Proceedings

Contributed Papers

C101: Dichotomous thinking: a problem beyond NHST

Jerry Lai   La Trobe University, Australia

The cliff effect—a sudden drop of confidence that a real effect exists just above p=0.05—captures the way many researchers and students interpret p-values. It is consistent with dichotomous judgements based exclusively on statistical significance (SS). Many have argued that CI can overcome over-reliance on SS. In our study, 172 researchers rated the strength of evidence against the null hypothesis as a function of 8 p-values crossed with 2 sample sizes. A further 86 received the same results presented as CIs. Although the cliff was sometimes found with p-values (23% of 172), it was more frequent with CIs (32% of 86). Thus, the argument that CIs can reduce over-reliance on SS may be overstated. Students, and also researchers, should be trained to think in terms of (or to ask) quantitative (how much A and B differ) rather than dichotomous research questions, whether analysis relies on SS or CIs.

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C104: Identifying misconceptions about confidence intervals

Pawel Kalinowski   La Trobe University, Australia

Although confidence intervals (CIs) have many benefits over null hypothesis significance testing (NHST) they can still be misinterpreted. Identifying CI misconceptions is a first step in designing teaching tools that can be used to prevent or reduce them. I surveyed graduate level students and found they hold several misconceptions about CIs. Many believe there is a uniform likelihood distribution across a CI, with a high proportion of these showing a cliff effect (a sudden major drop in likelihood at each limit of a CI). Many students also misunderstand the relationship between the width of a CI and the confidence level. In this paper I present a taxonomy of CI misconceptions identified by empirical studies, and explore faulty conceptual models that may be the source of the misconceptions. I also propose an educational tool that could be used to confront CI misconceptions, particularly misconceptions about CI distributions.

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C105: Paradoxical games as a didactic tool to train teachers in probability

Carmen Batanero   University of Granada, Spain
Jose Miguel Contreras   University of Granada, Spain
José António Fernandes   University of Minho, Braga, Portugal
Mario Miguel Ojeda   University of Veracruz, México

In this paper the contents needed in the didactical preparation of teachers to teach probability are described and the possibility that classical paradoxes of probability offer to organise didactic activities that can help carry out this training are suggested. Results of working with one such activity in courses directed to teachers in México, Portugal and Spain are presented.

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C106: Students’ profile in higher education in Italy

Claudia Caruso   University Federico II Napoli, Italy

The aim of the present paper is to show the results of the analysis of the graduates’ evaluation questionnaires about the social profile of the students in higher education in Italy. A factor analysis has been carried on a national basis from 75,000 questionnaires administered to students representing 10 degrees. The factor analysis indicates the close proximity of responses between Statistics and Economy in the learning processes. These preliminary results are useful to improve the intended learning outcomes of the different courses, according with the Dublin Descriptors.

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C107: A statistical game: the silent cooperation problem

Ernesto Sánchez   Cinvestav, Mexico
Alejandro Hernández   Cinvestav, Mexico

In this paper an activity based on the following problem (Mosteller, 1965) is presented: Two strangers are separately asked to choose one of the positive integers and advised that if they both choose the same number, they both get a prize. If you were one of these people, what number would you choose? Some taste of statistical thinking and informal inference reasoning might be experienced by the students/teachers with this problem. Fifty-four teachers from different school levels participated in a two sessions experiment. In the first session, pairs of teachers were formed and each thought of a number in such way that they could not predict what number would be thought by his/her partner. The numbers thought were gathered, graphed in a distribution and analyzed. In the second, without advised in advance, the same experience was repeated. Distributions, patterns of variation, and making decisions are some themes that emerged.

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C108: A teaching experiment dealing with statistics in high school

Sandra Magina   Catholic University of São Paulo, Brazil
Irene Cazorla   State University of Santa Cruz, Brazil
Edgard Silva   Educational Department of São Paulo, Brazil

This study involves a teaching experiment to improve students’ understanding of statistics basic concepts, by integrating statistics and data analysis related to science and social studies, contextualized in Vitruvian Man of Leonardo da Vinci. The design followed the model proposed by Rumsey (2002) for the statistical competence. Twenty two 10th grade students from a public school in Sao Paulo, Brazil went through all phases, from the formulation of the hypothesis, the collection of their own data, the discovery, the use of tools to interpret the data (in both paper and pencil and computer based), and to the communication of the result. Participants were given a pre and a posttest. The results are discussed in terms of the nature of teaching strategies and innovative use of technology. Students showed an expressive improvement to deal with statistical concepts from pre to post-test.

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C109: Statistical training in humanities and social sciences in group and at distance: exploration of the effects of teaching and lerning on collaborative work through the observable traces of social interactions in a system of online distance education

Jean-Claude Régnier   University of Lyon, France
Annick Pradeau   University of Rouen, France
Muhammad Shahid Farooq   University of Lyon, France

This paper focuses on the organization and content of social interactions in a group of students engaged in learning Statistics. The importance of social interactions in the teaching and learning is largely based on socio-constructivist theories. We intended to look at the micro-level exchanges between students engaged in a complex task oriented teaching. Technical constraints and spatiotemporal characteristics influence on contributors engaged to achieve the common goal. This observation was made through quantitative and qualitative analysis of messages exchanged in a discussion of students. Learning Statistics through distance education and in a group situation are a new framework of experience. ‘What is at stake’ when a group of students learns Statistics without direct meetings, among themselves and with the teacher was the main question of the study.

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C110: Research in statistical education: competence level of secondary school pupils

María Vega   Professional Schools of the Sagrada Familia of Ecija, Spain
José M Cardeñoso   University of Granada, Spain
Pilar Azcárate   University of Cadiz, Spain

This communication presents an adaptation of one of the innovative learning scenarios in the European secondary education project, “EarlyStatistics”, whose main goal is to improve pupils’ competence in statistics. This project has just been selected for the “2009 Best Cooperative Project Award in Statistical Literacy”. In this implementation, the pupils worked in a collaborative and self-governing form throughout the process. To provide an objective description of the pupils’ level of statistical competence, an instrument was designed that incorporates various competence indices proposed in the literature.

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C111: Statistics education in the social and behavioural sciences: from dichotomous thinking to estimation thinking and meta-analytic thinking

Geoff Cumming   La Trobe University, Melbourne, Australia

Null hypothesis significant testing (NHST) dominates in the social and behavioural sciences, despite strong evidence of its disadvantages. Worst may be its reinforcement of dichotomous thinking (DT), which focuses on impoverished reject or don’t-reject decisions. By contrast, estimation thinking (ET) and meta-analytic thinking (MAT) focus on sizes of effects, and cumulation of evidence to increase precision. A shift from DT to ET and MAT is highly desirable. Statistics education for ET and MAT will emphasise effect sizes, confidence intervals and metaanalysis, starting with the introductory course. Interpretation of confidence intervals should emphasise estimation, not NHST. Students and researchers, when specifying research goals, or discussing and interpreting findings, should use language that reflects ET and MAT. The outcome should be more quantitative theories, more sophisticated disciplines and better research progress.

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C112: Comparing outcomes between online and face-to-face statistics courses: a systematic review

Kathleen Mathieson   A.T. Still University, Mesa, United States

The increase in online learning has led to research comparing student outcomes in online and face-to-face (FTF) statistics courses. This systematic review presents an analysis of studies comparing student achievement and student satisfaction in statistics courses taught online to those taught FTF. Multiple databases, conference programs, and bibliographies from selected articles were searched. Among the 411 studies identified, 13 met inclusion criteria. Student achievement was generally similar between online and FTF methods, but results on student satisfaction were inconclusive. Studies comparing online and FTF statistics courses are characterized by considerable methodological limitations. Instructors teaching statistics online would benefit from future research that is grounded in sound methodology, that is informed by past research and theory, and that examines specific ways to improve learning in an online environment.

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C113: Compare students’ attitudes to learn mathematics and statistics in China and Australia

Dong Q Wang   Victoria University of Wellington, New Zealand
Bingshu Wu   Ballarat Grammar School, Australia

This research seeks to explore the attitudes of Chinese and Australian senior secondary school students towards mathematics and statistics. An investigation is carried out to determine the relationships between these attitudes and certain factors. A preliminary analysis of the curriculum in China and Australia revealed that the subject in common in Year 12 is the study of statistics. Therefore, students’ attitudes towards the study of statistics will receive particular attention here. This research project outlines the social environment, the family environment and the individual status of Chinese and Australian students. A comparative study, an empiricist approach, an interpretive approach and a statistical analysis methodology were used to analyze the data. However, other conclusions of this study, such as sex not having an effect upon students’ attitudes towards learning mathematics and statistics, has not been previously concluded.

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C114: Assessing mathematics competence in introductory statistics courses: an application of the item response theory

Silvia Galli   University of Florence, Italy
Francesca Chiesi   University of Florence, Italy
Caterina Primi   University of Florence, Italy

A positive relationship between statistics achievement and mathematics competence has been consistently reported in literature. Given the influence that mathematical ability has on statistics achievement, it turns out to be useful to assess the mathematical competence in order to promote statistics course performance. In this work, we developed a scale to measure the mathematical ability deemed necessary for psychology students to successfully complete an introductory statistics course. The Item Response Theory was applied to construct the instrument in order to overcome the limitations of the classical approach. The predictive validity of the instrument was assessed considering achievement as the criterion measure. Advantages offered by using the scale in introductory statistics teaching are discussed.

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C115: Teaching regression models: an application with simulations

Irene Schiattino   University of Chile, Chile
Rosa Montaño   University of Santiago, Chile
Claudio Silva   University of Chile, Chile
Carmen Acuña   Bucknell University, United States
Isabel Ormeño   University of Santiago, Chile

The availability of efficient statistical software makes it possible to enhance the strategies for teaching statistics with activities based in methods of stochastic simulation. The objective of this work is to offer, from an educational perspective, a review and presentation of several articles that address the subject of simulations. Simulated data sets with different features, but that result in the same estimates of the regression parameters are presented. Extensions to multivariate methods, such as multiple regression, are reviewed. Some ad-hoc programs written in R, the PROC IML of SAS, and PROC MATA of STATA are produced and used in the illustrations presented.

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C116: Students’ opinion on the subjects of statistics and probability in secondary schools of Lisbon, Portugal

Sara Caldeira   University of Lisbon, Portugal
Helena Mouriño   University of Lisbon, Portugal

Nowadays, Statistics and Probability take an important role in Secondary Education Mathematics curriculum. This work aims at analysing students’ opinion about these subjects. During the third term of 2007/08 school year, we conducted a survey on 1128 students–7th grade to 12th grade–from public schools in the area of Lisbon and Vale do Tejo. Students filled in the questionnaire at math classes and they reported on their beliefs about Statistics and Probability. The questions were mainly closed and we used the 5-point Likert type scale. Analysing the inquiries, we conclude the majority of the students recognise that the subjects of Statistics and Probability are interesting, and admit that, on the overall, their contents are neither easy, nor difficult.

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C117: The opinion of the family about the performance of the schoolchild bringing knowledge to his/her own family: statistics on prevention of mouth cancer

Maria Lucia Marçal Mazza Sundefeld   University of São Paulo, Brazil
Lucas Correa Homse   University of São Paulo, Brazil
Annelise Katrine Carrara Prieto   University of São Paulo, Brazil
Marco Aurélio Borella Rodrigues   University of São Paulo, Brazil

The “Statute of the Child and Adolescent”, 8.069 Federal Law of 1990, ensures that children and adolescents should have basic rights to health care and they should have some participation in decisions of their interest. This research aims to verify whether the schoolchildren are capable of transmitting some knowledge of statistics and health to their families. It was a non-probabilistic and intentional sampling of very low socio-economic public school. A questionnaire was answered by the schoolchildren. Lectures using data in a real context in order to improve the planning on the family budget and good habits were carried out. The schoolchildren were provided with educational materials to use them with their family. The schoolchildren were assessed again and the parents were interviewed. The result showed that there was improvement in the number of the schoolchildren’s right answers and the families confirmed that the students spread this knowledge to their home.

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C118: Supporting shifts in teachers’ views and uses of problem context in teaching statistics

Jana Visnovska   University of Queensland, Australia
Paul Cobb   Vanderbilt University, United States

We report on our 5-year collaboration with a group of teachers whose statistics instruction initially concerned producing graphs and calculations. Towards the end of the collaboration, the teachers routinely planned for statistical activities in which generation and analysis of data were driven by a need to gain insight in a specific problem at hand. We document the shifts in the teachers’ views of the role of problem context in statistical activities and the means of support.

