Invited Talks

Topic 3 : Education and development of staff who teach statistics

Statistics teaching demands sound statistical understanding and a sense of current student understanding of any curriculum elements. These must be complemented not only with a personal understanding of the content, but some sense of the processes by which students acquire the material, and some sensitivity to common stumbling blocks to progress. As statistics education evolves towards sustainable modes of enabling learners at all ages to tackle these challenges and make appropriate use of statistical tools and technology, the importance of preparing an incoming generation of teachers, both school and tertiary, and supporting an existing teacher cohort require our commitment and innovation.

Session 3A: Statistics instructors’ content knowledge

3A1: Developing pre-service teachers’ technological pedagogical content knowledge (TPACK) of sampling

Maria Meletiou-Mavrotheris   European University Cyprus, Cyprus
Efi Paparistodemou   Ministry of Education, Cyprus
Irene Kleanthous   Cyprus Ministry of Education, Cyprus

This research sought to explore and improve pre-service primary school teachers’ statistical knowledge for teaching informal ideas related to samples and sampling through the conduct of a two-phase exploratory study. In Phase I, a randomly selected sample of n=42 teacher candidates completed an open-ended questionnaire designed to assess their reasoning about sampling concepts and their understanding of student thinking in this area. Insights gained informed the design and implementation of a teaching experiment within an undergraduate mathematics methods course, which aimed at enhancing the participating primary school teachers’ (n=8) technological pedagogical content knowledge (TPACK) of sampling. Findings from Phase II indicate a positive impact on participants’ TPACK of sampling and other key ideas related to informal inferential statistics.


3A2: Analysis of teachers’ understanding of variation in the dot-boxplot context

Cláudia Borim da Silva   University of São Judas, Brazil
Verônica Yumi Kataoka   State University of Santa Cruz, Brazil
Irene Cazorla   State University of Santa Cruz, Brazil

This study examined how dotplots and boxplots helped 23 secondary school mathematics teachers engaged in didactic activity to develop reasoning about variation. Teachers described height and head circumference by using data arranged in a dotplot and in a dot-boxplot. Their reasoning about variation was explored further with these dotplots and dot-boxplot, with a task displaying data from samples in simple boxplots, and with a task displaying data in a stacked boxplot. Teachers used mode, minimum and maximum values, and central intervals of values to describe the distributions and used nonstandard terminology such as clustering, spread out, majority, and trend in their reasoning after using dotplots. Teachers struggled to represent quartiles on a dotplot, but their reasoning about variation improved by using boxplots.


3A3: Beyond calculations: fostering conceptual understanding in statistics graduate teaching assistants

Jennifer L Green   Montana State University, United States
Erin E Blankenship   University of Nebraska-Lincoln, United States

Incoming statistics graduate students who are expected to teach introductory statistics as part of their assistantships are very prepared to teach the procedural portions of the course. However, they are less comfortable with the statistical thinking/reasoning aspects of the course. To better prepare novice teaching assistants (TAs), we developed a course that focuses on how TAs can foster critical thinking and enhance learning in their classrooms. In this course, a team of faculty and exemplary TAs employs a variety of activities to promote conceptual understanding of key statistical ideas. The TAs leave the course with not only a cadre of examples, assessment questions and tips for how to teach introductory statistics, but also an enhanced understanding of statistical concepts. The course has helped to improve the level of teaching in the introductory course, not only by giving the TAs a set of classroom tools, but also by improving their confidence.


Session 3B: Statistics instructors’ knowledge of students’ development of fundamental statistics concepts

3B1: A certification system for statistics knowledge and skills by Japanese Statistical Society

Yoshinori Fujii   University of Miyazaki, Japan
Michiko Watanabe   Keio University, Japan
Akinobu Takeuchi   Jissen Women's University, Japan
Hiromi Fukazawa   Tokyo Healthcare University, Japan

In 2011 the Japan Statistical Society (JSS) started a set of examinations, called the JSS Certificate (JSSC), for students and professional statisticians or interviewers working in various fields related to statistics. The exams consist of four levels for students and two levels for professional survey workers and researchers. The exams try to assess not only statistical knowledge and skills, but also statistical reasoning and thinking. Recently the national curriculum of Japan has changed, expanding the amount of statistics content. In this paper we focus on the lower level student exams, which target students who graduated from high school (level 3) and junior high school (level 4). We show the properties of the exams during two years and some results. The results indicate some problems with statistics education in Japan.


