Contributed Papers

C101: THE ROLE OF STATISTICS AND NUTRITION AT CARLITOS SCHOOL (SÃO PAULO, BRAZIL) — A PEDAGOGICAL PROPOSAL FOR THE STATISTICS CURRICULUM FOR THE FIRST YEARS OF BASIC SCHOOL

Regina Albanese Pose
Escola Carlitos, São Paulo, Brazil
Mauro Fisberg, Adriana Marins Lima
Universidade Federal de São Paulo, Brazil
Edson Marcos Leal Soares Ramos, Adrilayne dos Reis Araújo
Universidade Federal do Pará, Brazil

This project aims at comprehending statistics and crossing themes in basic schooling. A team of teachers, a doctor, a nutritionist and statisticians are to carry it out. First, parents and employees are made aware through lectures on nutrition. Then, lunch and snacks offered at school are controlled. After that, classes on food nutrients, anthropometrical evaluations and double input tables will be executed. According to the diet offered, probabilities referring to BMI will be calculated. Functions will be used as mathematical models to express energy necessities. Menus will be developed according to the food pyramid, and caloric value will be evaluated according to linear algebra counting techniques. Final results are to be counted up and analyzed. An open software R will be used as technology support.

C102: EVALUATING THE SOCIO-ECONOMIC RELATIONSHIP WITH THE ABSENCE OF READING BETWEEN THE STUDENTS OF A PRIVATE SCHOOL AND OF A PUBLIC SCHOOL

Adrilayne dos Reis Araújo, Edson Marcos Leal Soares Ramos,
Silvia dos Santos de Almeida, Risoleide Cristina da Costa Barbosa
Universidade Federal do Pará, Brazil

This work has as objective to verify if the socioeconomic relation of the students of two schools of the metropolitan area of Belém, one of a public school and another of a private school, interferes in the habit of reading of the same ones. To obtain those results the techniques statistical Analysis of Correspondence and Faces of Chernoff were used to present those students’ profile.

C103: COOPERATIVE WORK IN STATISTICS PROJECTS FOR VERY BUSY STUDENTS

Kenneth M. Brown
College of San Mateo, United States

Some academic settings are more favorable to cooperative project work in than others. We show how a meaningful group project can be used in one such unfavorable setting.

C105: META-ANALYSIS: PICTURES THAT EXPLAIN HOW EXPERIMENTAL FINDINGS CAN BE INTEGRATED

Geoff Cumming
La Trobe University, Australia

Meta-analysis (MA) is the quantitative integration of empirical studies that address the same or similar issues. It provides overall estimates of effect size, and can thus guide practical application of research findings. It can also identify moderating variables, and thus contribute to theory-building and research planning. It overcomes many of the disadvantages of null hypothesis significance testing. MA is a highly valuable way to review and summarise a research literature, and is now widely used in medicine and the social sciences. It is scarcely mentioned, however, in introductory statistics textbooks. I argue that MA should appear in the introductory statistics course, and I explain how software that provides diagrams based on confidence intervals can make many of the key concepts of MA readily accessible to beginning students.

C106: HOW THE NONCENTRAL T DISTRIBUTION GOT ITS HUMP

Geoff Cumming
La Trobe University, Australia

Once upon a time there was only one t distribution, the familiar central t, and it was monopolised by the Null Hypotheses (the Nulls), the high priests in Significance Land. The Alternative Hypotheses (the Alts) felt unjustly neglected, so they developed the noncentral t distribution to break the monopoly, and provide useful functions for researchers—calculation of statistical power, and confidence intervals on the standardised effect size Cohen’s d. I present pictures from interactive software to explain how the noncentral t distribution arises in simple sampling, and how and why it differs from familiar, central t. Noncentral t deserves to be more widely appreciated, and such pictures and software should help make it more accessible to teachers and students.