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C120: A comparative analysis between statistical tools adopted in scientific research of the speech therapy area and contents present in the area course syllabuses

Maria Cláudia C Grácio   São Paulo State University, Brazil
Cora S T Paiva   São Paulo State University, Brazil
Patrícia S O Souza   São Paulo State University, Brazil

The aim is to compare the statistical tools employed in research of the Speech Therapy area and contents present in course syllabuses of Statistics related disciplines in the Speech Therapy Education, with the purpose of verifying congruence/coherence. The supposition is that the contents of the Statistics syllabus should be congruent to those that have been considered relevant to scientific research activities. The investigation covered 343 scientific papers published in three Speech Therapy periodicals from the Online Brazilian Scientific Electronic Library–SciELO and 12 Statistics course syllabuses of the Speech Therapy area, in Brazil. Concerning the results of the analysis, although descriptive statistical tools present in the course syllabuses are congruent with the ones most adopted by researchers, there are many inferential statistical tools also considered relevant to the area that are not present.

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C121: Toward improving the quality of doctoral education: a focus on statistics, research methods, and dissertation supervision

Rossi Hassad   Mercy College, New York, United States

Doctoral education (PhD) in the USA has long been characterized as being in a crisis, yet empirical research to identify possible determinants is limited, in particular, faculty competence has received only scant research attention. This study ascertained from students, faculty and consultants, their concerns about the teaching of statistics and research (including dissertation supervision). The responses encompass the curriculum, pedagogy, content knowledge, support, and accountability. The current U.S. doctoral education model needs to be systematically reviewed toward assessing its relevance to the changing needs of the disciplines and the job market. In this regard, the almost universal emphasis on evidence-based practice, especially in the disciplines of health and behavioral sciences must be given major consideration. Reform initiatives must also address the roles and qualifications of dissertation committee members (including consultants), the composition of the dissertation committee, and training geared toward preparing and certifying faculty to serve as dissertation committee members

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C125: Confidence intervals using interval arithmetic

Juan José González-Henríquez   University of Las Palmas, Spain
Nicanor Guerra-Quintana   University of Las Palmas, Spain

This paper deals with the surprising and interesting question posed by some students about constructing confidence intervals for mean differences in independent samples. The question was: is it possible to construct a confidence interval for the difference between two means by subtracting the intervals (an arithmetic interval operation) obtained for each parameter? Several activities created by the teacher in order to obtain an answer to this question are presented. Some other confidence intervals obtained via arithmetic interval are studied.

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C126: Linking probabilities to real-world situations : how do teachers make use of the mathematical potential of simulation programs?

Laurent Theis   University of Sherbrooke, Canada
Annie Savard   McGill University, Canada

In Quebec secondary schools, the teaching of probabilistic concepts is mandatory, but most teachers feel insufficiently prepared. Furthermore, middle school students are confronted to gambling activities at a young age, without necessarily understanding the underlying probability. In order to analyze the development of a more realistic and mathematically correct understanding of gambling activities, we conducted a one-year design experiment involving 4 high school teachers. We trained the participants in various concepts of probability and accompanied them to prepare classroom situations, which they used in their classrooms. In this paper, we analyze how the participating teachers used a simulation software we provided them. Mainly, the teachers used the software to show that gambling activities do not pay off over the long term. However, it was more difficult for the teachers to discuss probabilistic concepts through the simulation software.

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C127: Statistic for the social sciences: a challenge

Nora Lac Prugent   Rosario State University, Argentina
Liliana Severino   Rosario State University, Argentina

The Creditable Postgraduate Seminar tries to give an answer to the growing demand on training and practice in the quantitative analysis for researchers and professionals of the Social Sciences. The pedagogic proposal points the training of theoretical-practice data analysis, linking the acquisition of statistical concepts to the application on reference material that it "makes sense" for the professional field of the Social Sciences. For the practical training the methodological material used is bring by the tutor and the databases are national surveys on conditions of life in urban homes of the Argentina Republic. In this way, this integrated approach of social data analysis coming from surveys, tries to enable professionals from this area to use in a critical way official databases that are of public access. In this paper we present some results from our experience of a course for Undergraduates that was given in our University.

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C128: Improving capacities of translation through an educational process

Carlos Carrión-Pérez   University of Las Palmas, Spain
María Candelaria Espinel-Febles   University of La Laguna, Spain

Capacities of translation between different statistical representations of data are essential to read and understand a graph. A questionnaire has been designed, using 12 items with multiple answers, grouped in four tasks where translations between text, tables and dots charts, histograms, bar charts, stem and leaf charts and boxes graphs take part. A number of 72 students of Primary Teacher Training have answered the test, before and after they have passed a process of Descriptive Statistics learning session, for approximately 12 hours. Results show little differences in capacities of translation in different tasks, but only some graphs show a bigger difficulty, although it gets reduced but do not disappear after the educational process has been done. The data has been analyzed using the Rasch methodology, the study shows that the order of difficulty of items doesn’t change after the process but, this analysis allows us to consider that students improve remarkably their knowledge and understanding.

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C129: A content analysis of the statistics education discussion list, EDSTAT-L

Robert N Goldman   Simmons College, Boston, United States
John D., Jr. McKenzie   Babson College, Babson Park, United States

EDSTAT-L is a discussion list for statistics education, begun in October, 1991. This listserv allows statisticians to discuss the topics, techniques, and technology used in their classes. Our 18-year longitudinal study will include an analysis of the number of messages generated each month. We will identify the most discussed subjects for each year. Another analysis will also focus on the most popular threads/subjects in the discussion, which should benefit present and future statistics educators. Finally, there will be a comparison of EDSTAT-L and other discussion lists dealing with statistics education, such as the APSTAT-L and the Isolated Statistician’s listserv.

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C130: The impact of using pupils’ daily social practices as well as computerized simulators as a teaching medium on motivation and knowledge construction regarding probabilities among high school pupils

Vincent Grenon   University of Sherbrooke, Canada
François Larose   University of Sherbrooke, Canada
Jimmy Bourque   University of Moncton, Canada
Johanne Bédard   University of Sherbrooke, Canada

Probability education, from a purely mathematical and decontextualized point of view, notably regarding frequency-based probabilities, leaves barely any evidence of long-term learning among middle school pupils. When contextualized in a playful manner, and by calling on pupils’ daily social practices, probability education becomes a powerful tool for giving meaning to statistics in a school setting. Within the framework of a funded research conducted among high school pupils in 8 classes with 5 different participating teachers in the Montreal region, we integrated the use of computer games to teach probabilities. In this paper, we will summarize survey results and results of group interviews conducted with these pupils at the end of the study. Our research data show that learning while playing, by using computerized simulators as a teaching medium, is effective in motivating pupils and in building knowledge.

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C131: The concept of mean by primary school students

Gilda Guimarães   Federal University of Pernambuco, Brazil
Verônica Gitirana   Federal University of Pernambuco, Brazil
Mabel Marques   Federal University of Pernambuco, Brazil
Diego dos Anjos   Federal University of Pernambuco, Brazil

This research, which was undertaken in Brazil, focuses on the different invariants of the concept of mean. Activities from 16 mathematics textbooks were analyzed, and the invariants explored were identified. Afterwards, a test was designed and later undertaken by 179 elementary school students (3rd and 5th grades) and 31 teachers. The results show that the textbooks emphasize “the usage of mean as a number different from any value of the group” and “the usage of mean with no correspondence on real life”. A lacking on the textbooks' approach of mean was identified, as regarded by the following invariants: “the relation between mean and standard deviation”; “the mean is in between extreme values”; “the inclusion of null and negative values”. Regarding the students’ capacity, the majority of 3rd grade students failed on solving problems regarding mean, and some of the 5th grade students were able to solve problems by compensating values.

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C132: Independence of events: an analysis of knowledge level in different groups of students

Verônica Yumi Kataoka   Bandeirante University of São Paulo, Brazil
Hugo Mael Hernandez Trevethan   National Autonomus University of Mexico, Mexico
Claudia Borim da Silva   University of São Judas Tadeu, Brazil

The objective of this work is discussing independent events, which have been the cause of theoretical confusions showed by students and mathematics in-service teachers. The proposed didactical activity was developed with 34 master students and 22 college students in Brazil, and 27 high school students in Mexico. The students, of different levels, didn’t answer the problems effectively because they’ve used only the intuitive idea of independence, (chronological or informal independence). They were asked also to decide if two events were dependent or independent in a dice tossing situation, and the results showed something like “events are independent because there is only one kind of event: throw dice”. The outcomes show that misconceptions of independent events and conditional probability persist even in people who had studied formally these concepts, pointing out the need to develop didactic situations to teach more effectively this content at high school and mainly to mathematics undergraduates.

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C133: The effect of contextualising probability education on differentiating the concepts of luck, chance, and probabilities among middle and high school pupils in Quebec

François Larose   University of Sherbrooke, Canada
Jimmy Bourque   University of Moncton, Canada
Viktor Freiman   University of Moncton, Canada

On the one hand, the field of probabilities is certainly the most obscure and the least developed area in the sphere of statistical education in Canadian middle and high schools. On the other hand, mastering probabilities is doubtless the field of school learning that offers the most potential for transferring knowledge to other fields of experience in the pupils’ lives, notably regarding gambling and money. Within the scope of this study, carried out among over 1,600 pupils in middle and high schools, we have collected their implicit definitions of gambling, luck, and probabilities. A textual data analysis of their discourse shows that they confused these concepts and strongly associated them to luck, while the notion of random variability remained obscure. Contextualising probability education from the point of view of what youth really does facilitates in this respect the construction of distinct notions.

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C134: Youth and Adults students interpreting bar and line graphs

Izauriana Lima   Center of Education, Federal University of Pernambuco, Brazil
Ana Selva   Center of Education, Federal University of Pernambuco, Brazil

The objective of this study was to investigate the influence of schooling on the performance of Youth and Adults (EJA) students in solving activities of construction and interpretation of bar and line charts. The participants were 30 students divided into three groups: 10 students in the early years of elementary school, 10 students in the final years of elementary school and 10 high school students. The results indicated no significant differences in the performance presented by participants according to the segments of education to which they belonged. There were significant differences in performance on the basis of the activities of interpretation of the bar charts, but not between the bar and line charts.

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C135: Teaching statistics at high school: an alternative approach

Lorí Viali   Federal University of Rio Grande do Sul, Brazil
Renate Grings Sebastiani   Pontifical Catholic University of Rio Grande do Sul, Brazil

The main purpose of this work is to verify the learning and the students’ interest in Statistics, from a contextual approach with the help of technological resources. To get students attention and their involvement spreadsheet was used in the classes. The work was done with a group from the third year (last year) of High School of a public school from the country side of the state of Rio Grande do Sul, Brazil. The classes were taught in a computer lab, using a data show and the spreadsheet. Prior to the classes, the students were asked to answer a questionnaire in order to verify their previous knowledge about the subject. Straight after the classes the students were submitted to questionnaires and evaluations, in order to get information about their learning, motivation and performance on those subjects.

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C136: Implications of educational reform in Cyprus on the teaching of probability and statistics at the secondary school level

Irini Papaieronymou   Michigan State University and P.A. College, Larnaca, United States and Cyprus

Since 1995, the participation of Cyprus in TIMSS has been consistently marked by poor student performance in mathematics (Muller, Martin, & Foy, 2008; Papanastasiou, 2002). In view of this, it is encouraging that as of 2005–shortly after the accession of Cyprus to the European Union–the government of Cyprus has initiated educational reform efforts. Revisions in the national curriculum aim, among other goals, towards helping students develop their critical thinking skills and research capabilities, and becoming active citizens (Ministry of Education and Culture, 2008). Studies have shown that statistics courses have the potential to enhance such skills in students (Derry, Levin, Osana, Jones, & Peterson, 2000). This paper examines the educational reform currently taking place in Cyprus and its implications on the teaching of statistics and probability at the secondary school level.

