The Teaching and Learning of Statistics: International Perspectives

325 Pages·2016·11.777 MB·English

by  Dani Ben-Zvi, Katie Makar (eds.)

Dani Ben-Zvi · Katie Makar Editors
The Teaching
and Learning
of Statistics
International Perspectives
The Teaching and Learning of Statistics

Dani Ben-Zvi (cid:129) Katie Makar
Editors
The Teaching and Learning
of Statistics
International Perspectives
Editors Katie Makar
Dani Ben-Zvi School of Education
Faculty of Education The University of Queensland
The University of Haifa St Lucia , QLD , Australia
Haifa , Israel
ISBN 978-3-319-23469-4 ISBN 978-3-319-23470-0 (eBook)
DOI 10.1007/978-3-319-23470-0
Library of Congress Control Number: 2015958808
Springer Cham Heidelberg New York Dordrecht London
© Springer International Publishing Switzerland 2016
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Contents
1 International Perspectives on the Teaching
and Learning of Statistics ....................................................................... 1
Dani Ben-Zvi and Katie Makar
Part I Integrating the Contextual and the Statistical Worlds
2 Young Students’ Mental Modelling of Statistical Situations............... 13
Andreas Eichler and Markus Vogel
3 Children’s Wonder How to Wander Between Data and Context ....... 25
Dani Ben-Zvi and Keren Aridor-Berger
4 Supporting Students to Develop Concepts Underlying Sampling
and to Shuttle Between Contextual and Statistical Spheres ............... 37
Adri Dierdorp , Arthur Bakker , Jan van Maanen , and Harrie Eijkelhof
Part II Learning Statistics at the School Level
5 The Language of Shape .......................................................................... 51
Pip Arnold and Maxine Pfannkuch
6 Development of an Understanding of a Sampling Distribution .......... 63
Eun-Sung Ko
7 Korean High School Students’ Understanding of the Concept
of Correlation .......................................................................................... 71
A-Ra No , Soo-Yun Han , and Yun Joo Yoo
8 Connections Between Statistical Thinking and Critical
Thinking: A Case Study ......................................................................... 83
Einav Aizikovitsh-Udi , Sebastian Kuntze , and David Clarke
v
vi Contents
9 Tasks Associated to the Treatment of Tables
at Elementary School and Its Level of Diffi culty ................................. 95
Soledad Estrella , Arturo Mena-Lorca , and Raimundo Olfos
10 An Analysis of the Statistical Contents Covered In China,
Singapore and Taiwan Mathematics Textbooks
at the Primary Level ............................................................................... 97
Hak Ping Tam and OU Yung Chih
11 Mathematical Modelling for Critical Statistics Education ................. 99
Luana Oliveira Sampaio and Maria Lucia Lorenzetti Wodewotzki
12 Survey and Research on the Levels of High School
Students’ Critical Evaluation of Statistical Information
and the Infl uence Factors ....................................................................... 101
Ma Ping
13 The Conceptual Understanding of Variability
in the Data Distributions ........................................................................ 117
Eun-Jeung Ji and Won Kyoung Kim
14 Students’ Misconceptions and Mistakes Related
to Measurement in Statistical Investigation
and Graphical Representation of Data ................................................. 119
Hyung Ju Yun , Eun-Sung Ko , and Yun Joo Yoo
15 Overall Understanding of the Middle School Mathematics
Course in Teaching Statistics Main Line .............................................. 121
Guan Jian , Bai Xue , Wu Peng , and Li Qiusheng
16 Growth on Fourth-Grade Students’ Mathematical
Understanding of Average ...................................................................... 123
Jun Wu
17 Exploring Dot Plot in the Perspective of Embodied Cognition .......... 125
Verônica Yumi Kataoka , Irene Cazorla , Eurivalda Santana ,
and Claudia Borim da Silva
Part III Learning Statistics at the Tertiary Level
18 Students’ Diffi culties in Understanding of Confi dence Intervals ....... 129
Ana Henriques
19 A Modeling and Simulation Approach to Informal Inference:
Successes and Challenges ....................................................................... 139
Jennifer Noll , Mulugeta Gebresenbet , and Erin Demorest Glover
20 Students’ Understanding of Statistical Terms Having
Lexical Ambiguity ................................................................................... 151
Soyeon Jung and Jihyun Hwang
Contents vii
21 Student Understanding of Symbols in Introductory
Statistics Courses .................................................................................... 163
Hyung Won Kim , Tim Fukawa-Connelly , and Samuel A. Cook
22 Two-Year College Mathematics Instructors’
Conceptions of Variation ........................................................................ 175
Monica Dabos
23 Students’ Sense-Making of Graphical Representation