C107: STOCHASTICS AND THE PROFESSIONAL KNOWLEDGE OF TEACHERS

Celi Espasandin Lopes
Universidade Cruzeiro do Sul, Brazil

Teachers widen their professional knowledge and their pedagogical practice by writing and publishing about their experiences in preparing and developing activities in statistics and probability. In this study data were collected and then analysed by triangulation. The role of reflection in teacher development, the relation with the curriculum and the relation with the collaborative work emerged. The results promote the development of the teacher’s professional role to create the teaching and learning process in terms of children’s cognitive development. Teachers worked within many constraints but still created very sensible solutions for practical situations and are active innovators of the curriculum.

C108: GENERATING DIFFERENT DATA SETS FOR LINEAR REGRESSION MODELS WITH THE SAME ESTIMATES

Silvio Sandoval Zocchi, Bryan F.J. Manly
University of São Paulo, Brazil

For teaching purposes it is sometimes useful to be able to provide the students in a class with different sets of regression data which, nevertheless give exactly the same estimated regression functions. In this paper we describe a method showing how this can be done, with a simple example. We also note that the method can be generalized for situations where the regression errors are not independently distributed with a constant covariance matrix.

C110: QUESTIONS TO ASSESS THE UNDERSTANDING OF STATISTICAL CONCEPTS

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

The GAISE College Report recommends that introductory applied statistics courses should place greater stress on statistical concepts and less stress on definitions, computations, and procedures. The report also urges instructors to align assessments with learning goals. In this paper the authors explain how instructors can implement these two recommendations. They first review the extent to which questions directly related to concepts are found in popular texts and on websites created by the publishers of these texts. Following this review they provide examples of such questions in a variety of formats (multiple choice, fill-in-the blank, open-ended, etc.). The examples will be classified by the approximate level of educational objective contained in Bloom’s Taxonomy. Finally, the paper will discuss the advantages and disadvantages associated with having students answer such questions electronically.

C111: ONE STEP BEYOND FORMULAS: STATISTICAL PROJECTS FOR FUTURE MATHEMATICS TEACHERS

Clayde Regina Mendes
PUC-Campinas, São Paulo, Brazil

Statistical Projects incorporating questions relative to quantitative literacy for interdisciplinary work are presented as a learning strategy very appropriate for Brazilian Mathematics teachers in Fundamental and Middle Education. In order to work well on projects, it is necessary that future Mathematics teachers have this experience during their Teacher Training years of 2004 and 2005. For this purpose we developed Statistical Projects with students in the Mathematics Teacher Training Course of a private University in Campinas, São Paulo, Brazil. These students worked in groups on project themes relative to the field of actuation of Mathematics teacher. In spite of difficulties encountered by the Professor as well as the students, the final result can be considered positive.

C113: HOW SHOULD WE TEACH THE USE OF PROBABILITIES TO TAKE DECISIONS WHEN TESTING STATISTICAL HYPOTHESIS?

Maria Manuel da Silva Nascimento
UTAD, Portugal
Nilson Luiz Castelucio Brito
UNIMONTES, Brazil

Nowadays we can not ignore the use of computers in statistics calculations and the main reason for its use is that computations become faster and trustworthy. Almost all statistical software computes p-values so students and researchers can take their decisions only based on its "usual" value. If the p-value is lower than 0.05 then the null hypothesis for a statistical test is "simply" rejected. Do statistical tests users ask about the meaning of this software output? If we are testing statistical hypothesis we have the null hypothesis tested against an alternative hypothesis. Do statistical tests users think about them? Since the decisions are based on sampling, the statistical tests decisions involve uncertainty and so two types of errors can be made. Do statistical tests users think about them? A questionnaire was constructed and administered to students and researchers in order to make a first approach about those subjects.

