type of expounding. As an example of using the training-interval paradigm for teaching first-year students of a technical university, a specially designed lab session is presented in the article. The topic of the session is “The concept of a confidence interval”. Laboratory Work 1 “The Buffon-de Morgan Experiment”. This lab session meets several important requirements: a) the number of computations is minimised; b) a directly measurable quantity is considered; c) students are provided with a “fulcrum” in the form of a priori known true value of a quantity. A general view on measuring physics quantities is summarised in four quite unexpected for students “unpleasant axioms”: 1) none of measured values coincides with the true value of a quantity; 2) the mean of measured values does not coincide with the true value of a quantity; 3) even if, by a lucky chance, one of measured values or the mean coincided with the true value of a quantity, we would never know about it; 4) a confidence interval catches the true value of a measured quantity only in 68% of cases. The authors claim that the presented lab lesson allows demonstrating the equity of these “axioms” clearly and vividly, and that the organised laboratory sessions in the new way are significantly more successful in improving students’ basic skills of error analysis than traditional laboratory sessions.

Keywords

• laboratory work
• physics practical course
• confidence interval
• training-interval paradigm
• syncretic paradigm
• point paradigm.