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C137: Movies as a tool for improving our classes

Luis J Rodríguez-Muñiz   University of Oviedo, Spain

Cinema and TV series can be a helpful tool to improve some of the aspects in Statistics classes. Motivation is an obvious point to reinforce by using movies scenes, especially those in which we can find applications of the topics to be taught in class. Also we can use specific scenes to make clearer some notions or ideas in the class. Thinking in a University level, we can find some of the fore mentioned scenes in a small number of films and a few TV series. In this communication we state our ideas about how to use movies to improve our classes and we illustrate them with some concrete examples of scenes which can be used in a University-level class.

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C138: Strengthening the understanding of sampling distribution and errors associated to the hypothesis testing in students of agricultural and environmental sciences

María Virginia López   University of Buenos Aires, Argentina
María del Carmen Fabrizio   University of Buenos Aires, Argentina
María Cristina Plencovich   University of Buenos Aires, Argentina

The concept of sampling distribution is not easily understood by university students of agricultural and environmental sciences. Although students can define correctly the errors involved in hypothesis testing, they show lack of a deep understanding of the subject when they have to draw conclusions. To strengthen the learning of these concepts, a practical assignment was planned in the second course of Statistics. Starting from an experimental situation, students had to design their own experiments by randomizing four varieties of canola in twenty plots. In the following class, they received the results of the “virtual sowing”, with data provided by the teaching assistant. The data were simulated from normal probability distributions. Students analyzed their own data and the variability of results was commented. It was also discussed that a type II error does not imply a mistake. This study discusses the results of the teaching and learning experience.

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C139: Social representations of French-speaking undergraduate students in humanities and social studies in the use and difficulties in learning statistics

Alain Bihan-Poudec   Catholic University of the West, Angers, France
François Larose   University of Sherbrooke, Canada

In this paper, we shall present the results of two successive surveys carried out among Frenchspeaking students at the undergraduate level regarding their representations of the training they received in statistics, of this subject matter’s academic and professional uses, and of the stumbling blocks encountered while learning it. The first set of data was gathered in 2007-2008 from 666 students. The following year, a more in-depth survey, which included semi-structured interviews, was conducted with 146 other students. Data show that representations of statistics vary according to whether the students are in pre-service or continuing education, and according to their academic or professional experience. In addition, and in accordance with Shaughnessy (2006), results show that statistical education is only as effective as the level that students integrate it into their education project.

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C140: A semiotic analysis of “Mônica’s random walk”: activity to teach basic concepts of probability

Tânia Gusmão   State University of Southwest Bahia, Brazil
Eurivalda Santana   State University of Santa Cruz, Brazil
Irene Cazorla   State University of Santa Cruz, Brazil
José Cajaraville   University of Santiago de Compostela, Spain

We analyzed the activity “Mônica’s random walk” in the learning environment of paper-and-pencil, which presents the basic concepts of probability. We use the onto-semiotic approach of cognition and mathematics instruction to study the types of mathematical objects (language, situations, concepts, procedures, propositions, properties and arguments), and the semiotic potential conflicts that may compromise the understanding and meaning of these concepts. The activity was implemented with 29 mathematics teachers in an in-service training program. The method adopted for this study was action research. The results showed the viability of the activity to contextualize such concepts. However, they indicate different semiotic conflicts, due to the teachers’ poor prior knowledge of probability, since many of them were seeing these concepts for the first time. These results imply rethinking of some of the assumptions, especially if we want to insert them into virtual learning environments, so that teachers can implement it with autonomy.

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C141: Analysis of activity at statistical literacy: contributions of the activity theory

Aida Carvalho Vita   State University of Santa Cruz, Brazil
Eurivalda Santana   State University of Santa Cruz, Brazil
Irene Cazorla   State University of Santa Cruz, Brazil
Silvana Oliveira   State School Eduardo Catalão, Ilhéus, Bahia, Brazil

This paper analyzes the actions, whilst activities concern Statistical Literacy were applied. The analysis was based on the Activity Theory using the Engeström’s complex model of an activity system. It was considered teaching as activity system and it was carried through the activity “Vitruvian Man”. This activity took place in a Virtual Environment Supported by Statistical Literacy–AVALE and involved 34 teachers. By using the Engeström’s model, we characterized subject, community, objects, tools, rules and division of labor all together. We also investigated the classroom interactions and tensions, characterizing the microanalysis Subjects’ actions had been observed, filmed and audio-recorded. The analysis pointed out that activity contributes to develop: subject’s criticizes dimension, the scientific discovery, and social practices.

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C142: Fostering students’ statistical reasoning, self-efficacy, and attitudes: findings from a comprehensively reformed undergraduate statistics course

Aboma Olani   University of Groningen, The Netherlands
Rink Hoekstra   University of Groningen, The Netherlands
Egbert Harskamp   University of Groningen, The Netherlands
Greetje van der Werf   University of Groningen, The Netherlands

This study investigated to which degree a reform-based introductory statistics course improved its participants’ statistical reasoning ability, their statistics self-efficacy, and their attitude toward the usefulness of statistics. In addition, it examined whether the learning outcomes differed with respect to the students’ mathematical background, their class attendance, and their perceived teacher support. Ninety-six first year university students (97% female, mean age 19) participating in an introductory statistics course were assessed both at the beginning and at the end of the course. The results showed that the students’ statistical reasoning ability and statistics self-efficacy increased significantly during the course. However, no significant changes were observed in their attitude toward the usefulness of statistics. The improvements in the students’ statistical reasoning ability and statistics self-efficacy were regardless of their mathematical background, course attendance, and perceived teacher support. In this paper we present the results of this research study and discuss their implications for instruction, after which we will make some suggestions for further research.

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C143: The confidence intervals: a difficult matter, even for experts

Gabriel Yáñez Canal   Industrial University of Santander, Colombia
Roberto Behar Gutiérrez   University of Valle, Colombia

We present the results of a research whose purpose was to find out what a sample of experts (statisticians and statistics university professors) and university students understood exactly by confidence intervals. To this end, a questionnaire was answered by 41 experts and 297 students. The results show that both, students and professors, possess misconceptions regarding confidence intervals. The conception that these intervals contain sample means or single values of the population instead of possible parameter values, and the interpretation of significance levels as a measure of certainty, without any frequency referent, were found to be the most generalized misconceptions.

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C146: Adjusting cognitive load to the student’s level of expertise for increasing motivation to learn

Jimmie Leppink   Maastricht University, The Netherlands

Developing conceptual understanding of statistics requires an instructional format that adjusts cognitive load to the student’s level of expertise in order to optimize motivation to learn. Structuring the material to be learned and guiding self-explanation of what is learned will diminish fear and postponing behavior on the part of the student, it will stimulate students to engage in meaningful learning, which will help them to keep an overview and develop conceptual understanding of the subject matter. These aims of education form the pillars of the educational method presented in this paper: the method of propositional manipulation (MPM).

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C147: Non-statisticians learning statistics

Ayse Bilgin   Macquarie University, Australia

Learning approaches of students could be either deep, surface or achievement oriented. If students choose to study a unit (elective unit instead of a core unit) then we might expect them to use a deep approach to their learning since they have chosen the unit themselves, probably anticipating the benefits of the unit to their careers. If they choose two elective units that are related to each other, and one of them is prerequisite to the second one, then we might expect students to utilize the deep or achieving approaches to their learning at least for the lower level unit to maximize their grades (achievements) for these units. The main results of this study is show that the learning approaches of students do not change from second to third year in two large statistics units. The student characteristics such as country of gender, the degree enrolled and intention to enroll to higher degree are not significant factors for learning approaches.

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C148: Personal Response Systems for teaching postgraduate statistics to small groups.

Andrew Titman   Lancaster University, United Kingdom
Gillian Lancaster   Lancaster University, United Kingdom

Technology is increasingly used to aid the teaching of statistics. Personal Response Systems (PRS) involve equipping students with a handset allowing them to send responses to questions put to them by a lecturer. PRS allows lectures to be more interactive and can help reinforce material. It can also allow the lecturer to monitor students’ understanding of course content. PRS is most commonly used in large lectures where interaction from the students is particularly difficult. However, we consider its use in a small group (around 15 students) of MSc in Statistics students. Recommendations based on this experience are discussed, in particular the importance of good question design. We consider possible diagnostics for the appropriateness of questions based on response data.

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C149: Teaching statistics at a superior school of business management. Realities and challenges.

Sandra Nunes   Polytechnic Institute of Setúbal, Portugal
Sandra Oliveira   Polytechnic Institute of Setúbal, Portugal
Sandra Monteiro   Polytechnic Institute of Setúbal, Portugal

This paper outlines the reality of the teaching of statistics in a superior school of business management in Portugal. We begin by presenting the difficulties that teachers encounter, resulting from a variety of problems. A major cause is the enormous heterogeneity of the level of knowledge that students have. We must point out that the introduction of the Bologna process has aggravated this situation. The assumption of reduced classroom hours and an increase in self-study is extremely penalizing for such students. There are many challenges we have to face: How to teach statistics to a class where half the students cannot interpret the basic concepts of mathematics? Is the approach of teaching statistics through software beneficial? Should the teaching of statistics be addressed in a practical way? Should we instill a critical thinking in the students, to enable them to use the knowledge acquired to solve problems?

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C150: The impact of video-based resources in teaching statistics: A comparative study of undergraduates to postgraduates

Norhayati Baharun   University of Wollongong, Australia
Anne Porter   University of Wollongong, Australia

This paper presents the results of a study investigating the use of video-based resources in teaching statistics. This study compares two cohorts of students, which were eighty-six postgraduate, and eighty-nine undergraduate students who enrolled in the subject of introductory statistics at the University of Wollongong. The comparison is based on the impact of learning resources, in particular video resources towards the student learning outcomes and student understanding of topics as well as confidence and anxiety in the subject. At the end of session, students were asked to participate in an online survey via E-learning site. The results showed significant differences in the impact of video resources between postgraduate and undergraduate students. Postgraduate students were much more confident and less anxious compared to undergraduate students after completing this subject.

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C151: Webquest: information and communication technology tool for statistical problem solving for middle school students

Ana Serradó-Bayés   University of Cadiz, Spain

We describe the design of a Statistical Unit “What is the incidence of smoking among young people?” based in developing a cycle of investigation. From a didactical point of view it is an authentic learning environment for grade 10 students. We present the results of the affectivity of this didactic unit through the analysis of the assessment based on students’ reflection on their learning.

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C152: Coin-sequences and coin-combinations taught as companion tasks

Anthony Bill   University of Tasmania, Australia
Peter Gayton   Department of Education, Australia

Using both physical and Fathom™ virtual coins Year 10 students explored the distinction between coin-sequences and coin-combinations (where the order is not important) presented as companion tasks within an integrated coin system. This approach sought to highlight two key concepts within the one teaching unit: coin-sequences, to examine independent events, and coin-combinations, to examine the binomial distribution. The misconception that a particular coin-sequence (e.g. HHHHH) is less likely to occur may arise when a coin-sequence task is re-interpreted incorrectly as a coin-combination (e.g. 5 Heads). Pedagogy was based on principles that emphasised profound understanding through the use of multiple approaches to problem solving.

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C153: Developmental changes in Australian school students’ interest for statistical literacy

Colin Carmichael   University of Tasmania, Australia
Ian Hay   University of Tasmania, Australia

Research in the mathematics context demonstrates that in general students’ interest declines during their secondary school education. Such research has not, however, explored student interest for specific aspects of their learning. This study reports on apparent age differences in student responses to items in a statistical literacy interest inventory. A sample of 791 Australian secondary school students responded on a five-point Likert scale to 31 self-descriptions relating to their interest for statistical literacy. The analysis of cross-tabulations of school year with level of interest revealed that younger students are more likely to be interested in activities related to chance and the use of computers. Older students, on the other hand, are more likely to value the ability to interpret statistics in media and scientific contexts. Interview data is used to illuminate these findings and implications for the teaching of statistics are discussed.

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C154: Statistical analysis from the viewpoint of primary-school teachers and their teaching practice: explorative survey of an Italian region

Renata Clerici   University of Padova, Italy
Emanuela Cisco   University of Padova, Italy

This paper presents a survey of the experience and attitudes of teachers regarding statistics and its teaching in Italian primary schools, and the perception of the importance of statistical culture in children’s education, not only limited to the mathematical sphere, but extended to other disciplines and learning contexts. A snowball sampling procedure was used. The sample involved 300 teachers, covering the NE Italian region of the Veneto. An exploratory analysis was made of the main emerging evidence, particularly teachers’ low level of preparation in the subject and its influence on teaching practice.

