LOCAL AND GLOBAL THINKING IN STATISTICAL INFERENCE

David Pratt, Peter Johnston‐Wilder, Janet Ainley, John Mason

Type: Article

Publication Date: 2008-11-29

Citations: 24

DOI: https://doi.org/10.52041/serj.v7i2.472

Abstract

   In this reflective paper, we explore students’ local and global thinking about informal statistical inference through our observations of 10- to 11-year-olds, challenged to infer the unknown configuration of a virtual die, but able to use the die to generate as much data as they felt necessary. We report how they tended to focus on local changes in the frequency or relative frequency as the sample size grew larger. They generally failed to recognise that larger samples provided stability in the aggregated proportions, not apparent when the data were viewed from a local perspective. We draw on Mason’s theory of the Structure of Attention to illuminate our observations, and attempt to reconcile differing notions of local and global thinking. First published November 2008 at Statistics Education Research Journal: Archives  

Locations

Statistics Education Research Journal - View - PDF

Similar Works

Action	Title	Year	Authors
+	Local and Global Thinking in Statistical Inference	2008	David Pratt Peter Johnston‐Wilder Janet Ainley John Mason
+	Student's emerging inferential reasoning about samples and sampling	2011	Theodosia Prodromou
+ PDF Chat	STUDENTS’ EMERGENT ARTICULATIONS OF STATISTICAL MODELS AND MODELING IN MAKING INFORMAL STATISTICAL INFERENCES	2017	Hana Manor Braham Dani Ben‐Zvi
+	EMERGENCE OF REASONING ABOUT SAMPLING AMONG YOUNG STUDENTS IN THE CONTEXT OF INFORMAL INFERENTIAL REASONING	2010	Einat Gil Dani Ben‐Zvi
+ PDF Chat	Statistical investigations in primary school – the role of contextual expectations for data analysis	2021	Daniel Frischemeier Susanne Schnell
+	The Reasoning Behind Informal Statistical Inference	2011	Katie Makar Arthur Bakker Dani Ben‐Zvi
+	Repeated sampling in a digital environment: A remix of data and chance	2019	Marianne van Dijke-Droogers Paul Drijvers Arthur Bakker
+ PDF Chat	THE CO-EMERGENCE OF AGGREGATE AND MODELLING REASONING	2017	Keren Aridor Dani Ben‐Zvi
+	Students’ emerging expressions of uncertainty while making informal statistical inferences about data	2013	Theodosia Prodromou
+	Repeated Sampling as a step towards Informal Statistical Inference	2018	M.J.S. Droogers Arthur Bakker Paul Drijvers
+	The Practice of Statistics	2017	Jane Watson Noleine Fitzallen Jill Fielding-Wells Sandra Madden
+	COMPARING TWO DISTRIBUTIONS: INVESTIGATING SECONDARY TEACHERS' STATISTICAL THINKING	2002	Katie Makar Jere Confrey
+	Children’s emergent inferential reasoning about samples in an inquiry-based environment	2011	Dani Ben‐Zvi Katie Makar Arthur Bakker Keren Aridor
+ PDF Chat	Exploring Connections between Sampling Distributions and Statistical Inference: an Analysis of Students’ Engagement and Thinking in the Context of Instruction Involving Repeated Sampling	2007	Luis Saldanha Patrick W Thompson
+	Learning About Statistical Inference	2017	Katie Makar Andee Rubin
+ PDF Chat	STUDENTS’ EXPRESSIONS OF UNCERTAINTY IN MAKING INFORMAL INFERENCE WHEN ENGAGED IN A STATISTICAL INVESTIGATION USING TINKERPLOTS	2016	Ana Henriques Hélia Oliveira
+	Lessons from Inferentialism for Statistics Education	2011	Arthur Bakker Jan Derry
+	Informal inference – approaches towards statistical inference	2019	Manfred Borovcnik
+	Intricacies of statistical inference and teachers’ understandings of them	2012	Patrick W Thompson Yan Liu Luis Saldanha
+	Students and Teachers’ Knowledge of Sampling and Inference	2011	Anthony Harradine Carmen Batanero Allan J. Rossman

Works That Cite This (23)

Action	Title	Year	Authors
+	Early statistics in kindergarten: analysis of an educator's pedagogical content knowledge in lessons promoting informal inferential reasoning	2022	Soledad Estrella Maritza Méndez-Reina Raimundo Olfos Jocelyn Aguilera
+	Taking an argumentation approach to statistical investigations: developing student data-ing practices	2024	Jill Fielding-Wells
+	Learning to reason from samples: commentary from the perspectives of task design and the emergence of “big data”	2015	Janet Ainley Robert Gould David Pratt
+	Toward <scp>data‐scientific</scp> thinking	2021	Robert Gould
+ PDF Chat	The development of informal statistical inference content knowledge of pre-service primary school teachers during a teacher college intervention	2018	Arjen de Vetten Judith Schoonenboom Ronald Keijzer Bert van Oers
+ PDF Chat	Towards more Accessible Conceptions of Statistical Inference	2011	C. Wild Maxine Pfannkuch Matt Regan Nicholas J. Horton
+ PDF Chat	SAMPLING IN THE WILD: HOW ATTENTION TO VARIATION SUPPORTS MIDDLE SCHOOL STUDENTS’ SAMPLING PRACTICE	2018	Michelle Forsythe
+ PDF Chat	HYPOTHETICAL LEARNING TRAJECTORY ON INFORMAL HYPOTHESIS TESTING IN A PROBABILITY CONTEXT	2023	PER NILSSON
+	Challenges and Opportunities in Experimentation-Based Instruction in Probability	2018	Per Nilsson Andreas Eckert David Pratt
+ PDF Chat	CHALLENGES IN SEEING DATA AS USEFUL EVIDENCE IN MAKING PREDICTIONS ON THE PROBABILITY OF A REAL-WORLD PHENOMENON	2013	Per Nilsson

Works Cited by This (8)

Action	Title	Year	Authors
+	Informal Conceptions of Probability	1989	Clifford Konold
+	Making Sense of the Total of Two Dice	2000	David Pratt
+	Cognitive models and problem spaces in ?purely random? situations	1992	Marie‐Paule Lecoutre
+ PDF Chat	THE ROLE OF CAUSALITY IN THE CO-ORDINATION OF TWO PERSPECTIVES ON DISTRIBUTION WITHIN A VIRTUAL SIMULATION	2006	Theodosia Prodromou David Pratt
+	INFORMAL INFERENTIAL REASONING	2006	Maxine Pfannkuch
+	How do primary school students begin to reason about distributions	2005	Dani Ben‐Zvi
+	Beyond the bar graph: Teaching informal statistical inference in primary school	2007	Katie Makar Andee Rubin
+	LEARNERS' SHIFTING PERCEPTIONS OF RANDOMNESS	2006	Peter Johnston‐Wilder