3B2: Teachers’ knowledge of students’ conceptions and their development when learning linear regression

Stephanie Casey   Eastern Michigan University, United States

This paper synthesizes the results of three research studies centered around the teaching and learning of linear regression. In addition to regression's practical importance, in many cases linear regression is students’ first experience with the fundamental concepts of statistical association and dependence. Two of the studies researched how students progress in their learning of linear regression, from the initial conceptions of eighth grade students to the understanding expected of twelfth grade students. The third study examined the work of teaching grade nine students informal line of best fit, their first introduction to linear regression, to generate a description of the pedagogical content knowledge needed by teachers to effectively guide students towards understanding of the topic.


3B3: The impact of a teachers’ attention deriving on students’ statistical discourse

Min-Sun Park   Seoul National University, Republic of Korea
Kyeong-Hwa Lee   Seoul National UniversityTokyo Healthcare University, Republic of Korea

Improving students’ learning has been emphasized as a major purpose of formative assessment. In formative assessment, teachers need to gather information from students and provide feedback. Several methods for facilitating students’ learning through formative assessment have been raised in statistics education. However, published research on how teachers understand students’ responses and provide feedback during the statistics teaching and learning process is not sufficient. In statistical reasoning, since it is important to consider which aspects students focus upon in a given data set, teachers should guide students’ focus through feedback or questions. Watson (2007) emphasized “attention” as a way of facilitating students’ mathematical development by teachers’ actions. This study aims to suggest a way of implementing formative assessment which is applicable in statistics education through the concept of attention. We present the impact of a teacher’s attention deriving on the statistical discourse and reasoning of 11th grade students.


Session 3C: Statistical instructors’ knowledge of assessing students’ learning of statistics

3C1: Trends in students’ conceptual understanding of statistics

Robert C delMas   University of Minnesota, United States

The ARTIST project has been collecting data since 2005 on students’ understanding of statistics through the administration of the Comprehensive Assessment of Outcomes in Statistics (CAOS) instrument. The CAOS test consists of 40 multiple-choice items that cover six topics: data collection and design, graphical representations, variability, sampling variability, tests of significance, and bivariate data. From 2005 through 2013, over 30,000 secondary and tertiary level students in the United States of America who were enrolled in a college-level first course in statistics completed the CAOS test at the end of their respective courses. A confirmatory factor analysis (CFA) was conducted to provide evidence for the dimensionality and reliability of the CAOS test. Students’ responses were used to look at trends in students’ understanding of the six statistical topics across the 8-year period.


3C2: Discerning students’ statistical thinking: a researcher’s perspective

James Baglin   RMIT University, Australia

In the most comprehensive treatment of the topic to date, Wild and Pfannkuch (1999) propose a structural overview of the various domains of what constitutes statistical thinking. This paradigm provides a useful framework for approaching statistical thinking assessment. However, translating this model into assessments that are practical, reliable and valid for the purpose of statistics education research remains a challenge. This paper discusses the challenge of assessing statistical thinking and the development of a preliminary research-based assessment task based on Wild and Pfannkuch’s paradigm. Data collected from a large introductory statistics course where students completed the preliminary task are critically evaluated. Suggestions for future improvements to the task and ideas for alternative methods are raised. Statistical thinking may very well prove to be as difficult to assess as it is to define, but without further research, our understanding of how people learn to think statistically will be limited.


3C3: The LOCUS assessment at the college level: conceptual understanding in introductory statistics

Douglas Whitaker   University of Florida, United States
Tim Jacobbe   University of Florida, United States
Steve Foti   University of Florida, United States
Catherine Case   University of Florida, United States

LOCUS is a collection of assessments designed to measure conceptual understanding of statistics at the levels hypothesized by the GAISE framework. The original target population of the assessments is students in grades 6-12, but a version (pre/post) was constructed to meet the needs of introductory statistics instructors and students. With the implementation of the Common Core State Standards, the statistical knowledge of enrolled students is expected to change, and the LOCUS assessment for introductory statistics will be able to measure that change and possibly serve as a placement test. The LOCUS assessment is compared to the CAOS instrument and the ARTIST project. Preliminary results of the validity study with introductory college students are presented with attention given to the utility of the LOCUS assessment for placement purposes.