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C155: Implementing the change: teaching statistical thinking not just methods

Irene David   University of Canterbury, New Zealand
Jennifer Brown   University of Canterbury, New Zealand

In 2009 we changed the way of teaching our first year statistics course at the University of Canterbury. This paper discusses the changes and presents results from student feedback. The major change in emphasis was to think ‘Why? not ‘How?’ An introductory survey collected student data and the information was used to explore students’ backgrounds and perceptions, to give personal context and relevancy. Teaching and learning is now a combination of lectures, on-line tutorials, computer-based testing, written assignments, and a written exam focused on critical thinking. This combination provides varied pathways of study, important for this large course with over 1,000 diverse students. Feedback from the students during and after the course shows they were very receptive and enthusiastic towards the changes.

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C156: The American Psychological Association Publication Manual sixth edition: implications for statistics education

Fiona Fidler   La Trobe University, Australia

The American Psychological Association (APA) Publication Manual sets the editorial standards for over 1000 journals in the behavioural, life and social sciences. Well known for its referencing standards, the Manual is also an authoritative source of statistical advice for many journals. It is therefore crucial that statistics education in these disciplines address its requirements and recommendations. The sixth edition of the Manual (published 2010) includes new guidelines about reporting effect sizes, confidence intervals and meta-analysis. These changes are a response to calls for the statistical reform of psychology—in particular, calls to decrease reliance on Null Hypothesis Significance Testing—which have been made with increasing vigor over the last 60 years. This paper critically reviews the new guidelines and discusses the implications for statistics teaching within psychology and other disciplines.

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C157: Motivation and self-efficacy related to probability and statistics: task-specific motivation and proficiency

Martin Gundlach   Ludwigsburg University of Education, Germany
Sebastian Kuntze   Ludwigsburg University of Education, Germany
Joachim Engel   Ludwigsburg University of Education, Germany
Laura Martignon   Ludwigsburg University of Education, Germany

Motivational characteristics of learners have shown to be more predictive for proficiency when they are measured for a specific content domain. For proficiency in the area of probability and statistics, there is still a need for research on the role of motivational variables. In particular, taskspecific motivation and interest might contribute to our understanding of the impact of motivational dispositions on the use of learning opportunities. Accordingly, this paper presents empirical results in this area, which are part of the research project RIKO-STAT. We concentrate on the data of 350 prospective teachers, who were asked about content domain-specific and taskspecific motivation and self-efficacy and about solutions to given tasks which were parallelised with the motivation questionnaire. The results suggest interdependencies between task-specific motivation and the proficiency of solving the tasks.

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C158: Teachers’ perceptions of best practice in statistical literacy education

Ian Hay   University of Tasmania, Australia

This paper reports on teachers’ perceptions about how to teach students’ statistical literacy effectively. The interview data used in the analysis were collected from high school teachers located in 7 different schools across one Australian state as part of a 3-year longitudinal study investigating students’ development of statistical literacy. The interview transcripts were examined using the software package Leximancer (Smith, 2009). This program read the text and created a concept map of the data. The resulting map supports the notion that students’ engagement with statistical programs and statistical literacy activities are enhanced when there is a focus on the students: doing; using; understanding; and discussing.

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C159: Aspects of statistical literacy between competency measures and indicators for conceptual knowledge: empirical research in the project “RIKO-STAT”

Sebastian Kuntze   Ludwigsburg University of Education, Germany
Joachim Engel   Ludwigsburg University of Education, Germany
Laura Martignon   Ludwigsburg University of Education, Germany
Martin Gundlach   Ludwigsburg University of Education, Germany

Competencies in the area of statistical literacy have been the subject of several studies which have succeeded in establishing competency measure instruments. However, the approaches differ from each other. Moreover, even though there is a body of research on conceptual knowledge potentially linked with components of statistical literacy, there is a need of collecting empirical evidence on the role of conceptual knowledge for the development of statistical literacy. Consequently, in the research work of the project RIKO-STAT, we focus on the interrelatedness of conceptual knowledge in different areas and the competency of using representations and models in statistical contexts. In the first phase of the project, more than 450 primary students, 600 secondary students and 350 university students were assessed. The paper reports on goals and on the design of the first phase of RIKO-STAT as well as on preliminary empirical results.

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C163: Crisis of statistics pedagogy in India

Madhu Paranjape   University of Mumbai, India

The daunting task for a Statistics teacher in India at tertiary level, to remain relevant in a world driven by technology and increasing demand for data based understanding of reality is two- fold. First is the challenge of motivating students to specialise in Statistics. This is especially so in an environment where the curriculum remains trapped in extensive mathematical derivations with very little scope for students to handle real data-based problems. Secondly, the teacher must develop her expertise as a Statistics professional through research projects and tool building based on primary data. This needs urgent attention in an era when the application of statistical methodology is rapidly penetrating other disciplines and the statistical expertise is outstripping the boundaries of this discipline. This paper looks at the experience and efforts of the author, on both fronts, in her thirty years of teaching and research in Statistics at the undergraduate level.

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C164: Developing robust understandings of variation

Susan Peters   University of Louisville, United States

This retrospective phenomenological study investigates activities and actions identified by secondary statistics teachers who exhibit robust understandings of variation as deepening their understandings of statistical variation. Framed by Mezirow’s transformation theory, analysis revealed learning factors that include interest in the field of statistics, motivation to encounter and resolve dilemmas, reflection on content, and opportunities to engage in learning and rational discourse. The extent to which these teachers seek and embrace learning opportunities may distinguish them from other teachers. This work contributes to understanding circumstances that may be conducive to developing deep understandings of statistical content. It also advances the use of retrospective methods within a theoretical frame for adult learning to investigate teacher learning.

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C165: Creating YouTube videos that engage students and enhance learning in statisitics and Excel

Nicola Petty   University of Canterbury, New Zealand

Short video clips can help teach difficult concepts effectively. A series of videos of three to seven minutes each was developed to teach and reinforce elementary but challenging principles in a first year Quantitative Methods for Business course. The response was very positive from students in the course, and from the worldwide audience who viewed the videos on Youtube. This paper describes the rationale for and the benefits for learning from the provision of self-paced short video clips, and the process by which engaging videos can be developed. It reports on the feedback from students and international viewers and gives hints and cautions to aid in the creation of such videos.

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C166: Interpreting literacy and numeracy testing reports: what do teachers need to know?

Robyn Pierce   University of Melbourne, Australia
Helen Chick   University of Melbourne, Australia

Australia’s national testing of students’ literacy and numeracy provides schools with a range of statistical reports analysing the school’s results. The education authority intends that these data be used to inform planning to improve students’ learning. Although lower secondary mathematics and English teachers see potential for using reports to identify weak students and curriculum topics needing attention, they consider the reports difficult to understand. This paper examines one such literacy test report together with typical “everyday” statistical graphics, and identifies the statistical literacy required to interpret each. The analysis suggests that the statistical literacy needed for interpreting the test report is greater than might be expected of teachers without any specific statistical education. Context-driven, targeted statistical learning will be necessary if testing reports are to inform teachers’ professional practice as intended.

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C167: The use of statistics in real and simulated investigations performed by undergraduate health sciences’ students

Rui Pimenta   Polytechnic Institute of Porto, Portugal
Ana Nascimento   Polytechnic Institue of Porto, Portugal
Margarida Vieira   Portugese Catholic University, Portugal
Elísio Costa   Portugese Catholic University, Portugal
Margarita Viera   Portugese Catholic Univeristy, Portugal

In previous works, we evaluated the statistical reasoning ability acquired by health sciences’ students carrying out their final undergraduate project. We found that these students achieved a good level of statistical literacy and reasoning in descriptive statistics. However, concerning inferential statistics the students did not reach a similar level. Statistics educators therefore claim for more effective ways to learn statistics such as project based investigations. These can be simulated, based on previously supplied data, or real, based on data collected by the students themselves. In this work, we intend to evaluate and compare the statistical reasoning and thinking ability acquired by health sciences’ students when conducting both real and simulated investigations.

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C168: Comparison of attitudes towards statistics in graduate and undergraduate health sciences’ students

Rui Pimenta   Polytechnic Institute of Porto, Portugal
B. Mónica Faria   Polytechnic Institue of Porto, Portugal
Ilídio Pereira   Polytechnic Instititue of Porto, Portugal
Elísio Costa   Portugese Catholic University, Portugal
Margarida Vieira   Portugese Catholic Univeristy, Portugal

Many of the major decisions taken by health professionals have some statistical basis. Nowadays the interest in attitudes towards statistics has increased since there is some evidence that these can impede the effective learning of statistics and/or the correct development of useful statistical intuitions. In this work, we analyze the components of graduate (n=385) and undergraduate (n=507) health sciences students’ attitudes towards statistics through their responses to the Survey of Attitudes Towards Statistics (SATS) scale. Our results show that health sciences’ students have, in general, a positive attitude towards statistics and although graduate students value it more significantly, have better feelings and perception of self-competence, knowledge and intellectual skills, they rate it as difficult as undergraduate students.

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C169: Developing a framework for reasoning about explained and unexplained variation

Jackie Reid   University of New England, Australia
Chris Reading   University of New England, Australia

As a principal form of statistical thinking, consideration of variation impacts on all aspects of statistics. There has been extensive research about students’ reasoning about variation but little research focusing on helping students model variation as a combination of explained and unexplained variation. A study analysed responses to a measurement instrument that was developed to assess tertiary students’ informal reasoning about variation, focusing on explained and unexplained variation. Selected students were also interviewed. This paper reports the analysis of the responses that informed the refinement of a framework that describes six components of reasoning about explained and unexplained variation. Implications for researchers and educators will also be discussed.

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C170: Simulating the risk without gambling: can student conceptions generate critical thinking about probability?

Annie Savard   McGill University, Canada

It is known now that gambling among youth is a major problem around the world. Children and teenagers gamble and some of them become addicted to gambling. In order to help them develop mathematical knowledge about these activities without asking them to gamble, lesson plans about probability were designed and implemented in a grade four classroom. In this teaching experiment, students were asked to simulate the spinning of the wheel using a spinner. The analysis of the students’ representations showed that they used deterministic reasoning to predict the outcome. The awareness of variability of outcome occurred with the comparison of the frequency of each outcome, which helped them change their reasoning to a probabilistic one. Results also suggested that student conceptions about the fairness of the spinner could be considered as a form of critical thinking about the validity of the simulation.

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C172: E-learning of statistics in Africa

Ian Dale   University of Reading, United Kingdom
Cary Clark   University of Reading, United Kingdom
Roger Stern   University of Reading, United Kingdom
Sandro Leidi   University of Reading, United Kingdom
David Stern   Maseno University, Kenya

Some general conclusions are drawn from the experience of converting two face-to-face statistics courses into facilitated, part-time e-learning courses, and running them for several cohorts of African students. The 'Statistics in Applied Climatology' course is for National Meteorological Services staff who need to strengthen their statistical skills for the analysis of climatic data. Part of SIAC was turned into an e-learning course in 2005, and since then it has been completed by over 200 people from 29 African countries. The 'Statistics Made Simple' course was initially developed for UK science students starting a research degree, who have not yet successfully learned key statistical concepts. A number of MSc Statistics students in Kenya also participated: they appreciated both the learning approach and the course content. The success of the courses can be attributed to the enthusiasm and determination of the participants, the high-touch facilitation, and the good quality of the materials.

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C173: The use of computer-based tests to consolidate statistical concepts in Kenya

David Stern   University of Maseno, Kenya
Doug Stirling   Massey University, New Zealand
Ian Dale   University of Reading, United Kingdom
Roger Stern   University of Reading, United Kingdom

A customised African release of CAST (Computer Assisted Statistics Textbooks) has provided much-needed access to a series of modern statistics textbooks for many students in Africa. The recent addition of a collection of interactive CAST exercises has proved valuable in strengthening the learning of statistical concepts by students. A new CAST testing system has been developed to present the exercises as formal test questions. Students can practice beforehand with similar randomised exercises and can get immediate feedback as soon as the test is finished. This paper describes a pilot study in Kenya to evaluate the added benefit of using the CAST tests and is its first evaluation. Use of these tests is linked to an on-line course called “Statistics Made Simple”. The effectiveness of the tests is discussed.

