Comparing Different Uncertainty Measures to Quantify Measurement Uncertainties in High School Science Experiments

Karel Kok; Burkhard Priemer

doi:10.51724/ijpce.v14i1.214

Authors

Karel Kok Humboldt-Universität zu Berlin https://orcid.org/0000-0002-4767-1333
Burkhard Priemer Humboldt-Universität zu Berlin https://orcid.org/0000-0001-5399-7631

DOI:

https://doi.org/10.51724/ijpce.v14i1.214

Keywords:

variance;, science education, measures of spread, simulation

Abstract

Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In this article, we look at alternative uncertainty measures to describe the variation in data sets. A comparison is done in terms of mathematical complexity and statistical quality. The determination of mathematical complexity is based on different mathematics curricula. The statistical quality is determined using a Monte Carlo simulation in which these uncertainty measures are compared to the standard deviation. Results indicate that an increase in complexity goes hand in hand with quality. Additionally, we propose a sequence of these uncertainty measures with increasing mathematical complexity and increasing quality. As such, this work provides a theoretical background to implement uncertainty measures suitable for different educational levels.

Downloads

Download data is not yet available.

Author Biography

Burkhard Priemer, Humboldt-Universität zu Berlin

Department head of the Physics Education Department of the Humboldt University of Berlin.

References

Allie, S., Buffler, A., Campbell, B., & Lubben, F. (1998). First-year physics students’ perceptions of the quality of experimental measurements. International Journal of Science Education, 20, 447–459. https://doi.org/10.1080/0950069980200405

Barlow, R. J. (1993). Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences. John Wiley & Sons.

Brandt, S. (2014). Data Analysis. Springer International Publishing. https://doi.org/10.1007/978-3-319-03762-2

Buffler, A., Allie, S., & Lubben, F. (2001). The development of first year physics students’ ideas about measurement in terms of point and set paradigms. International Journal of Science Education, 23(11), 1137–1156. https://doi.org/10.1080/09500690110039567

Casleton, E., Beyler, A., Genschel, U., & Wilson, A. (2014). A Pilot Study Teaching Metrology in an Introductory Statistics Course. Journal of Statistics Education, 22(3), null. https://doi.org/10.1080/10691898.2014.11889710

Chinn, C. A., & Malhotra, B. A. (2002). Epistemologically Authentic Inquiry in Schools: A Theoretical Framework for Evaluating Inquiry Tasks. Science Education, 86(2), 175–218. https://doi.org/10.1002/sce.10001

Cowan, G. (1998). Statistical Data Analysis. Clarendon Press.

Ford, M. J. (2005). The Game, the Pieces, and the Players: Generative Resources From Two Instructional Portrayals of Experimentation. Journal of the Learning Sciences, 14(4), 449–487. https://doi.org/10.1207/s15327809jls1404_1

Gal, I., Rothschild, K., & Wagner, D. A. (1989). Which Group Is Better? The Development of Statistical Reasoning in Elementary School Children. Proceedings of the Meeting of the Society for Research in Child Development Conference, 9.

Garfield, J., & Ben‐Zvi, D. (2005). A framework for teaching and assessing reasoning about variability. Statistics EducationResearch Journal, 4(1), 92–99. https://doi.org/10.11120/msor.2004.04030058

Garfield, J., & Ben‐Zvi, D. (2007). How Students Learn Statistics Revisited: A Current Review of Research on Teaching and Learning Statistics. International Statistical Review, 75(3), 372–396. https://doi.org/10.1111/j.1751-5823.2007.00029.x

Hellwig, J., Schulz, J., & Priemer, B. (2017). Messunsicherheiten im Unterricht thematisieren—Ausgewählte Beispiele für die Praxis. Praxis Der Naturwissenschaften – Physik in Der Schule, 66(2), 16–22.

Holmes, N. G., Wieman, C. E., & Bonn, D. A. (2015). Teaching critical thinking. Proceedings of the National Academy of Sciences, 112(36), 11199–11204. https://doi.org/10.1073/pnas.1505329112

James, G., Witten, D., Hastie, T., & Tibshirani, R. (2007). An Introduction to Statistical Learning with Applications in R (Vol. 64). https://doi.org/10.1016/j.peva.2007.06.006

Joint Committee for Guides in Metrology. (2008). Evaluation of measurement – guide to the expression of uncertainty in measurement (JCGM 100:2008). Joint Committee for Guides in Metrology.