C114: FORMING SMALL CLASS GROUPS USING MULTIDIMENSIONAL SCALING

Iain Pardoe
University of Oregon, United States

In college courses that use group work to aid learning and evaluation, class groups are often selected randomly or by allowing students to organize groups themselves. This article describes how to control some aspect of the group structure, such as increasing schedule compatibility within groups, by forming the groups using multidimensional scaling. Applying this method in an undergraduate statistics course has resulted in groups that have been more homogeneous with respect to student schedules than groups selected randomly. For example, correlations between student schedules increased from a mean of 0.29 before grouping to a within-group mean of 0.50. Further, the exercise motivates class discussion of a number of statistical concepts, including surveys, association measures, multidimensional scaling, and statistical graphics.

C115: GRADUATE STUDENTS AND THEIR USE OF STATISTICAL KNOWLEDGE IN EDUCATIONAL PSYCHOLOGY

Cuauhtémoc Gerardo Pérez López, Sonia Villaseñor Pedroza, Arcelia Palacios Luciano
National Pedagogical University, Mexico

This work describes the use of statistics made by graduate students in the field of Educational Psychology at the National Pedagogical University, when writing their theses or dissertations in support of their candidature for a degree of professional qualification. The results show that, in general, the thesis writers used statistical analyses when their investigation required them; however, it was found that students mainly have the following difficulties: a) their choice of a suitable statistical test concerning their objective of research; b) the way of interpreting data; c) selection of the design consistent with their objectives; d) in their comprehension of the meaning of some statistical concepts; e) in their decision use of charts or graphs. Finally the work concludes by discussing the pertinence of the contents, strategies and procedures of instruction and evaluation of courses in statistics.

C116: SATS AT BALL STATE UNIVERSITY: APPROACHES AND ATTITIUDES

Rebecca L. Pierce
Ball State University, United States

SATS survey data collected from three introductory statistics courses – college algebra-based, college calculus-based, and a high school AP course. Instructors of these courses also completed a questionnaire concerning their approach to a 1st course in statistics. What are the similarities and differences in the students’ attitudes to each instructor’s approach?

C117: ASSESSING STATISTICAL REASONING THROUGH PROJECT WORK

Rui Pimenta
Instituto Politécnico do Porto, Portugal

New technologies involve a reformulation of statistical teaching contents and methodology and, at the same time, reinforce the need for a deeper training of students, including developing students’ statistical reasoning. In this work we evaluate the statistical reasoning ability acquired by health sciences students from the analysis of their final undergraduate projects.

C118: AN EXPLANATION OF STUDENT PERFORMANCE USING HIERARCHICAL LINEAR MODEL FOR SCHOOLS IN PERNAMBUCO, BRAZIL

Sandra Maria Conceição Pinheiro, Claudia Regina Lima, Maria Cristina Falcão Raposo
Universidade Federal de Pernambuco, Brazil

The hierarchical linear models or multilevels were developed for analysis of data which possess group structure, that is, a structure hierarchy which takes in account the data variability inside and among each hierarchical level. By using data analysis from SAEPE (2002 Educational Evaluation System of Pernambuco), hierarchical models (MH) are presented with two levels of evaluation in mathematics and Portuguese language classes applied to the 4th and 8th grades students of fundamental teaching and to the students 3rd grade students medium teaching. The results in this modeling are more appropriate due to data group structure. A comparison between multiple regression models and hierarchical models shows a better performance of the second model.

C120: STATISTICAL ANALYSIS OF THE GRADUATION COURSES OF THE CAMPUS OF CASTANHAL - UFPA

Edson Marcos Leal Soares Ramos, Adrilayne dos Reis Araújo,
Silvia dos Santos de Almeida, Ana Cristina Alves Garcêz
Universidade Federal do Pará, Brazil

This work presents the Statistical Analysis of the Graduation Courses in the Campus of Castanhal of the Federal University of Pará – UFPA in 2004. The results on the Statistical Analysis of the degree of satisfaction of the graduation courses of the Campus of Castanhal show that 65.33% of the students in relation to the infrastructure evaluate the laboratories of their courses as no appropriate to the objectives of their disciplines. In relation to course Coordination, 36.43% of the students evaluate that the coordinators of courses of the Campus of Castanhal don't stimulate organizations of events and 33.16% of the technicians that act in the courses don't get to solve the academic problems. During the application of the Multivariate Statistical Technique denominated Analysis of Correspondence existence of the relationship is verified between the course and degree of the student’s satisfaction by the course, where it is evidenced that the students of the Course of Mathematics are unsatisfied with his/her course. Relating the degree of the student's satisfaction for UFPA, it is noticed that no student feels very satisfied with UFPA, however the students of the Course of Pedagogy possess a small satisfaction relationship for the institution, but this relationship is very larger in the students of the Course of Veterinary Medicine.