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C174: Incremental modernisation of statistics teaching and curriculum at Maseno University, Kenya

David Stern   Masenp University, Kenya
Omolo N Ongati   Maseno University, Kenya
John Ogonji Agure   Maseno University, Kenya
Betty Ogange   Maseno University, Kenya

Modernisation of statistics teaching is a continual problem the world over. The advances in statistical methods and tools along with the growing demand of applied practitioners creates a dual need of people with the theoretical knowledge to take the subject further and those with the practical knowledge and skills for the many current problems requiring statistical support. The universities in Kenya are largely still teaching theory as was done 40 years ago. Change is possible and initiatives like the RUFORUM M.Sc. in Research Methods show that with sufficient resources a modern curriculum can be created in Kenya in a short space of time. Maseno is a young university, less than 20 years old. With very few resources the department of mathematics and applied statistics has been taking a more gradual approach to modernise their teaching. This paper describes what has been achieved, our current work and what is planned.

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C175: Visual representation of the syllabus content about “data”

Theodosia Prodromou   University of New England, Australia
Chris Reading   University of New England, Australia

Concept maps (cmaps) are graphical tools that illustrate complex networks of interconnections between concepts. These can be used to illustrate the concept connections implicit in teaching syllabus content thus facilitating sense-making and meaningful learning. This paper sheds some light upon pre-service teachers’ understanding of the interconnectedness of basic concepts for the topic of “Data” as evidenced in their construction of comprehensive cmaps. The illustrative networks designed by pre-service teachers were analyzed in relation to what connections were made and the quality of statements between connecting links/nodes. The results showed the variety and complexity of the interconnectedness of pre-service teachers’ understanding of the concepts. Implications for both teaching and research are provided.

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C176: Teaching statistics in the context of biology: the symbiosis experience

Edith Seier   East Tennessee State University, United States
Karl H Joplin   East Tennessee State University, United States

We are part of a team that designed and taught a sequence of three integrated courses combining biology, mathematics, and statistics, at the freshman/sophomore level (SYMBIOSIS project, HHMI grant # 52005872). This presentation describes the statistical content of the integrated courses and the stand-alone introductory statistics course that emerged from it. The focus of the paper is on the questions that arose in the design of the courses and the way they were addressed when preparing the syllabus and the teaching material.

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C177: The teaching of statistics and probability in mathematics undergraduate courses

Lorí Viali   Federal University of Rio Grande do Sul, Brazil

In Brazil the basic system of Education is divided in Elementary School I (ages 6 or 7 to 9 or 10 with a generalist teacher, usually a pedagogy undergraduate) involving the grades 1 to 4 and Elementary School II (ages 11 to 13 with a specialist teacher) including the grades 5 to 8 and a 3 and in some cases 4 years of high school involving, also, a specialist teacher. The faculties who teach Statistics courses in universities come from a number of areas such as Statistics, Mathematics, Economics, etc. However, in Elementary II and High school, teachers with a degree in Mathematics teach the Statistics courses. The promulgation of the 1996 LDB (Brazilian Education Basic Tenets Law) has made Statistics and Probability part of the content of the curriculum of Elementary (I and II) and High school. This study analyzed the curriculums of Mathematics undergraduates programs in Brazil.

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C178: Strategies to make counter-examples while comparing two groups

Kai-Lin Yang   National Taiwan Normal University, Taiwan
Wen-Han Chang   National Taiwan Normal University, Taiwan

In this paper, we aim at analyzing how pre-service and in-service mathematics teachers make a judgment about comparing two groups which requires several important concepts. The research questions include: (1) Which concepts are applied to make a judgment about comparing two groups? (2) How are the counter-examples made? In our study, teachers were asked to make a judgment about comparing two groups individually and then explained their judgments in class. The result shows that most teachers prefer using concept of mean to represent the outline of the whole distribution. And the strategies of successfully making counter-examples include thinking with (1) proportion-based, (2) properties-oriented, (3) statistics-modified, and (4) unfixing a sub-group. Implications and further research will be suggested in relation to roles of making counter-examples for learning statistical thinking.

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C179: Interaction in synchronous chat tutorials to facilitate learning in introductory statistics

Christine McDonald   University of Southern Queensland, Australia
Birgit Loch   University of Southern Queensland, Australia
Margaret Lloyd   Queensland University of Technology, Australia

This paper investigates interaction in synchronous chat tutorials trialed in an introductory statistics course offered in distance education mode. The Community of Inquiry (CoI) framework of Garrison, Anderson and Archer, while primarily developed to inform online asynchronous discussion groups in non-mathematical contexts, is used to describe the interactions in these online tutorials. Transcript analysis was performed on three chat logs of weekly online sessions and the three presences of the CoI framework - social, cognitive and teaching presence - were identified. The changing dynamic amongst these presences across the semester was explored. Preliminary results indicate that the balance of the presences changes over time and, while it is suggested that this may be associated with the difficulty of the content, further investigation is needed.

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C180: Pre-service teachers’ understanding of probability distributions: a multilevel statistical analysis

Theodore Chadjipadelis   Aristotle University Thessaloniki, Greece
Sofia Anastasiadou   University of Western Macedonia, Greece

In this paper the problem of pre-service teachers’ approaches in solving tasks in probability distributions is discussed. Statistical data were obtained from 98 Greek pre-service teachers from the Western Macedonia University that formed the experimental group and 132 Greek pre-service teachers from Macedonia University that form the control group, enrolled in two basic statistics courses. The control group participates in teacher-centred teaching environment. The experimental group participates in student-centred teaching environment connected with probability distributions. Results indicate the difficulty of control group in defining the difference between discrete and continuous distributions. In addition the estimation of the Poisson distribution parameter λ troubled the majority of the control group while the experimental group showed higher success rate.

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C181: On teaching basic statistics: a capture-recapture example

Flavia Mascioli   University of Rome, Italy
Carla Rossi   University of Rome, Italy
Daria Scacciatelli   University of Rome, Italy

Nowadays many of us know that in an introductory statistics course great emphasis should be placed on problem-solving and active learning. This paper presents a real capture-recapture experiment used as a starting point to introduce fundamental concepts as experiment, sample variation, sampling distribution and bootstrap. It has been used in an introduction to statistics 2 course for undergraduate biology students; a particular attention has been given to their special interest in learning how to use statistics to solve problems and to their general negative attitude towards this discipline. A bootstrap application, based on the observed experimental data, has been carried out using the R package. Student feedback and reactions are also discussed.

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C182: Trajectories of learning in middle years’ students’ statistical development

Rosemary Callingham   University of Tasmania, Australia

The middle years of schooling (Grades 5 to 9; ages 10 to 14 years), critical in students’ mathematical development, are also characterised by a dip in mathematics performance. Typically, the greatest drop occurs at the transition between primary and high school. StatSmart is a large-scale longitudinal study addressing statistics teaching and learning in the middle years in three states in Australia, one of which has Grade 7 as part of the primary school, whereas in the other two states Grade 7 marks the start of high school. Student understanding of statistics is measured three times using Rasch measurement to compare performances at different points in time. Two cohort measures indicated that there was a plateau in performance between the first and second year of high school, rather than at the primary/high school transition. The trajectories of learning identified are discussed.

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C183: Statistics for the mathematically challenged

Michael Bedwell   Wisconsin International University, Ukraine

In this paper I argue how we can impart deep understanding of inferential statistics by the early introduction of two approaches that students normally encounter only late in their studies, if at all. These are non-parametric methods and ANOVA. As illustration, we imagine a marathon race where firstly there are just two teams with two runners each, and secondly where there is a third team with two or more runners. We consider various statistics we could use to decide the result, thus discovering the concept of statistical tests in general, and why the chi-square statistic in particular is so important. Following the path of this discovery requires only elementary arithmetic. This is in accordance with the author’s belief that students weak in mathematics can learn the fundamentals of inferential statistics at least as readily as a Euclid or a Newton.

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C184: Dissemination of good practice in teaching, learning and assessment of statistics in higher education

Nasrollah Saebi   Kingston University, United Kingdom
Penelope Bidgood   Kingston University, United Kingdom

The Association of Statistics Lecturers in Universities (ASLU) was founded in 1983 “to foster and support the development of statistical education”. This paper aims to demonstrate how this has been achieved through the Association’s regular conferences. These bring together teachers of statistics in HE institutions to highlight teaching, learning and assessment issues and how these respond to a changing student intake and the knowledge and skills required by employers. Speakers are invited from those lecturers who can demonstrate good practice or who have novel ideas in teaching, learning or assessment that may benefit ASLU’s members. Other presenters are those who can report on wider issues in statistical education such as funded research.

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C185: The student project: the importance of using statistics in being an agricultural scientist

Annalene Sadie   Stellenbosch University, South Africa

The use of real world projects in introductory statistics courses has become common practice, and the advantages of active student participation in the learning process have been well documented. Involving students in small groups also addresses the problem of large class size and outcomes specified by the South African Qualifications Authority. However, finding a research topic that would generate common interest, and incorporates project management and experimentation, when students come from a variety of subject fields is a challenge. In the South African context diverse backgrounds and accommodation on/off campus also need to be considered. Although learning through play is not usually associated with teaching at tertiary level, feedback from third year Agricultural Science students has shown that project topics with a fun element not only enhance successful learning, but contribute to positive attitudes of students towards statistics.

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C186: Developing statistical consultancy skills in post-graduate students: a case study

Stuart Sharples   University of Lancaster, United Kingdom
Emily Yeend   University of Lancaster, United Kingdom
Brian Francis   University of Lancaster, United Kingdom
Gareth Ridall   University of Lancaster, United Kingdom
Jill Booth   University of Central Lancashire, United kingdom

The training of postgraduate students in transferable skills is becoming increasingly important in the UK across disciplines. For postgraduate statisticians, a crucial ability is to be able to develop consultancy skills. These include the ability to interact with a client, to distil the nature of the problem, to choose a suitable methodological approach and to communicate results effectively. This paper describes a case study in developing such skills from the point of view of the students.

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C187: New e-learning course for social survey and introductory statistics

T Hirose   Rikkyo University, Japan
Y Kanazawa   Rikkyo University, Japan
Y Arakawa   Rikkyo University, Japan
M Kagawa   Rikkyo University, Japan
T Mizuhara   Rikkyo University, Japan
Kazunori Yamaguchi   Rikkyo University, Japan

This paper introduces a new e-learning course for principles and methods of social survey and introductory statistics, which are for all students in Rikkyo University. The course consists of the following four subjects; Introduction to the social survey, Social Survey Methodology, Introduction to the Statistics: Descriptive Statistics, Introduction to the Statistics: Statistical Inferences. These subjects are accredited by Japanese Association for Social Researchers as the course for social researchers. Students can learn about survey methods, for example, designs of samples, how to make questionnaires and so on, as well as basic statistics in this course. Usages and linkages to the official statistics in Japan, videos titled statistics for daily life, and interactive learning contents are included in the course.

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C188: Simulation using R from within Excel for teaching first year biologists

Gareth Ridall   University of Lancaster, United Kingdom

In this paper we describe the efforts that we are making to engage and impart statistical understanding to a large group of first year degree-level biologists. By using an online assessment system we have confirmed the extent of large areas of statistical misunderstandings. In this paper we describe our strategy for breaking down these statistical understandings using software that is free and can be run within an Excel worksheet.

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C189: Teaching statistics through ExperimentsAtSchool

Mark Crowley   Nottingham Trent University, United Kingdom
Kate Richards   University of Plymouth, United Kingdom
Neville Davies   University of Plymouth, United Kingdom

In this paper we describe the development of a project to provide Internet-based resources for collecting and disseminating data collected from experiments based on ideas from science and psychology. We discuss how both the website and the method of capturing data have evolved and led to our recent redesign of the ExperimentsAtSchool website (www.experimentsatschool.org.uk). We explain how these interactive experiments, which are both fun and engaging for learners, provide innovative ways for helping them to develop and improve their data handling and statistical skills.

