Versatile thinking and the learning of statistical concepts

Abstract

Statistics was for a long time a domain where calculation dominated to the detriment of statistical thinking. In recent years, the latter concept has come much more to the fore, and is now being both researched and promoted in school and tertiary courses. In this study, we consider the application of the concept of flexible or versatile thinking to statistical inference, as a key attribute of statistical thinking. Whilst this versatility comprises process/object, visuo/analytic and representational versatility, we concentrate here on the last aspect, which includes the ability to work within a representation system (or semiotic register) and to transform seamlessly between the systems for given concepts, as well as to engage in procedural and conceptual interactions with specific representations. To exemplify the theoretical ideas, we consider two examples based on the concepts of relative comparison and sampling variability as cases where representational versatility may be crucial to understanding. We outline the qualitative thinking involved in representations of relative density and sample and population distributions, including mathematical models and their precursor, diagrammatic forms.

Flexible and adaptive use of strategies and representations in mathematics education

“…Graham, Pfannkuch and Thomas (2009) address the ability of ''representational versatility'', which encompasses in particular the ability to transform seamlessly between systems of given concepts, as well as to engage in procedural and conceptual interactions with specific representations. They exemplify their theoretical considerations with the aid of an illustrative example of statistical inference.…”

Markov Processes: Exploring the Use of Dynamic Visualizations to Enhance Student Understanding

“…process/object versatility-the ability to switch at will in any given representational system between a perception of a mathematical entity as a process or an object (e.g., the limiting distribution can be viewed as an object or a long-run process that stabilizes to a distribution); visuo/analytic versatility-the ability to exploit the power of visual schemas by linking them to relevant logico/analytic schemas (e.g., linking the visual representation of the equilibrium distribution to an algebraic analysis); representational versatility-the ability to work seamlessly within and between representations (e.g., transition diagrams and matrices) and to engage in procedural and conceptual interactions with representations (e.g., calculating the equilibrium distribution and conceiving it as a conceptual entity with its own properties). Furthermore, Graham, Pfannkuch, and Thomas (2009) demonstrated how the development of concepts in statistics could arise using technology-linked representations while Pfannkuch, Budgett, and Thomas (2014) provided indirect evidence that technology designed for learning inferential concepts through linking representations seemed to promote concept formation. Representations can also be expressed in words and therefore changing a word representation into a state diagram is also an example of linking representations.…”

Perspectives on the use of the Fraction Strips application in teaching fractions

“…en entornos flexibles estimulan los procesos cognitivos (Hwang et al, 2019;Heinze et al, 2009;Terwel et al, 2009). Es decir, los entornos de aprendizaje que presentan múltiples representaciones de un concepto son más eficaces para lograr que el estudiante desarrolle una comprensión conceptual auténtica de las nociones matemáticas (Graham et al, 2009).…”