Session 3D: Statistics instructors’ use of technology for teaching statistics

3D1: Using bootstrap dynamic visualizations in teaching

Jocelyn Cumming   University of Auckland, New Zealand
Maxine Pfannkuch   University of Auckland, New Zealand
Christine Miller   University of Auckland, New Zealand

The increasing availability of technology means that computationally intensive methods such as bootstrapping are now accessible to students. At the university level, where introductory classes are large (about 450 students per class), we introduce students to the idea of a confidence interval using the bootstrap method before they meet the traditional approach later in the course. In this paper we describe our teaching approach using the Visual Inference Tools (VIT) software, which was designed to enhance introductory statistics students’ conceptual understanding of bootstrap confidence interval construction. Using data from research we present some of the issues that arose in students’ reasoning processes. The implications of this initiative to improve how statistics is taught and to use technology in a way that improves students’ understanding will be discussed.


3D2: Reflections on using technology to teach statistics in Kenya

David Stern   Maseno University, Kenya

Over the last ten years or more there have been numerous successful integrations of technology in statistics teaching in Kenya. Between them they show overwhelming evidence that technology can significantly improve student learning, but none have really impacted the “status quo”. This paper examines some past initiatives to identify commonalities that have contributed to their successes while also investigating why they have not been widely adopted. Many of the challenges will sound familiar to educators all over the world, for example the lack of academic recognition for good teaching, heavy workloads and institutional resistance to change. Questions are posed relating to how resources, support structures, and incentives or reward schemes might create an educational environment within which good initiatives can “go viral”.


3D3: Using the Open Learning Initiative (OLI) to support teaching statistics to international politics students

Parina Patel   Georgetown University, United States
Oded Meyer   Georgetown University, United States

The School of Foreign Service at Georgetown University offers statistics courses for international politics students which include a lab component. The labs are supposed to support the lectures and enhance the courses’ learning objectives. The TA-led lab structure, however, failed to achieve this goal. In an effort to use the lab time more effectively, the labs were replaced with web-based modules using Carnegie Mellon’s Open Learning Initiative (OLI) platform. OLI is a scientifically-based, interactive online learning environment that has been shown to increase students’ learning when used to support face-to-face instruction. Our paper will discuss the design process of the modules and the features of the OLI platform which lead to effective learning processes. We will also present preliminary assessments and how statistics instructors can take advantage of the OLI platform to create materials to support their teaching.


3D4: The use of technology in a mentor teacher course in statistics education

Thomas Wassong   University of Paderborn, Germany
Rolf Biehler   University of Paderborn, Germany

In 2012 the two authors of this article planed and implemented a 4-month mentor teacher course. The content of this course concentrated on descriptive statistics and data analysis for 5th to 10th graders in Germany. One central topic of the course was the use of technology like Fathom as a tool for learning and doing statistics: How to use Fathom for the analysis of real data, what are usable tasks for the classroom, how to use Fathom for visualizing properties of mean and median, and how to use online-tools like GoogleDocs for collecting data? In our article we will focus on the technological knowledge for common and pedagogical content aspects: What were the concrete topics, we communicate? Which educational settings did we use? What were the feedback we got from the participants by questionnaires and interviews?


Session 3E: Professional development of statistics instructors

3E1: Building the capacity of mathematics and science teachers to teach statistics

Katharine Richards   Plymouth University, United Kingdom
Neil Sheldon   Plymouth University, United Kingdom
Neville Davies   Plymouth University, United Kingdom

Capacity building in statistics teaching requires teachers who wish to improve their pedagogy and knowledge to be, or become, artists, scientists and literists. This is because learning from data, the lifeblood of statistics, is an art and science: reporting any conclusions or findings in a trustworthy way requires a high level of writing skills. Consequently, continuing professional development (CPD) courses in statistics need to provide for teachers to be able to become better in these three areas in relation to many aspects of teaching and learning statistics. In this paper we describe the development of a CPD course, Certificate in Teaching Statistics up to Pre-university Level, first accredited as a professional qualification by the Royal Statistical Society in 2006, and its incarnation into masters-level modules that are now part of the Plymouth University International Masters Programme and can lead to the award of MA in Teaching Pre-university Mathematics and Statistics.


