# Why Teach Measurement and Uncertainty?

### Distinguishing Scientific Phenomena from Measurement Uncertainty

Most physical science instructors have had the frustrating experience of having measurement uncertainty obscure the results of student lab activities. For example, students measure the free fall acceleration of an object and find that it is not equal to 9.8 meters per second squared. Is this due to air friction? Or is the measured value not correct? Or, maybe students conclude, that not all objects accelerate the same way. Measurement uncertainty can obscure underlying science concepts that we are trying to teach students.

If you have experienced this, you are not alone. In his study "Understanding how to deal with experimental uncertainty: a 'missing link' in our model of scientific reasoning?", Robin Millar of the Department of Educational Studies, University of York, UK examined how measurement uncertainty affects students' ability to reach conclusions about which variables affect the behavior of a physical system like a pendulum. This study provides evidence that student misconceptions about measurement uncertainty can make it more difficult to understand the results of experiments meant to help develop conceptual understanding. He suggests that improving students' understanding of measurement uncertainty will improve their ability to see and understand scientific relationships and patterns. In fact, Millar concluded that "for many students, dealing with the presence of experimental uncertainty is a greater challenge than logical reasoning about variables and control" (Millar 2004).

The materials presented here are intended to provide a foundation for understanding measurement technique that will allow students to identify artifacts of their measurements and distinguish them from underlying concepts. In addition, the materials here show how to integrate these concepts into lab activities.

### The Uncertainty Approach vs Significant Figures

A second reason to incorporate uncertainty into measurement technique is that one obstacle to student understanding of measurement uncertainty could be the methods traditionally used to teach measurement and uncertainty. There are two methods to describe measurement uncertainty: the use of *significant figures to imply uncertainty*, and the method of *explicitly describing the uncertainty of a measured value*. Using significant figures to imply uncertainty, readers are meant to understand that a number written like 15.5 implies a range of possible values between 15.45 and 15.55. But when expressing uncertainty explicitly, we'd write this measurement as 15.5 ±0.05, making the range of possible values clear.

Most introductory science courses and texts (Holt 2008, Glenco 2007, Halliday 2004) use *significant figures* to describe uncertainty. But most advanced college courses and professional researchers (ISO GUM, NIST Guide) use the method of explicitly stating the uncertainty of a measurement rather than using significant figures to imply uncertainty. The material presented in this module is conceptually consistent with the methods of the NIST and ISO methods.

A group of researchers (Allie et al, 2003) have compared the results of teaching students the traditional approach to measurement with the measurement techniques described in the ISO Guide to Measurement (ISO GUM) (Allie et al, 2003). They found that students who had been taught with the traditional method could perform calculations using traditional methods, but had difficulty understanding what these results meant. Specifically, students had difficulty understanding that their measurement results represent a range of possible values and that this is an inevitable result of all measurement. This group went on to produce excellent materials for teaching college students effective measurement techniques consistent with the ISO GUM (*Introduction to Measurement in the Physics Laboratory. A Probabilistic Approach )*. However, this material might be too in-depth for younger students or non-science majors in college courses.

Materials presented in here are intended to expand this approach for students from 9^{th} grade to introductory college level, and to show instructors how to integrate these ideas into existing lab activities.

### Building Scientific Literacy

A final reason to adopt the methods presented in this module is that understanding effective measurement technique is an element of scientific literacy. The Benchmarks for Science Literacy, by American Association for the Advancement of Science, "are statements of what all students should know or be able to do in science, mathematics, and technology by the end of grades 2, 5, 8, and 12." Chapter 9 describes, in part, what students should know about measurement and uncertainty, including the ideas that all measurements are subject to uncertainty, and how to express the uncertainty of calculated results (2001 AAAS benchmarks, Ch 9).

The Intergovernmental Panel on Climate Change Synthesis Report (more info) and Summary for Policymakers (pdf file) are examples of how scientists communicate results to be used by non-scientists. As a matter of scientific literacy, readers of this report must be fluent in the concepts of measurement uncertainty. Data and calculation results presented in the report include uncertainties. The reader's ability to understand uncertainty is critical to being able to interpret and use these results to inform decisions. The fact that there is so much discussion of uncertainty should increase, not decrease, the confidence level in the science in the report.

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