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C191: Training of lecturers at Maseno University, Kenya

James Musyoka   Maseno University, Kenya
David Stern   Maseno University, Kenya
Joyce Otieno   Maseno University, Kenya

Lecturers in Kenyan universities usually start their work without any prior training on how to teach students. Hence the teaching tends to be traditional and new training techniques are rarely implemented. For effective teaching, lecturers need to develop skills on preparation and presentation of new course materials, using modern methods. One of many changes to the statistics teaching at Maseno University was to teach an MSc. course in a way that also provided staff training. The course combined an international e-learning course with lecture notes which had previously been taught by a visiting lecturer. Two junior staff were given the day to day responsibility of teaching the new MSc course, with a senior lecturer observing, advising and taking overall responsibility. This paper describes the course and the learning experience.

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C192: The growing role of computers for teaching statistics in Kenya

Parin Kurji   University of Nairobi, Kenya
Brigid McDermott   University of Nairobi, Kenya
David Stern   Maseno University, Kenya
Roger Stern   University of Reading, United Kingdom

Until recently, the teaching of statistics in East Africa has been a traditional chalk-and-talk affair. In the last few years computers have become more widely accessible. At the same time many statistical resources of the highest quality are freely available for Africa, including Computer- Assisted Statistics Textbooks (CAST), an electronic textbook, GenStat Discovery Edition, (a statistics package), and training resources such as the Southern African Development Community (SADC) Training Pack DVD prepared by Statistics Services Centre (SSC) , Reading University. This means that change is not only possible but is within reach of lecturers all over Africa. Experiences at two Kenyan universities are described. Initiatives for undergraduates and postgraduates in both service teaching and specialist teaching of statistics are discussed.

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C193: Teaching strategies to promote statistical literacy: review and implementation

Svetlana Tishkovskaya   University of Lancaster, United Kingdom
Gillian Lancaster   University of Lancaster, United Kingdom

In the past few years statistics educators have emphasised the importance of statistical literacy in the statistics education reform movement. Many educational researchers argue that the topic of statistical literacy should be part of an introductory statistics course syllabus. This article gives an overview of useful techniques for developing a reform-based statistics course, underlining the place of statistical literacy in this framework. Summarised recommendations incorporate many innovations employed in a variety of successful statistics classes today. We suggest that introductory statistics courses, and in particular the statistical literacy component, will benefit from additional curricular material aimed at encouraging students to become informed and critically thinking consumers of statistical information, thereby promoting motivation to learn statistics. The directions and approaches to developing such curriculum material are discussed.

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C194: Resource discovery for teaching datasets.

Valmira Hoti   Lancaster University, United Kingdom
Brian Francis   Lancaster University, United Kingdom
Gillian Lancaster   Lancaster University, United Kingdom

The use of relevant and appropriate datasets is recognised as an important prerequisite in teaching statistics to non-statisticians. Such examples help to provide motivation for the student and can aid both understanding and performance. While impressive resources such as the Data and Story Library and the datasets section of STATLIB exist, there is a need for a more comprehensive index of datasets which are freely available on the web. Datasets exist in a wide variety of locations, however, and it is often a hard task for the lecturer to find an appropriate dataset which both illustrates a particular technique and is relevant to the background of the student. This paper discusses the problem of constructing a resource to allow lecturers to discover appropriate data sources. It reports on a demonstration project which is trawling a wide number of types of data sources for relevant datasets, and describes the successes and pitfalls.

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C197: Distance learning for teacher professional development in statistics education

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

The paper provides an overview of EarlyStatistics, an online professional development course in statistics education targeting European elementary and middle school teachers. The course utilizes distance education to offer high-quality professional development experiences to teachers across Europe. It facilitates intercultural collaboration of teachers using contemporary technological and educational tools and resources. An online information base offers access to all of the course content and resources, resulting in a complete and flexible teacher professional development program.

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C198: Statstutor: an on-line statistics learning and teaching resource

Alun Owen   Loughborough University, United Kingdom
David Green   Loughborough University, United Kingdom
Moira Petrie   Loughborough University, United kingdom
Neville Davies   University of Plymouth, United Kingdom
John Marriott   University of Plymouth, United Kingdom

Statstutor is an on-line statistics learning and teaching resource, being developed by the sigma Centre for Excellence in Teaching and Learning (CETL) at Loughborough and Coventry Universities, in collaboration with the Royal Statistical Society Centre for Statistics Education. It differs from existing on-line resources, focusing on the practical application of statistics using both a topic based approach for learning, as well as opportunities for learning through a problem solving approach using case studies. It combines video, paper-based and other electronic media into one environment. It is a pilot project which will form part of the mathcentre family of on-line mathematics resources (www.mathcentre.ac.uk). This paper describes the project’s development, and lists the resources that are available. We hope the paper will motivate discussion of our approach and the content of statstutor and, in turn, help to inform us about directions we should take for post-pilot developments of the resource.

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C201: Developing research literacy in academic medical research institutions: introducing an online modular course in biostatistics and epidemiology

Mohamed Abdolell   Dalhousie University, Canada
Jennifer I. Payne   Dalhousie University, Canada

We describe our project to develop research literacy amongst medical residents in an academic medical research institution via an online modular course in biostatistics and epidemiology. Traditional introductory courses to statistics and epidemiology in this context have historically generally failed due to their esoteric rather than practical focus, the inflexible in-class format with fixed timeslots and locations, and the cumulative loss of knowledge associated with missing one or more lectures. Our use of real-world clinical data sets and the online modular course format eliminates these barriers. This course format leverages the synergistic relationships between content, pedagogy, and technology by employing video pod casts and accompanying lecture notes, open-source software for interactive graphical exploration of statistical concepts, and live online tutorials. Medical residency program directors can select any subset of modules to create customized courses for their programs. The course is delivered using Moodle and there are no associated registration costs for students.

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C202: Hidden jargon: everyday words with meanings specific to statistics

Christine Anderson-Cook   Los Alamos National Laboratory, United States

If students of statistics or our collaborators from other disciplines do not immediately understand the terms “probit regression” or “kriging”, we are not surprised and are happy to carefully explain these advanced statistical terms and concepts. A different class of words has one or more distinct statistical meanings in addition to their standard English definitions and is ripe for confusion among students. More subtly, some of the key words of statistics, such as design, parameters, model and analysis, are also the key words of other disciplines. Each discipline has assigned subtle associations to these words beyond their standard dictionary definitions with hidden connotations and implied connections to concepts. We consider some multi-discipline keywords, discuss how to build awareness about the potential for confusion by interdisciplinary collaborators or out-of-major students, and how to resolve the communication gap.

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C203: Student attitudes to real-world projects in an introductory statistics course

Ann Bingham   Peace College, United States

Constructivist research has shown that for real mathematics learning to occur, students need to be engaged, active learners rather than passive recipients of knowledge. Student projects can often facilitate this engagement. In an introductory statistics class for liberal arts students, a series of authentic projects were assigned. The projects showcased real world applications of material recently studied in the classroom. They varied from analysis of public data available on the internet to gathering and analyzing data collected via student-designed surveys. This paper discusses student reflections on the learning that occurred while completing these projects. Initial reactions were often dismay and discouragement, but a survey given to all students near the end of the course found more positive attitudes. Longer surveys were sent to a random sample of students. We consider students’ attitudes and perceptions of their learning successes and difficulties.

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C204: Statistics education in the context of critical education: teaching projects

Celso Campos   University Estadual Paulista, Brazil
Maria Lucia L. Wodewotzki   University Estadual Paulista, Brazil
Otavio Jacobini   Pontifical Catholic University of Campinas, Brazil
Denise Lombardo   Pontifical Catholic University of Campinas, Brazil

Statistics Education researchers identify the development of three competences: statistical literacy, thinking and reasoning as relevant in teaching and learning of Statistics. These competences are linked to an education aimed at the formation of critical citizenship, which is in accordance to the principles of Critical Education. In this article we present three projects where this combination of goals is explored. The contents of Statistics are linked to discussions about social and political problems; students work with real data relating them to the context which they are part of, understand the results, criticize and discuss ideas, and work in groups. Hence we encourage the development of the three competences above, together with the principles that surround Critical Education. Consequently, we see that Statistics Education and Critical Education interact and complement each other, showing harmony of purposes, which is favorable to a truer education.

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C205: Recipe for a Cobb salad in a time of easy computability

Robert H Carver   Stonehill College, United States

Technology continues to change not only how we teach, but also what we teach in the introductory course. Recently there has been lively discussion about which topics belong in the course. George Cobb has challenged us to rethink the curriculum in light of the computational power of our technologies. This paper proposes a framework for structuring a course using JMP, omitting some traditional topics, leaving space for emphasis on concepts, on data production, on visualization, and on topics that are rarely included in an introductory course. Through such a structure, we can more directly connect statistics education to students’ disciplinary contexts in business, engineering, social and natural sciences, etc. Additionally, we can strengthen students’ conceptual foundations in the field so that, in their roles as citizens and professionals, they can become more critical consumers of statistical arguments.

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C206: Enhancing statistical literacy through short open-ended questions that involve context, data, and upper level thinking

Mahtash Esfandiari   University of California, Los Angeles, United States
Hai Nguyen   University of California, Los Angeles, United States
Yuliya Yaglovskaya   University of California, Los Angeles, United States
Robert Gould   University of California, Los Angeles, United States

Communication of statistical results through writing has been recognized as one of the major objectives of any statistics course. The first step we took toward this objective was developing a bank of multiple-choice questions that involve real context and data relevant to students’ lives. While the majority of students (more than 70%) are able to identify the correct answer to concepts such as confidence interval and P value, they are not able to generate correct written responses to the same concepts. We report on a National Science Foundation project to create short open-ended questions involving real context and data, three typical answers (excellent, satisfactory, and inadequate), a detailed rubric, and a computerized system to score the students’ responses. Consequently, the students will enhance their statistical literacy though examination of the typical answers, generating written responses, and creating connections between major concepts covered in the lecture and data analysis labs.

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C207: Introducing large data sets into the classroom: a graphical user interface for teaching with databases

Ulrike Genschel   Iowa State University, United States
Heike Hofmann   Iowa State University, United States
Danielle S. Wrolstad   Iowa State University, United States

Analysis of large, complex data sets is increasingly relevant for today’s statisticians. To help facilitate training of databases and SQL (Structured Query Language) at the undergraduate level, we propose a graphical user interface allowing for statistical analyses of large databases using subsampling techniques. The example database contains information on 25 variables for over 120 million commercial flights across the United States since 1987, including information on originating and destination airport and temporal information, such as planned flight schedule, actual take-off and landing times and further qualitative variables. Textual output of a session's SQL commands summarizes students' attempts in interacting with the database providing not only feedback to the instructor but also serving as starting points for more complex aspects of the SQL language similar to SAS (Statistics Analysis Software) scripts initiated from JMP sessions.

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C208: Enhancing conceptual understanding with data driven labs

Robert Gould   University of California, Los Angeles, United States
Gretchen Davis   University of California, Los Angeles, United States
Rakhee Patel   University of California, Los Angeles, United States
Mahtash Esfandiari   University of California, Los Angeles, United States

Teaching introductory statistics with a data-driven curriculum presents many challenges for the instructor. One challenge is to provide students with opportunities to work with data in a realistic context. If not done carefully, students spend their time struggling to learn the software, not engaging with the data. Students might be able to follow step-by-step instructions to "see" how data analysis is done, but still fail to connect this to important concepts. We report on a project to create a set of data analysis activities that use Fathom to engage students in exercises that emphasize the challenges of statistical inference beginning in the very first week of the course; involve students with real data and real research questions; and require students to discover analysis procedures on their own. The resulting set of labs emphasizes simulation and randomization-based inference procedures while working in the context of real data.

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C210: Linking the randomization test to reasoning about p-values and statistical significance

Sharon Lane-Getaz   Saint Olaf College, United States

This quasi-experiment compares student learning outcomes from three college statistics courses to investigate whether greater randomization test content explains gains in conceptual understanding of inference, adjusting for prior knowledge and mathematical ability. The study uses a 34-item Reasoning about P-values and Statistical Significance (RPASS) scale to measure gains in students’ inferential understanding. Of two introductory courses, one has limited randomization content (n1 = 55). The second emphasizes randomization, simulation, and P-values throughout (n2 = 26). The third is a second course in statistics that reviews randomization tests at the beginning of the course (n3 = 24). Comparative results, score reliability, and the changes in respondents’ correct conceptions and misconceptions are reported. Directions for future research are discussed.