3E2: Project-SET materials for the teaching and learning of sampling variability and regression

Ann Watkins   California State University, Northridge, United States
Robert Gould   University of California, Los Angeles, United States
Randall Groth   Salisbury University, United States
John Haddock   University of Memphis, United States
Christine Franklin   University of Georgia, United States
Michelle Everson   University of Minnesota, United States
Anna Bargagliotti   Loyola Marymount University, United States
Stephanie Casey   Eastern Michigan University, United States
Celia Anderson   University of Memphis, United States

To address the increased need for statistical literacy across the world, high quality statistical preparation of teachers is needed. Project-SET is an NSF funded project aimed at developing materials to prepare secondary teachers to teach statistics. In this paper, we present results from a professional development (PD) project designed to test whether the materials are effective in preparing teachers to teach sampling variability and regression. Eleven teachers were recruited to take a 45-hour PD that utilized the materials. Participants took the Comprehensive Assessment of Outcomes in Statistics (CAOS) as a pre- and post-test. Results indicate that Project-SET materials were effective in increasing teacher scores. PD participants were also given open-ended assessments. Teacher answers revealed that misunderstandings were present in their thinking.


3E3: Implementing GAISE recommendations through “doing statistics” tasks

Brandon Hanson   Middle Tennessee State University, United States
Jeremy Strayer   Middle Tennessee State University, United States
Jeffrey Pair   Middle Tennessee State University, United States
Katherine Mangione   Middle Tennessee State University, United States
Jessica Brown   Middle Tennessee State University, United States

The Pre-K-12 GAISE report identifies four components of statistical problem solving: formulate questions, collect data, analyze data, and interpret results. Traditional tasks often require the teachers, not the students, to complete a significant portion of one or more of these components. To meet the need for students to engage in the complete statistical process, we have developed tasks that require students to make critical decisions for all four GAISE components. We term these doing statistics tasks. This paper describes our implementation of doing statistics tasks with grades 7-12 in-service mathematics and science teachers during a professional development institute in the summer of 2013. We present an analysis of work samples that illustrate the ways in which doing statistics tasks enabled participants to engage in all four components of statistical problem solving.


Session 3F: Theory and practice of statistics: curriculum for statistics teachers

3F1: Suitability criteria for teachers’ education programs in mathematics and statistics education

Juan D Godino   University of Granada, Spain
Hernán Rivas   Catholic University of Chile, Chile
Pedro Arteaga   University of Granada, Spain

The design and evaluation of prospective statistics teachers’ education programs require developing reference models for the desirable characteristic of these programs. It is necessary to consider the knowledge required to organize and manage statistics teaching processes, as well as the various aspects involved in the application of that knowledge by the teachers. The aim of this report is to identify components and indicators of didactical suitability for statistics teachers’ education processes (following the model suggested in the onto-semiotic approach to mathematics education). Consequently, we propose a model of didactic-statistics knowledge and some criteria for developing this knowledge in prospective teachers.


3F2: Relationships between curriculum knowledge of in-service Mexican teachers and statistics

Ernesto Sánchez   Cinvestav-IPN, Mexico
Verónica Hoyos   National University of Education, Mexico

Mexican curriculum is a competency-based curriculum; it promotes the use of teaching situations relevant to the students’ life. Such curriculum is more difficult to realize in mathematics education, since it is not easy to find situations that promote the kind of mathematical thinking that should be taught, but it is not the case for statistics education. It is however not clear how to promote the teaching content of statistics to best prepare secondary school teachers to highlight this point. We ask: How do mathematics pre-service teachers understand the connection between competencies and statistics? Thus a questionnaire to evaluate the pre-service teachers’ knowledge about the relationships between statistics and competency-based curriculum is proposed. The teachers’ knowledge of such relationships is analyzed through the responses to 7 questions from 12 in-service teachers. The results show evidences on what in-service teachers know and what they keep hidden with respect to those relationships.


3F3: Preparing teachers to teach statistics: developing professional knowledge and practice

Ana Henriques   University of Lisbon, Portugal
João Pedro da Ponte   University of Lisbon, Portugal

Teachers’ professional knowledge is complex and trans-disciplinary, and is both informed by theory and practice. This paper addresses how teacher education systems may support the development of professional knowledge and teaching practices required for teaching statistics successfully. We discuss the content and nature of teacher knowledge about statistics as well as the teaching of statistics and their relation to teaching practices. We describe the aims, assumptions, and work carried out in an ongoing in-service teacher education program, that integrates teaching and learning with technology, for the professional development in statistics education of middle-school teachers. The teachers’ professional development is supported by a continuous and reflexive movement that considers the articulation between theory and practice. Based on this work, we provide suggestions for teacher education practice and for further research.