Teaching Descriptive Statistics using JSXGraph in STACK

Santiago Maria Borio Peñaloza, David Stern, Danny Parsons, Chiara Facciolà (IDEMS International), James Musyoka (Maseno University) and Christine Laetitia (INNODEMS)

Abstract

Over the last few years IDEMS (Innovations in Development, Education and the Mathematical Sciences) International has delivered and provided support for several descriptive statistics courses involving online assessment, including: Descriptive Statistics at Maseno University in Kenya, and Statistical Problem Solving at AIMS Cameroon. The design of questions for these courses was informed by the CAST (Computer-Assisted Statistics Textbooks) project (Stirling, 2010) and focused on analytical and dynamic activities centred around carefully generated data to promote higher order learning. While some of the courses include CAST activities, due to changing technologies these have become less accessible, which has led to a search for alternative delivery mechanisms to extend the access to the impactful CAST exercises (Manyalla, Mbasu, Stern, & Stern, 2014). One such alternative was the JSXGraph integration within STACK (System for Teaching and Assessment using a Computer algebra Kernel), which offers the possibility of generating meaningful data through STACK’s underlying computer algebra system Maxima, displaying it through JSXGraph, and assessing answers and providing feedback through STACK. The reimagining of the CAST questions in this way also enables local contextualisation, easier sharing as open educational resources and the potential for further customisation adapted to other contexts.

This presentation outlines the structures built to enable the development of such questions, illustrating with examples, starting from the creation of statistical diagrams in JSXGraph and its implementation in STACK, using Maxima within STACK to generate data from statistical distributions and feeding it into JSXGraph, and evaluate them using STACK. It will distinguish between questions that assess understanding by extracting information from graphs and answering questions about these, and dynamic questions in which the accurate manipulation of JSXGraph objects is required and assessing the state of graphs after such manipulation. It will also outline how JSXGraph interacts with computer algebra systems, such as maxima within STACK, and argue that there is potential for further growth of JSXGraphs by integrating elements of the Grammar of Graphics ideas developed in (Wilkinson, 1999) and popularised by Hadley Wickham through the well-known GGPlot2 R-Package (Wickham, 2010).

The presentation will build on efforts to rethink statistics education (Cobb, 2015) (Stern, et al., 2020) and outline the contexts in which courses are delivered. It will also describe how the same ideas can be applied to courses from secondary school level to postgraduate or professional contexts. Two types of questions have been distinguished: analysing graphs to make inferences and applying statistical concepts to complete graphs. These assess two distinct sets of skills and provide opportunities to develop higher order understanding of statistical concepts. The materials produced, as well as any future content developed, will be published under an Open Educational Resources license and could be shared for integration by other interested education providers, and the presentation will open up the potential for future collaborations with IDEMS to further expand the current question bank and suggest mechanisms for integration of these to other courses.

References

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