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C212: A key problem: pedagogical tradeoffs along familiar and generic dimensions

Dragan Trninic   University of California at Berkeley, United States
Dor Abrahamson   University of California at Berkeley, United States

The design and selection of pedagogically effective problem situations is a critical yet undertheorized facet of reform-oriented mathematics education. Drawing on instructional-design frameworks and cognitive-science theory, we propose a situation taxonomy centered on the dimensions “familiar” and “generic” and hypothesize the contrasting learning affordances of exponents thereof. 51 undergraduate students solved either a familiar or a generic version of a compound-probability problem, and subgroups thereof then participated in semi-structured clinical interviews. Familiar problems evoked common sense, yet their treatment was liable to be mathematically non-normative; generic problems triggered mathematically suitable treatments, yet these treatments were liable to remain opaque. We discuss implications of these tradeoffs with an eye to fostering mathematical-probabilistic literacy that is both powerful and grounded.

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C213: Teaching introductory statistics using student generated data in a large class

Aklilu Zeleke   Michigan State University, United States
Carl Lee   Central Michigan University, United States

During the past few years, we used hands-on activities generated by students in a large introductory statistics course for science majors. In this paper, we will share some strategies of incorporating in-class and online real time activities and discuss issues related to group projects, group formation and learning outcome assessment. Our experience suggests that student attitudes towards statistics and motivation of learning statistics have increased, and the learning outcomes related to conceptual reasoning have also increased. We will also address approaches we took to overcome some major challenges we encountered.

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C215: Teaching statistics in a language other than the students’

Khidir Abdelbasit   Sultan Qaboos University, Oman

In many developing countries the language of instruction at universities is English, while teaching at pre-university level is in the local language. The common reason is that most of the scientific literature is in English and teaching in the native language may leave graduates at a disadvantage. Statistical concepts and methods are most effectively taught through real life examples that the students appreciate and understand. Almost all the textbooks used satisfy this requirement for western students, but most of the examples and exercises used are completely alien to students in the developing world. With limited English they have serious difficulties understanding what is explained in lectures and textbooks. The result is loss of interest in the subject and concentration on passing tests instead of acquiring the intended knowledge and skills. The paper discusses language and cultural difficulties faced by the students in learning Statistics and the challenges to instructors.

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C217: Interpretative skills and capacity to communicate statistically: a differential analysis

Emília Oliveira   Escola Secundária de Tomaz Pelayo, Portugal
Pedro Campos   University of Porto, Portugal

One of the common dilemmas in the teaching and learning of statistics is the (lack of) reasoning that students demonstrate to deal with data. It is indeed a major problem in Initial Data Analysis: there is not a clear understanding of the data in order to highlight useful information and suggest conclusions to support decision making. To better understand the types of problems involved in this dilemma we have made a survey, based on simple problems in which students are invited to interpret the original data as well as tables and graphics. The main results of this survey indicate that students have a need of creativity to interpret statistical data, particularly when the concepts are learned in previous levels. The consolidation of the statistical concepts is missing as there is not enough memorization by students in order to apply the descriptive facet of the statistical cognition.

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C218: University introductory statistics courses in Iceland

Auðbjörg Björnsdóttir   University of Minnesota, USA

The purpose of this study was twofold: first to gather information regarding teaching of the introductory statistics courses at the university level in Iceland and to gain more insight about educational beliefs of those teaching these courses and to see how well their teaching is aligned with the Guidelines for the Assessment and Instruction in Statistics Education (GAISE, 2005). An online survey was used. Results suggest that the reform in statistics education that has taken place in the last three decades has not yet reach Iceland. The comparison with the GAISE recommendations supports this as it suggests that instructors of introductory statistics courses at the University level in Iceland are not aligned with the GAISE recommendations. The exception is the use of technology GAISE guideline. It appears that technology is well underway in introductory statistics courses taught at the University level in Iceland, with the exclusion of using technology in developing concepts in class.

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C251: Statistical data analysis in psychology. generation of self examination questionnaires for students: approach to the item

Joan Guàrdia-Olmos   University of Barcelona, Spain
Maribel Peró-Cebollero   University of Barcelona, Spain
Montserrat Freixa-Blanxart   University of Barcelona, Spain
Jaume Turbany-Oset   University of Barcelona, Spain
Amàlia Gordóvil-Merino   University of Barcelona, Spain
María Carrera-Fernández   University of Barcelona, Spain

The aim of this contribution is to present an approach to item analysis in a self-examination questionnaire for students in Statistical Data Analysis for Psychology. We have worked with a sample of 413 students from the Faculty of Psychology from the University of Barcelona during the 2008-09 academic year. They answered three different closed questionnaires (20 to 30 items each) about general and specific statistics topics. The study of the results was made according to the item response theory. The third questionnaire (tools of inference statistics) was the best one in discrimination rates, while the second one (probability models) presents a balanced distribution of items in terms of their rates of difficulty. Finally, the first questionnaire seems to be the easiest one (descriptive statistics). The conclusions show that self-examination can be a useful system of student assessment but not for the entire topic in a course on statistics for psychology students.

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C253: Meta database for datasets regarding statistical education

Peter Pipelers   Ghent University, Belgium
Ellen Deschepper   Ghent University, Belgium
Heidi Wouters   Ghent University, Belgium
Olivier Thas   Ghent University, Belgium
Jean-Pierre Ottoy   Ghent University, Belgium

This project involves collecting didactic examples and datasets in the statistical field used for educational motives. Teachers often find it hard to come across good example datasets, accompanied with metadata of the collection procedure, the statistical methods used to analyze the data, which specific problems must be taken into account when conducting the analysis and specific background information regarding the dataset. The core of the project is the realization of a meta database, classifying the data and metadata with their sources (book, research and consultancy assignments), and the implementation of a user-friendly environment to generate structured search requests on the properties of the analyses on the (MySQL) database using a graphical user interface (Java Swing). The generic structure of the database allows to add analyses in conformity with the database design.

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C254: How students learn about data distribution when addressing a problem affecting their community

Yury M. Rojas   District University and University of the Andes, Bogotá, Colombia

This research examines the way in which 9th graders learn about and come to understand data distribution and the related statistical notions of center and spread measures. In the study discussed herein the students in question identify and then collaborate to address the problems affecting their community. Using two sample groups, the students examine and make inferences about how the existing socioeconomic structure of their community affects nutrition. From the data gathered I find that cooperative work on a problem that is culturally relevant and meaningful to the students who propose it aids comprehension and recognition of data distribution and its measures.

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C255: Chilean primary teachers challenged to build PCK for statistics

Raimundo Olfos   Pontifical Catholic University of Valparaíso, Chile
Soledad Estrella   Pontifical Catholic University of Valparaíso, Chile

This paper analyzes three questions about teachers understanding of teaching statistics as part of a study that addresses the relationship between the pedagogical knowledge of statistics in primary teachers in Chile and its impact on students learning. This work is part of a study that looks for evidences of the association between teacher Pedagogical Content Knowledge and the effectiveness in teaching statistics that is focuses in 4th and 7th grade. Thirty-one teachers from different schools of Valparaíso district were tested after reading a short text referred to non typical values and properties mean. They answered the questions showing a rigid understanding of statistic, as part of mathematics, like a formal discipline. This account evidences primary teachers’ privilege procedural approach than understanding problem solving approaches.

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C256: Changing the understanding of probability in talented children

Soledad Estrella   Pontifical Catholic University of Valparaíso, Chile
Raimundo Olfos   Pontifical Catholic University of Valparaíso, Chile

This paper refers to the effectiveness of an instructional sequence of lessons related to Probability, which were implemented to 11 to 13 years old talented children. This instructional sequence as part of a one semester math course, aims to develop children’s understanding of probability. Contextualized situations involve decision making into uncertainty, confrontation of intuition with experimental probability, and adhesion to theoretical probability. The pretest included equiprobable and non-equiprobable, independence and dependence concepts. Lessons were focused on students´ work, especially in pairs and small groups. Experimental situations always included plenary discussion, where the teacher acted as moderator. The posttest gave evidence of overcoming preconceptions and adhesion to the principles of theoretical probability.

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C257: Development and validation of the statistics teaching inventory (STI)

Jiyoon Park   University of Minneapolis, USA

The reform movement in science, technology, engineering, and mathematics has prompted calls for research to provide a better understanding of factors related to desired learning outcomes in introductory statistics courses. However, little is known about instructor factors involved in teaching statistics. This study describes the development and validation of the Statistics Teaching Inventory (STI) designed to assess the practices and beliefs of teachers of introductory statistics courses across the disciplines. Survey data were collected from 101 instructors from different institutions in the United States. Reliability coefficients were high (>0.75) for two subscales (practice and beliefs) and item-total correlations were generally at an acceptable level (>0.30). Summaries of individual response patterns and the relationship between the beliefs and practice subscales are presented. The study concludes with limitations related to the sample size, sample characteristics, and psychometric properties based on summated scores, and suggests future research.

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C258: Ethical-political aspects of statistical literacy

Karen François   Free University Brussels, Belgium
Jean Paul Van Bendegem   Free University Brussels, Belgium

The aim of this paper is to give a philosophical insight into the ethical and political aspects of the concept of statistical literacy from a historical perspective. The growing interest into the accessibility of statistics goes hand in hand with the fact that statistical information is penetrating in growing measure the forms of personal and public life. It was part of the ethical-political agenda of the Wiener Kreis in 1929 to bring the scientific world-conception closer to human beings living in this world. We can see the same ethical-political programme within educational theory where the questions of literacy became a matter of ethics based on the general idea of emancipation which can be found in the UNESCO’s view on education (1948). Moreover we see in its mission a tight connection with the socio-economic development, focusing on an enduring and peaceful world, while respecting diversity and maintaining human rights.

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C259: The significance of residuals on modeling data

Markus Vogel   University of Education Heidelberg, Germany

When modeling data one important rule to consider states: the model should fit the data and not vice versa. There is one problem well known by teachers and researchers: Students often do not realize the gap between data and model, they mistakenly consider the model as reality. In this situation the residuals defined as the difference between data and model become important: they remind us of modeling the trend in data and not the data itself. Whereas the model stands for the explained variation, the residuals represent the unexplained variation. This is at the core of statistical thinking. In this paper, the significance of the residuals for modeling data is examined from different perspectives.

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C260: An experience in curriculum design for high school statistics education

Felipe Fernández   Universidad Pedagógica Nacional, Colombia
Luisa Andrade   Universidad Pedagógica Nacional, Colombia

This paper reports on an exercise of laying out a series of teaching sequences aimed at developing statistical reasoning in high school students. From a conceptual perspective, we examined the distinctions concerning the notions of statistical literacy, reasoning and thinking and considered three working scenarios reported in literature (data sets, sampling and probability situations) as referents for the design of information sampling and analysis. Based upon the methodology of teaching experiments, we proposed hypothetical learning trajectories, which served to guide both before- and after-design instruction in a dynamic way. Instruction results provided elements that point at reviewing the curricular design as well as the preconceptions of participants in the research.

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C265: Is median an easy concept? Semiotic analysis of an open-ended task

Silvia Mayén   National Polytechnic Institute, México
Carmen Díaz   University of Huelva, Spain

In this paper we analyse the responses given by 643 Mexican students from Secondary Education and High School to a problem involving the comparison of ordinal data. Using some ideas from the Onto-semiotic approach proposed by Godino and colleagues, we carry out an analysis of the open responses, taking into account the central tendency measure used in the comparison and the students’ conflicts. We use the Chi-square test to study the possible dependence between responses and school level. We observe better results in secondary school students who use median and mode more frequently, although they also tend to omit the response more frequently.

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C266: Teaching statistics to a heterogeneous group: a “Goal-Oriented” approach

Saleha Habibullah   Kinnaird College For Women, Pakistan

Teaching elementary concepts of statistical methodology to a heterogeneous group in a small span of time such as a workshop presents a peculiar challenge: how to create a balance between presenting content that is “too difficult” for the beginners and “too boring” for those who already have some orientation of Statistics! This paper presents an account of a particular strategy that was adopted for teaching basics of statistical methodology to a heterogeneous group of facultymembers at a workshop in Lahore, Pakistan–one involving a ‘goal-oriented’ approach. Feedback from the workshop participants indicates that such a strategy is likely to be successful in arousing the interest of the entire group, of creating the urge in beginners for learning that which is ‘too difficult’, of developing patience among those who 'already ‘know it all’, and–eventually–creating a sense of accomplishment and satisfaction in the entire group.

