Developing Knowledge for Teaching Graphing of Bivariate Categorical Data

Casey, Stephanie; Albert, Jim; Ross, Andrew M.

doi:10.1080/10691898.2018.1540915

Cited by 5 publications

(3 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4. Such a graph may be regarded as more compact than the other two forms and can facilitate comparison of the lava types' duration of flow (Casey et al, 2019), but can also be more difficult to interpret because of the number of variables indicated on a single bar.…”

Section: Q1 Students' Data Structuring and Representationsmentioning

confidence: 99%

Fifth-grade Students’ Quantitative Modeling in a STEM Investigation

English

2022

Journal for STEM Educ Res

View full text Add to dashboard Cite

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.

show abstract

Section: Q1 Students' Data Structuring and Representationsmentioning

confidence: 99%

Fifth-grade Students’ Quantitative Modeling in a STEM Investigation

English

2022

Journal for STEM Educ Res

View full text Add to dashboard Cite

show abstract

“…5). Although such graphs could be considered a more economical representational form and can facilitate a comparison of the inundation distances across the slopes (Casey et al, 2019), they can also be more difficult to construct and interpret.…”

Section: Research Question 2: the Nature Of Students' Multidisciplina...mentioning

confidence: 99%

Multidisciplinary Modelling in a Sixth-Grade Tsunami Investigation

English

2022

Int J of Sci and Math Educ

View full text Add to dashboard Cite

This study investigated sixth-grade students’ development of multidisciplinary models involving the integration of mathematics, science, and statistics, together with shared STEM practices. Mathematics and science featured a reciprocal relationship within the real-world context of tsunami inundation. Experimenting with water tubs comprising “landmasses” and “shore slopes” of varying angles, students explored how varying the slope of the shoreline affects the inundation distance. Given that organising and structuring data are essential to the creation of models as systems of representation, students’ modelling revealed a basic understanding of key statistical concepts and processes, including variation and covariation, and an ability to identify trends both within and across data sets. Students were able to apply their learning in recommending ways of minimising the impact of a real-world tsunami, demonstrating how such an investigation can facilitate understanding of natural phenomena. The overall findings indicate how elementary-grade students can successfully engage in independent multidisciplinary modelling within integrated STEM investigations and develop important conceptual understandings in the process.

show abstract

“…Few subsequent studies included or focused on bivariate categorical data using representations beyond contingency tables. Casey, Albert, and Ross (2018) investigated future and practicing teachers' knowledge for teaching the graphing of bivariate categorical data. They used novel curriculum materials that included representations of bar charts with relative frequencies and mosaic plots.…”

Section: Background and Motivationmentioning

confidence: 99%

A Case Study: Zander Reasons With Incomplete Contingency Tables and Mosaic Plots

Johnson¹,

Franklin²

2022

Bridging the Gap: Empowering and Educating Today’s Learners in Statistics. Proceedings of the Eleventh International Conference

View full text Add to dashboard Cite

Reasoning across multiple representations and incorporating reversibility can enhance and reveal an in-depth view of a student’s understanding. In this paper, we explore how a school-age student reasons about the independence of two categorical variables using contingency tables and mosaic plots. This case study reveals some fine-grained reasoning that highlights the differences between mathematical and statistical thinking, shows an inclination to use a part-part or odds approach, and demonstrates how a mosaic plot was used to solve a problem with incomplete contingency. Ultimately, this study supports the use of incomplete contingency tables and mosaic plots for students to reason about statistical independence.

show abstract

Developing Knowledge for Teaching Graphing of Bivariate Categorical Data

Cited by 5 publications

References 16 publications

Fifth-grade Students’ Quantitative Modeling in a STEM Investigation

Fifth-grade Students’ Quantitative Modeling in a STEM Investigation

Multidisciplinary Modelling in a Sixth-Grade Tsunami Investigation

A Case Study: Zander Reasons With Incomplete Contingency Tables and Mosaic Plots

Contact Info

Product

Resources

About