in a Basic Statistics Module .................................................................... 177
Hui Teng Chia
Part IV Technology in Statistics Education
24 Bootstrapping Confi dence Intervals ...................................................... 181
Ross Parsonage , Maxine Pfannkuch , Chris J. Wild , and Kate Aloisio
25 Undergraduate Students’ Conceptions of Variability
in a Dynamic Computer-Based Environment ...................................... 193
George Ekol and Nathalie Sinclair
26 Transforming Statistics Education Through ICT Application ........... 205
Tae Rim Lee
27 Selecting Technology to Promote Learning in an Online
Introductory Statistics Course ............................................................... 215
Megan Mocko
28 The Role of Technology in Indian Statistics Education:
A Review .................................................................................................. 227
D. S. Hooda and B. K. Hooda
29 Building Up the Box Plot as a Tool for Representing
and Structuring Data Distributions: An Instructional Effort
Using Tinkerplots and Evidence of Students’ Reasoning ..................... 235
Luis Saldanha and Michael McAllister
Part V Statistics Teachers and Teaching
30 Integrated Reasoning About Statistical Variation: Secondary
Teachers’ Development of Foundational Understandings .................. 249
Susan A. Peters and Ksenia S. Kopeikin
31 Preservice Teachers’ Diffi culties with Statistical Writing ................... 261
Min-Sun Park , Mimi Park , Eun-Jung Lee , and Kyeong-Hwa Lee
32 Teachers’ Questions in the Statistics Class ........................................... 271
Lucia Zapata-Cardona and Pedro Rocha-Salamanca
viii Contents
33 Statistical Training of Pre-service Teachers
with Application in School Practice ...................................................... 279
Miriam Utsumi , Irene Cazorla , and Verônica Yumi Kataoka
34 Statistics in Primary Education in Greece: How Ready
Are Primary Teachers? ........................................................................... 289
Eugenia Koleza and Aristoula Kontogianni
35 Developing Statistical Literacy (DSL): Student Learning
and Teacher Education ........................................................................... 299
Hélia Oliveira , Ana Henriques , and João Pedro da Ponte
36 Teacher Capacity as a Key Element of National
Curriculum Reform in Statistical Thinking: A Comparative
Study Between Australia and China ..................................................... 301
Qinqiong Zhang and Max Stephens
37 A Framework for Assessing Statistical Knowledge
for Teaching Based on the Identifi cation of Conceptions
of Variability Held by Teachers ............................................................. 315
Orlando González
38 An Investigation into the Statistics Education of Preservice
Mathematics Teachers in an Irish University ....................................... 327
Olivia Fitzmaurice , Ailish Hannigan , and Aisling Mary Leavy
Index ................................................................................................................. 329
Chapter 1
International Perspectives on the Teaching
and Learning of Statistics
Dani Ben-Zvi and Katie Makar
“Statistics is a general intellectual method that applies
wherever data, variation, and chance appear. It is a
fundamental method because data, variation, and chance are
omnipresent in modern life”
(Moore, 1 998 , p. 134).
1.1 Introduction
Being able to provide sound evidence-based arguments and critically evaluate data-
based claims are important skills that all citizens should have. It is not surprising
therefore that the study of statistics worldwide at all educational levels is gaining
more attention. The study of statistics provides students with tools, ideas and dispo-
sitions to react intelligently to information in the world around them. Refl ecting this
need to improve students’ ability to think statistically, statistical literacy and reason-
ing are becoming part of the mainstream school and university curricula in many
countries. As a consequence, statistics education is becoming a thriving fi eld of
research and curricular development. This book refl ects this trend by introducing
cutting edge research in statistics education done by scholars from twenty different
countries across six continents. The studies in this book introduce and empirically
tackle unique challenges—challenges that students face as they learn statistics, that
teachers face as they teach students to understand and reason about data, and other
important theoretical and techno-pedagogical challenges.
D. Ben-Zvi (*)
Faculty of Education , The University of Haifa , Haifa , Israel
e-mail: [email protected]
K. Makar
School of Education , The University of Queensland , St. Lucia , QLD , Australia
e-mail: [email protected]
© Springer International Publishing Switzerland 2016 1
D. Ben-Zvi, K. Makar (eds.), The Teaching and Learning of Statistics,
DOI 10.1007/978-3-319-23470-0_1