Fifth-grade Students’ Quantitative Modeling in a STEM Investigation

Abstract

Fifth-grade students applied quantitative reasoning in exploring the flow times of three simulated lavas of different viscosities down the slope of a hand-made volcano. After modeling the lava flow times for 6 km down the volcano slope, students used their quantitative models to predict the evacuation times for villagers living 10 km down. Reported are how students structured and represented their data in model creation, how they applied their knowledge of viscosity in identifying variation and covariation displayed in their models, and how they applied quantitative reasoning in making predictions from their models. Students’ quantitative models included graph forms not formally taught at their grade level, including ordered case value, stacked bar, and line graphs. Models comprising ordered case value and line graphs appeared to facilitate students’ detection and interpretation of covariation between lava viscosity and flow time. Although there was some difficulty in explicating a global view of covariation, students could identify the variation in the viscosity and time separately. Linking their knowledge of viscosity with lava flow times suggested at least an implicit understanding of covariation, and illustrated a reciprocal relationship between mathematics and science. In making predictions about evacuation times, students applied both quantitative interpretation and quantitative literacy (Mayes, 2019), together with their understanding of viscosity and their contextual knowledge of volcanoes. Students’ diverse applications of quantitative reasoning were not anticipated, especially since they were not given any particular directions. In expressing the certainty of their predictions, students referred to viscosity and lava flow rates, the dimensions of the volcano, and environmental factors.

Integration of Physics and Mathematics in STEM Education: Use of Modeling

“…In this context, Lo et al [4] also recommended that modeling activities be carried out precisely with students with prior physics and mathematics knowledge. Incorporating data-driven modeling across diverse academic disciplines can amplify mathematical problem solving and investigative capabilities, particularly when applying engineering design principles [5,[30][31][32].…”

“…Similarly, Zhai [28] explores the dynamics of sinking stones within the framework of Newton's laws, offering another example of research that models everyday phenomena. English [31] investigates the flow times of simulated lavas of different viscosities, providing valuable insights for students' reasoning. Borish and colleagues [39] extend this line of inquiry by examining various physical phenomena to model real-world situations.…”

Multidisciplinary Modelling in a Sixth-Grade Tsunami Investigation

“…6) and horizontal bar graphs. Students were familiar with both these representational forms and had applied them independently in a previous investigation (English, 2022).…”

“…Models comprising stacked bar graphs (Fig. 5) were also not common, even though students had independently developed such models in previous investigations (English, 2022). Although stacked bar graphs may be regarded as economical and displaying data trends effectively, they can be challenging for younger students and, when used in mass media, can become ineffective if many variables are displayed on a single bar (Indratmo et al, 2018).…”