Students’ Emergent Modelling of Statistical Measures – A Case Study

Abstract

The present study investigates the processes of how German middle school students (age 14) interpret, contrast and evaluate different (informal) statistical measures in order to summarise and compare frequency distributions. To trace the developing insights into the properties of these measures, this paper uses the ‘emergent modelling’ perspective: measures are understood as models, which can either be used to make sense of a given situation or to reason about the statistical measures themselves, e.g. in terms of when they can be applied adequately. The emergent modelling approach is used (1) as a theoretical framework for describing students’ conceptual development, and (2) as a design heuristic for developing a teaching-learning arrangement aiming at developing insights about (frequency) distributions and statistical measures. In the qualitative analysis of a design experiment, two students’ emerging contextual and statistical knowledge is identified, revealing the intertwined nature of both types of knowledge. Overall, this paper illustrates the important role the emergent modelling perspective can play for designing as well as describing students’ learning pathways in statistics education.
 First published November 2017 at Statistics Education Research Journal Archives

A Comparative Textbook Analysis on Measures of Center in Selected School Mathematics Textbooks of Australia and Turkey

“…These changes urge us to reconsider curricular learning experiences (Watson, 2017). To gain a fuller picture in the presentation of measures of center in the textbooks, there is a need to extend Cai et al (2002)'s study by considering recent studies in measures of center conducted in educational settings, which gave clues about learning trajectories for teaching measures of center (Bakker et al, 2006;Büscher & Schnell, 2017;Makar, 2014) and other crucial elements in teaching statistical concepts including measures of center such as contextual features (e.g., real, authentic context) (Gal, 1995;Makar, 2014;Watson, 2016), graphical displays (Pfannkuch et al, 2010), and technological tools (Bakker et al, 2006;Watson, 2016). Furthermore, international comparison studies would inform countries by pointing to the ways of developing their current curriculum materials (Watson, 2017).…”

Students’ informal statistical inferences through data modeling with a large multivariate dataset

“…Once students determined the safe level of PM10, considering the mean PM10 values by year and location seemed to make sense to them. Hence, the inferences required by these questions facilitated students' use of average measures in meaningful contexts as seen in other studies aimed at promoting students' informal inferential reasoning (Makar, 2014) and modeling (Büscher & Schnell, 2017; to develop their understandings of statistical concepts. Some of the students also looked at the individual recordings of PM10 levels in the dataset and noted a few anomalies at dangerous levels.…”

“…In this article, we examined how students explored data and drew conclusions from a The use of statistical measures to summarize distribution properties, such as center and variability, and data representations to visualize those properties are found to be useful models for comparing and reasoning about data distributions in the existing literature (Büscher & Schnell, 2017;Doerr et al, 2017;Fielding-Wells, 2018). Within the 'Explore data' phase of the DA cycle in this study, students primarily relied on statistical summaries (particularly averages) to see a trend in the data when exploring whether PM10 levels reached a dangerous level (Q1-'Level of danger') and have been rising over time (Q2-'Rising overtime').…”

“…Over the past three decades, there has been a growing acceptance of statistics as part of mathematics education around the world. Overall, the statistics strand of the school models for making inferences (e.g., Büscher & Schnell, 2017;Doerr, delMas, & Makar, 2017;Fielding-Wells, 2018;Makar & Allmond, 2018) and 2) engaging students in building models of real data using random generating devices available in TinkerPlots to produce outcomes (simulated data) resembling the real data distribution (e.g., Ainley & Pratt, 2017;Aridor & Ben-Zvi, 2018;Patel & Pfannkuch, 2018). The latter approach involves creating models using chance ideas to represent an uncertain phenomenon.…”

“…These concepts and tools become a model for drawing inferences from data. While the existing research (Büscher & Schnell, 2017;Doerr, delMas, & Makar, 2017;Fielding-Wells, 2018;Lehrer & Schauble, 2004;Makar & Allmond, 2018) tended to study young students' data modeling with small samples, further research can provide insights into students' data modeling process through engaging students in working with larger multivariate datasets.…”