C122: A HIERARCHY OF TERTIARY STUDENTS’ CONSIDERATION OF VARIATION

Jackie Reid, Chris Reading
University of New England, Australia

In this study a hierarchy of consideration of variation was developed from students’ responses to a questionnaire given at the beginning of a tertiary introductory statistics course. The hierarchy was then used to code responses to the same questionnaire post-study. Comparison of student performances showed that the development of consideration of variation differs with the context of the question. The proposed hierarchy could provide a basis for a more general hierarchy of consideration of variation that is applicable across a variety of tasks. It also supports educators in identifying the level of a student’s consideration of variation, providing direction for teaching and learning activities that will help that consideration develop.

C124: NEW METHODOLOGY FOR TEACHING STATISTICS IN BIOLOGY: AN INTERACTIVE GUIDE TO LEARNING WITH SPSS

J. García Leal, A. Lara Porras, E. Hidalgo Ruiz, J. Quesada Rubio, E. Ramos Ábalos,
R. Raya Miranda, I. Sánchez Borrego, J. Tarifa Blanco, J.E. Ruiz Castro
University of Granada, Spain

An interactive guide of the SPSS programme is presented, consisting of a web portal and a programme emulator. From the webpage, students will be able to download didactic material that will introduce them to the programme. The developed SPSS emulator allows the student to learn how to use the programme and guides in the execution of Statistics exercises in an interactive way. Once the student has worked with these tools, the SPSS statistics package can be experimented on directly. It is intended that the student have available a complementary teaching aid to that of the instructor facilitating the learning of statistics by computer.

C125: STATISTICS EDUCATION IN VENEZUELA: THE CASE OF THE BASIC AND MIDDLE EDUCATION

Audy Salcedo
Universidad Central de Venezuela

The purpose of this paper is to offer a wide picture of statistics education in Venezuela, specially at the Middle and Basic Education. To accomplish this objective I compare the both mathematics curriculum for the Basic Education (nine grades of compulsory schooling) and Middle Education (two or three years of secondary education which are also compulsory). These curriculum prescribe probability and statistic content for 7 to 17 years-old students. I analyze some problems in the teaching of probability and statistics. I conclude offering some suggestions for improving statistics education en Venezuela.

C126: THROWING A DIE WITH A COMPUTER ALGEBRA SYSTEM – IN THEORY AND PRACTICE

Karsten Schmidt
University of Applied Sciences, Schmalkalden, Germany

Most management science and economics students attending an advanced statistics course appreciate a quick repetition of the concept of random variables. We describe the application of the Computer Algebra System Derive to the familiar “throwing a die” example which turns out to be a substantial time saver, e.g. since tedious manual calculations can be avoided. Our approach also allows straightforward application to the investigation of other gambling examples. Last but not least, using a Computer Algebra System also makes looking at the empirical side of gambling more comfortable by providing built-in functions for pseudo random number generation as well as for the computation of statistical parameters.

C129: UNDERSTANDING HIGH SCHOOL STUDENTS’ IDEAS ABOUT PROBABILITY: SOME FINDINGS FROM FIJI

Sashi Sharma
The University of Waikato, New Zealand

This paper reports on data from a large study which explored form five (14 to 16-year-olds) students’ ideas in statistics (probability, descriptive statistics, graphical representations, investigations). This paper discusses the ways in which students made sense of probability tasks obtained from the individual interviews. The findings revealed that many of the students used strategies based on beliefs, prior experiences and intuitive strategies. Additionally, in some cases the meaning intended by myself on the interview tasks was not that constructed by the students. As a result, students constructed responses based on these unintended interpretations. While students showed more competence on the formal item, they were less competent on the question involving an everyday context. This inconsistency could be due to contextual or linguistic issues. The paper concludes by suggesting some implications for further research.

