How Can an Instructor Best Introduce the Topic of Significant Figures to Students Unfamiliar with the Concept?

Abstract

Students unfamiliar with the concept of significant figures have difficulty making sense of this concept when put in the role of passive note-takers recording lists of rules. The focus of this paper is how best to introduce the concept of significant figures so that students find it meaningful before a stage is reached at which they become turned off. The approach described begins with measurements students are already familiar with from their life experiences and involves the students as active learners. This interaction is accomplished by means of demonstrations involving student volunteers, and question-and-answer exercises using an overhead projector, to measure the length of an object to increasingly greater precision.The implied relative uncertainty concept is presented as a means for determining the number of significant figures in any recorded measurement--a concept that avoids using any list of rules. The meaning of the uncertainty labels on beakers and flasks (often ±5%) and the cumulation of uncertainties are presented briefly; the latter illustrated by the need to read a buret at least twice and the manner in which the associated errors cumulate.

Teaching Significant Figures Using Age Conversions

“…George W. Bush was born on July 6, 1946, which was approximately Julian date 2,432,008. 1 For a class discussion held September 1, 2004 (JD 2,453,250), Mr. Bush would be approximately 21,242 days old or 58.157 years. The instructor could use this value to reveal an increasingly precise age in years (i.e., one more decimal place for each successive calculation) for Mr. Bush to allow students to calculate the age in days with increasing precision as outlined in Table 1.…”

“…Many students will likely learn the rules by rote, but not necessarily understand the rationale and meaning. Some useful approaches have appeared in this Journal to assist students with the uncertainty of measurements and the necessity of significant figures through exercises (1) and activities (2). Herein is an alternative, requiring little preparation and no equipment, that allows students to intuitively discover and discuss the uncertainty of measurements and conversion factors and the necessity of significant figures.…”

A Pilot Study Teaching Metrology in an Introductory Statistics Course

“…If no calibration is specified for the device, it is common practice to assume that the last digit reported is imprecise, i.e., the measurement is reported as plus/minus one in the final digit. This practice accounts for device resolution and operator precision and is borrowed from what is frequently taught in chemistry education (Pacer 2000;Terezakis 2010). In addition, reporting measurements as an interval of plausible values reiterates or alludes to the idea behind confidence intervals.…”

Precision and Accuracy: Knowledge Transformation through Conceptual Learning and Inquiry-Based Practices in Introductory and Advanced Chemistry Laboratories

“…Research has shown that incorporation of scientific practices into a learning environment promotes the development of expert-like thinking in students, and the chemistry laboratory is the ideal place for students to practice and evaluate their own data. Several laboratory exercises have been developed for exploring the correct use of significant figures through length measurements and for understanding experimental errors through density , and mass determination. Nevertheless, many students struggle to explicate experimental errors in their own data.…”