Measurement, Uncertainty, and Significant Figures 

One of the presentations I gave this summer was at the Massachusetts Association of Vocational Administrators using my vocabulary sort as a framework to talk about Modeling InstructionTM. Because the presentation was a chemistry lesson, a woodworking teacher asked for concrete ways the pedagogy could be adapted for a vocational classroom. I turned the question back to him and asked “what topic do you consistently teach that your students still struggle with?” All the teachers in the room: woodworking, plumbing, child care, cosmetology, electric, all responded in a resounding voice “measurement.” 

As high school teachers, we know that understanding how measurement works is crucial for lab skills and for understanding significant figures. We think measurement should be an easy topic for students to learn; especially because we know that teachers begin working with students in elementary school to teach these skills. However, I, and many other teachers, have spent countless hours teaching and reteaching a seemingly simple skill.

This year I tried something different. As I had done in the past, I had students fill out a worksheet where they recorded measurements of various scale readings (see figure 1).

Figure 1: Unit 1 Worksheet 2, Scale Reading¹ (Modeling Instruction^TM, American Modeling Teachers Association)

Instead of collecting the work to correct outside of class or reviewing the correct answers as a class, I had the students write the answers on the blackboard.  After the students put their answers up on the board, we went through the problems together and tried to determine which answers made the most sense.

For the first problem, student answers included 9, 8 15/16, 8.9, 8.95 etc. At first we agreed  that the answer could not be nine because the arrow was clearly before the nine. After we agreed on that, I erased all the answers that began with a nine. Then we discussed what system of measurement we should use; whether the imperial system or the metric system.  Looking at all the measurements, students determined that as a class we needed to use the metric system, so we erased anything that was based in inches. 

But how did we know what the “right” measurement was? As a class, we looked at the measurements and tried to determine what the next digit was. Students agreed that it was after a decimal point and discussed what answers were reasonable. They agreed that 8.8 was reasonable as was 8.9. But if we didn’t know for sure what the number was in the tenths place, how could the number in the hundredths place mean anything?

After this activity, the students gained a better understanding of measurement. But would it stick with actual lab data? The next day, I set up a variety of pieces of lab equipment and had students write down their measurements on small whiteboards. When they finished, they could look at the measurements and see what the similarities and differences were (see figure 2). 

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 Figure 2: Students completing measurements

Though students still made a few errors, there was a better sense of how to measure and how to use that skill in and out of the lab.

Having a strong introduction to measurement, the next step in the bigger conversation about significant figures went much easier than in past years. If we can measure to a level of uncertainty, then we can apply the concepts to the calculations instead of just memorizing a set of rules. 

Reference

1. Unit 1 Worksheet 2: Read Scales. American Modeling Teachers Association, 2013.