C130: IDENTIFYING CONTENT KNOWLEDGE FOR TEACHING STATISTICS

M. Alejandra Sorto
Texas State University – San Marcos, United States

The purpose of the study reported herein was to identify important aspects of statistical knowledge needed for teaching in the middle school grades. A systematic study of the current literature, including state and national standards, was conducted to identify these important aspects and to measure the degree of emphasis or importance suggested for the content. Results show that state and national standards differ greatly in their expectations of what topics in data analysis and statistics students and teachers should master. The variation is also large in the degree of emphasis given to the content. The majority of the documents analyzed suggest giving greater emphasis to the selection and proper use of graphical data representation and measures of center and spread. Additionally teachers’ standards also suggest as important the proper selection and use of teaching strategies and inference of students’ understanding from their work and discourse.

C131: USING BUSINESS-STYLE CASES IN AN INTRODUCTORY STATISTICS COURSE

Eduardas Valaitis, Mary Gray
American University, United States

Most institutions of higher learning in the United States offer introductory statistics courses in a variety of flavors. Integration of the subject-specific concepts with the basic applied statistical techniques should be the primary goal of these flavored courses. Solely lecture-based traditional instruction method is not suitable to satisfying this objective. We argue for the incorporation of business-style cases into the introductory statistics curriculum using Constructivist learning theory and the notion of the “liberal arts” education. A typical business case setup is presented and its compatibility with an introductory statistics course is assessed. Finally, a sample business-style case for the application of the simple linear regression is provided.

C133: ATTITUDES TOWARD STATISTICS AND THEIR RELATIONSHIP WITH SHORT- AND LONG-TERM EXAM RESULTS

Stijn Vanhoof, Ana Elisa Castro Sotos, Patrick Onghena, Lieven Verschaffel
Katholieke Universiteit Leuven, Belgium

This paper presents an empirical study that used the Attitudes Toward Statistics (ATS) scale (Wise, 1985) to investigate the relationship between attitudes toward statistics and short- and long-term statistics exam results for Flemish university students taking statistics courses in a five year Educational Sciences curriculum. The aim was to examine whether the previous reported relationship between attitudes toward statistics and first year statistics exam results also exists for later statistics exam results and general exam results. The results indicate that there indeed exists a relationship between attitudes toward statistics (at the beginning of the curriculum) and later statistics performance (indicated by the dissertation grade), but that this relation between attitudes and results is content-specific.

C135: YSTATTEST: A SYSTEM FOR AUTOMATED ONLINE TEST CREATION AND CORRECTION

David G. Whiting, Del T. Scott
Brigham Young University, United States

Using exclusively open-source software, we have developed and implemented an online testing system dubbed YStatTest. This system allows instructors to create homework, quizzes, and exams by querying a database containing question templates. A template is selected based on such elements as keywords, categories, and historical difficulty. Numerical values, data, and correct answers for each question template are randomly generated upon exam creation. Thus, although two students may receive identical templates, they will likely differ in placement on the exam and most assuredly in the data and numerical values associated with the question. We discuss the impact this testing system has had upon student learning and highlight future planned development for our software.

C136: NUMERACY AND STATISTICAL REASONING ON ENTERING UNIVERSITY

Therese Wilson, Helen MacGillivray
Queensland University of Technology, Australia

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on mathematics anxiety. Gnaldi (2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning, basic numeracy skills, mathematics background and attitudes towards statistics. This work reports on some key relationships between these factors and in particular the importance of numeracy to statistical reasoning.