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C271: Reviewing and promoting research in probability education electronically

Ramesh Kapadia   University of London, England
Manfred Borovcnik   Alpen-Adria Universität Klagenfurt, Austria

In the topic study group on probability at ICME 11 a variety of ideas on probability education were presented. In an international, collaborative, project after the conference, many of these papers have been developed much further, incorporating novel electronic techniques, which also feature in this paper, with links to many references rather than a simple listing. This joint presentation provides a summary of the main threads of research in probability education across the world; there is a linked paper on possibilities of electronic communication (The future of interactive electronic research). This paper provides an incisive and reflective summary on which researchers can build, while the latter enables developments relevant for other areas of research too. Hyperlinks are included throughout.

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C273: The effects of an Audience Response System (ARS) on achievement and attitudes towards statistics in a introductory statistics class

Megan Mocko   University of Florida, USA
Tim Jacobbe   University of Florida, USA

Audience Response Systems are devices that allow for instant communication and involvement by the students in the classroom by the use of handheld remotes. The system allows students to anonymously respond to questions posed by the instructor. A study was done in the Spring of 2009 to test the impacts of using these remotes in a learning disabled classroom. Two sections of Introduction to Statistics I were taught identically except for the use of the handheld remotes: one of these sections used a handheld remote to respond to questions; whereas, the other class discussed the answers to the questions as a class. In addition to looking at graded assessments, each student took the Survey of Attitudes Toward Statistics 36+ Pre and Post Test. The impact of using the remotes on graded assessments and attitudes towards statistics will be compared in the paper as well as recommendations for future study.

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C274: The future of interactive, electronic research: an exemplar from probability education

Manfred Borovcnik   Alpen-Adria University Klagenfurt, Austria
Ramesh Kapadia   University of London, England

In the topic study group on probability at ICME 11 a variety of ideas on probability education were presented. In an international, collaborative, electronically supported project after the conference, many of these papers have been developed much further, incorporating electronic techniques. Following McLuhan, the medium of research has influenced the message (massage) of the results and–not surprisingly–the research has changed its character during this process. This presentation comments on future possibilities of electronic communication. This will enable developments relevant for other areas of research too. Hyperlinks are included.

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C275: Teaching: estimation of minimum sample size and the impact of effect size and altering the type: I & II errors on it, in clinical research

K R Sundaram   Amrita Institute of Medical Sciences & Research Centre, Kochi,Kerala, India
Amrutha Jose   Amrita Institute of Medical Sciences & Research Centre, Kochi,Kerala, India

In any research study, one of the most important questions asked for at the time of planning the study is ‘what should be the sample size in my study’. Estimation of minimum sample size depends upon- design of the study, whether it is an estimation problem or a hypothesis testing problem, the type of variable(s) to be studied, type-I & II errors acceptable and rough estimates of the parameters to be studied. In this presentation estimation of sample size for a clinical trial, comparing the efficacy of two different drugs, in case of categorical variables and the effect of altering the type I & II errors and the effect size have been discussed with examples. The results showed that the sample size increases when the type-I or / and II errors are decreased. Symmetric nature of sample size on either side with respect to the effect size has also been explained.

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C276: Creating statistically literate global citizens: the use of integrated census microdata in teaching

Ann Meier   University of Minnesota, United States
Robert McCaa   University of Minnesota, United States
David Lam   University of Michigan, United States

We describe the use of international census micro data for teaching undergraduate students in two population related courses. The Integrated Public Use Micro Series (IPUMS) of international census data contains social and population data from 84 countries from 1960 to the present. We detail the use of the IPUMS data in courses at the University of Minnesota and the University of Michigan to help students understand population issues in historical and comparative perspective. One of the most significant learning outcomes of these courses was the acquisition of a baseline level of statistical literacy among non-statistics students in the social sciences. An added benefit was the global understanding gained through the investigation of countries other than their own across time and in comparison to other countries.

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C277: Statistics learning and batiks: an innovative way of doing mathematics

Lucília Teles   University of Lisbon, Portugal
Margarida César   University of Lisbon, Portugal

Students should appropriate statistics knowledge through diverse/meaningful learning experiences connected to their daily life. We discuss an intercultural and interdisciplinary project (IDMAMIM) developed in Granada (Spain), Pisa (Italy) and Lisbon (Portugal). We focus on the Portuguese data. Statistics learning was based on the elaboration of batiks. We assume an interpretative approach and a case study design. Participants were students from the 8th/9th grades (12/14-yearolds), their mathematics teachers, teachers from other subjects, external observers and significant others. Students worked in small groups. Data were collected through observation (audio/video taped; photographed), questionnaires, interviews, documents, reports and students’ protocols. Results, based on the analysis of a statistical task, illuminate how an intercultural micro-project could promote group work and statistics learning, engaging students in a common project.

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C278: Analysis of a basic statistic course using item response theory

Dalton Andrade   Federal University of Santa Catarina, Brazil
Marcos Magalhães   University of São Paulo, Brazil

The objective of this study is to evaluate students’ learning from the contents presented in class. Data from undergraduate students were collected in three consecutive years since 2005 and from five different careers in the area of Mathematics. For a sample of these students, who successful completed the two basic classes in statistics, a test was applied 3 months after the end of the school year. It was composed of 50 true-false items divided as follows: 19 items on descriptive statistics and measures for random variables, 17 items on probability and random variables and 14 items on statistical inference. A two-parameter item response model was considered and 36 out of the 50 items were selected to build a scale measuring students’ basic statistics concepts knowledge. Also, we discuss the difference among the students from the five different careers and the suggestions to improve the teaching-learning process.

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C279: Principles and strategies in teaching probability

Talma Leviatan   Tel Aviv University, Israel

We propose to teach tertiary probability focusing on general probabilistic principles that lead to general probabilistic problem-solving strategies. The method enhances theoretical understanding of general models and at the same time, supplies students with a toolbox for handling the extremely wide range of possible applications of probability theory. According to experience, the method is particularly effective when applied to prospective teachers, as it helps in building up selfconfidence both as students and as future teachers, a confidence that may later be transferred to their students.

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C280: Elementary school students’ understanding of concept of arithmetic mean

Evanthis Chatzivasileiou   Aristotle University of Thessaloniki, Greece
Ioannis Michalis   Aristotle University of Thessaloniki, Greece
Christina Tsaliki   Aristotle University of Thessaloniki, Greece

The research (spring of 2008) investigated the understanding of concept of arithmetic mean of 208 4th and 6th grade students of elementary school, in Thessaloniki in Greece. The result agrees with the conceptions of Mokros & Russell (1995, 22) that “the arithmetic mean is a mathematical object of unappreciated complexity”. The students participated in research were able to calculate the mean using the arithmetic algorithm, although they couldn’t use the metre to summarize data neither applied it in real life problems, that is interpreted as absence of statistical thought (Phannkuch & Wild, 2003). Children limit themselves in the simple knowledge of the algorithm (computational knowledge) that constitutes the lower level of instrumental understanding of the concept (Pollatsek et al, 1981). With regard to the comprehension of representativeness students recognized this attribute but they didn’t lead to the confrontation of data as an entity.

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C281: Improving research in statistics education

Djordje Kadijevich   Megatrend University and Mathematical Institute SANU, Serbia

Researchers in education tend to operate within their own narrow research circles ignoring the work of others in the field. Aimed at improving research in statistics education, this paper presents two requirements that should be respected by new research studies. These requirements deal with promoting the human face of statistics and utilizing research in mathematics education in research in statistics education. Each of them is briefly described and justified in general terms and illustrated with concrete examples.

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C282: Teaching students to use the chi-square test when observations are dependent

Austina S S Clark   University of Otago,, New Zealand

The purpose of statistical analysis is to extract and assess information contained in data and draw inferences based on the analysis. Students, especially those doing experimental work and not majoring in statistics, need to apply the statistical methods they have learned to their collected data. These data often arise in diverse situations and standard methods cannot be applied directly. The statistical methodology must be developed to address problems associated with such data. Here we use the chi-square test with dependent data to illustrate methodology modification in order to analyse data correctly. The underlying mathematics is summarised, but students are only expected to analyse such data using software and to check modification procedure using simulations. The aim here is to show students that statistical procedures can be modified then applied even though the data does not fit assumptions for a standard procedure. The importance of simulation is evident as an additional benefit for learning.

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C283: Life after graduation: do statisticians fare better than other graduates in the Brazilian labor market?

Sonoe Sugahara   National School of Statistics ENCE-IBGE, Brazil
Kaizô Beltrão   National School of Statistics ENCE-IBGE, Brazil

In this text we analyze the situation of statisticians vis-à-vis other university degree holders with respect to some characteristics in the labor market, using indicators such as salary, formal labor market links, economic sector of employment, position in the occupation and spatial distribution among the Brazilian states. Female statisticians seem to fare better than their male counterpart when compared to other graduates with respect to salaries. The gender gap is smaller for statisticians than for all graduates considered together. But in general when considering the insertion in the labor market, Brazilian statisticians of both sexes fare better than other university graduates: the proportion of Statisticians in informal jobs is proportionally smaller. On the other hand, the proportion of statisticians holding positions that do not require a university degree is slightly higher than that of all graduates.

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C284: Electronic spreadsheets as a teaching aid to a generalized linear model course

Kaizô Beltrão   National School of Statistics ENCE-IBGE, Brazil
Sonoe Sugahara   National School of Statistics ENCE-IBGE, Brazil

Using a software package to obtain parameters estimates for a given model can be straightforward and fast, but does not inform the user about the underlying process involved. On the other hand, using a spreadsheet to implement the operations, to eventually arrive to a final answer, assumes the analytical development of some previous steps necessary to attain this goal and therefore, besides making explicit the underlying GLM estimating procedure, reinforces previous knowledge and competences enriching the learning process.

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C285: Understanding of arithmetic mean

Mateja Sirnik   National Education Institute, Slovenia
Silva Kmetič   National Education Institute, Slovenia

The article deals with the experiences which learners have with the concept of average. This term is very common in their daily and school lives. The instruction of mathematics includes the arithmetic, geometric and harmonic mean as well as median and modus after data handling was introduced into the syllabus. Based on the sample of two different age groups of learners we were trying to find out what the understanding of the concept of arithmetic mean is, if students are more able to understand arithmetic mean as an algorithm or they can use it to solve an open ended task, and if there is a perceivable qualitative difference in the comprehension related to the learners' age. In accordance with the results we propose some guidelines in order to better understanding the concept of arithmetic and other means.

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C286: Data handling and statistics in external assessments

Mojca Suban Ambrož   National Education Institute, Slovenia
Sonja Rajh   National Education Institute, Slovenia
Jerneja Bone   National Education Institute, Slovenia

The paper presents a selection of data handling and statistics tasks at elementary and secondary level of education. These tasks were used on the national external examinations in mathematics in elementary school, high school and vocational schools in the years 2007, 2008 and 2009. In most cases we give the goals to the task of examining, classification of tasks in the appropriate taxonomic level (Gagne’s taxonomic classification), the index of difficulty and discrimination index. In addition, we present findings of a qualitative analysis of the students’ work in the example of two examination tasks. The analysis studies students’ task-solving strategies, peculiarities in completing the tasks as well as typical and repeated errors students have made. The paper concludes with some findings regarding the representation of data handling and statistics on the external examinations, the students’ performance and a list of terminology used.

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C287: Data processing and statistics in the Slovenian curriculum

Amalija Žakelj   National Education Institute, Slovenia

Besides the basic capabilities of reading, writing and calculating, also other capabilities of literacy are emphasised, such as information, statistic, digital, media, mathematical and other literacies which are important for acting in the society. In our article we are going to present certain views on information, statistical and data literacies as well as on the integration of the contents on data processing and statistic in the Slovenian curriculum. An individual is considered literate in information if he/she is capable of critical thinking about information, of assuming and argumentation, and of interpreting and evaluating information. An important component of the information literacy is statistical literacy, the capacity of critical thinking about the basics of the descriptive statistics. A special skill is analysis, interpretation and evaluation of statistics functioning as the evidence. Data literacy is the component of both literacies, which means the capacity of accessing, manipulating, merging and presenting data

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