Kader, G. D. (1999). Means and MADS. Mathematics Teaching in the Middle School, 4(6), 398–403. https://doi.org/10.5951/MTMS.4.6.0398

Kanari, Z., & Millar, R. (2004). Reasoning from data: How students collect and interpret data in science investigations. Journal of Research in Science Teaching, 41(7), 748–769. https://doi.org/10.1002/tea.20020

Kok, K., & Boczianowski, F. (2021). Acoustic Standing Waves: A Battle Between Models. The Physics Teacher, 59(3), 181–184. https://doi.org/10.1119/10.0003659

Kok, K., Priemer, B., Musold, W., & Masnick, A. (2019). Students’ conclusions from measurement data: The more decimal places, the better? Physical Review Physics Education Research, 15(1), 010103. https://doi.org/10.1103/PhysRevPhysEducRes.15.010103

LISUM. (2018). Rahmenlehrplan für die Sekundarstufe I - Mathematik (p. 62). LISUM – Landesinstitut für Schule und Medien Berlin-Brandenburg.

Lubben, F., Campbell, B., Buffler, A., & Allie, S. (2001). Point and set reasoning in practical science measurement by entering university freshmen. Science Education, 85(4), 311–327. https://doi.org/10.1002/sce.1012

Lubben, F., & Millar, R. (1996). Children’s ideas about the reliability of experimental data. International Journal of Science Education, 18(8), 955–968. https://doi.org/10.1080/0950069960180807

Masnick, A. M., & Klahr, D. (2003). Error Matters: An Initial Exploration of Elementary School Children’s Understanding of Experimental Error. Journal of Cognition and Development, 4(1), 67–98. https://doi.org/10.1080/15248372.2003.9669683

Metz, K. E. (2004). Children’s Understanding of Scientific Inquiry: Their Conceptualization of Uncertainty in Investigations of Their Own Design. Cognition and Instruction, 22(2), 219–290. https://doi.org/10.1207/s1532690xci2202_3

Möhrke, P. (2020). Messunsicherheiten im Physikunterricht—Befragung von Lehrkräften in Baden-Württemberg. In S. Habig (Ed.), Naturwissenschaftliche Kompetenzen in der Gesellschaft von morgen (Vol. 46, pp. 876–879). Universität Duisburg-Essen.

Moore, D. S. (1990). Uncertainty. In L. A. Steen & National Research Council (U.S.) (Eds.), On the shoulders of giants: New approaches to numeracy (pp. 95–138). National Academy Press.

Munier, V., Merle, H., & Brehelin, D. (2013). Teaching Scientific Measurement and Uncertainty in Elementary School. International Journal of Science Education, 35(16), 2752–2783. https://doi.org/10.1080/09500693.2011.640360

National Governors Association Center for Best Practices. (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices, Council of Chief State School Officers.

Petrosino, A. J., Lehrer, R., & Schauble, L. (2003). Structuring Error and Experimental Variation as Distribution in the Fourth Grade. Mathematical Thinking and Learning, 5(2–3), 131–156. https://doi.org/10.1080/10986065.2003.9679997

Pols, F., Dekkers, P., & Vries, M. de. (2019). Introducing argumentation in inquiry—A combination of five exemplary activities. Physics Education, 54(5), 055014. https://doi.org/10.1088/1361-6552/ab2ae5

Priemer, B., & Hellwig, J. (2018). Learning About Measurement Uncertainties in Secondary Education: A Model of the Subject Matter. International Journal of Science and Mathematics Education, 16(1), 45–68. https://doi.org/10.1007/s10763-016-9768-0

Séré, M., Journeaux, R., & Larcher, C. (1993). Learning the statistical analysis of measurement errors. International Journal of Science Education, 15(4), 427–438. https://doi.org/10.1080/0950069930150406

Sharma, S. V. (2006). High School Students Interpreting Tables and Graphs: Implications for Research. International Journal of Science and Mathematics Education, 4(2), 241–268. https://doi.org/10.1007/s10763-005-9005-8

Taylor, J. R. (1997). An Introduction to Error Analysis—The Study of Uncertainties in Physical Measurements (2nd ed.). University Science Books.

Torok, R., & Watson, J. (2000). Development of the concept of statistical variation: An exploratory study. Mathematics Education Research Journal, 12(2), 147–169. https://doi.org/10.1007/BF03217081

Zangl, H., & Hoermaier, K. (2017). Educational aspects of uncertainty calculation with software tools. Measurement, 101, 257–264. https://doi.org/10.1016/j.measurement.2015.11.005

Zwaart, P. van der. (2007). Concretisering van de kerndoelen wiskunde: Kerndoelen voor de onderbouw VO. SLO – Nationaal Expertisecentrum Leerplanontwikkeling.