C137: STATISTICAL GRAPHICS AND EXPERIMENTAL DATA

Emily Nikolic-Doric, K. Cobanovic, Z. Lozanov-Crvenkovic
University of Novi Sad, Serbia and Montenegro

Statistical graphics play an important role in many fields of statistical work. Statistical graphics are used both in the teaching statistics, as well as, in the research. Data analysis based on graphics is the first step in many statistical investigations. Statistical graphs are usual form of visual communication. In the utilization of statistical graphs the emphasis is focused either on the presentation of data or their analysis. The primary function of graphs was the visual presentation of data. But, with the development and application of electronic computers and software the analytical function of graphs has increasing importance (Schmid, 1983). Today’s graphical techniques allow comparisons between groups of data. Box-and-whisker plot is simple graphical method that is introduced to students in teaching descriptive statistics as useful exploratory data analysis tool for studying main characteristics of distribution detecting outliers and extreme values. This paper considers application of this diagram and its categorized form (trellis diagram) in analysis and modelling data from designed experiments in agriculture.

C139: DIPLOMA IN APPLIED BIOSTATISTICS: AN EXPERIENCE IN CONTINUING EDUCATION

Irene Schiattino, Claudio Silva, Gabriel Cavada, Rodrigo Villegas,
Rosa Montaño, Marinella Mazzei, Sergio Alvarado
Universidad de Chile

This work describes the program “Diploma in Applied Biostatistics”(DAB) which is designed to train or to bring up to date in Biostatistics and its applications the teaching professionals and researchers in the fields of Public Health and Biomedicine. This program has been offered since the year 2001, and to this date 67 health sciences professionals have participated in it; 67% of them physicians. This is a continuing education program that combines in person teaching with online distance education and it is fully accredited by the University of Chile. DAB is currently organized into three modules of biostatistics applications that span a total of 269 hours. The program runs from June to December with 100 hours of “in attendance” instruction distributed into seven intensive periods of two days each (Friday and Saturday), and 169 hours of distance education, distributed into six periods.

C140: ELEMENTS OF MEANING AND ITS ROLE IN THE INTERACTION WITH A COMPUTATIONAL PROGRAM

Teresita E.Terán, Mercedes Anido de López
Universidad Nacional de Rosario, Argentina

This paper is part of a research study, the objective of which is to investigate the meaning of confidence intervals for first year students in the Statistics course in the Universidad Nacional de Rosario. Within the framework of Godino’s theory (1999), by means of students’ dialogues in front of the computer, we try to surmise the presence of the diverse elements of meaning – extensive, ostensive, actuating, intensive and validating – which reveal the topic comprehension. Statistical inference is one of the largest branches of Statistics and a fundamental methodological tool in the empiric sciences, in particular. It allows us to quantify our confidence in conclusions drawn from random samples, and therefore, to verify our impressions by means of calculations (Batanero, 2001); hence, the importance of an updated teaching.

C141: REFLECTION ON TRAINING, EXPERIENCE, AND INTRODUCTORY STATISTICS - A MINI-SURVEY OF TERTIARY LEVEL STATISTICS INSTRUCTORS

Rossi A. Hassad
Mercy College, United States

Instructors of statistics who teach non-statistics majors possess varied academic backgrounds, and hence it is reasonable to expect variability in their content knowledge, and pedagogical approach. The aim of this study was to determine the specific course(s) that contributed mostly to instructors' understanding of statistics. Courses reported were described as advanced or graduate level, and classified as application-based, math, multivariate, probability, and research. The majority, 9 (56%) attributed their understanding of statistics to either an application-based or research course, and of those, 7 (44%) reported negative feelings about their introductory courses. These findings underscore the importance of authentic activities, and constructivist pedagogy toward facilitating statistical literacy. Research is needed to determine the effect of instructors' academic preparation on their knowledge, attitudes, and practices.

C142: I HAVE SOME DATA, WHAT CAN I DO WITH THEM?

A. Lara Porras, Y. Román Montoya, J. García Leal
University of Granada, Spain

This paper is motivated by the need for a methodological change for Statistics teaching in experimental degree courses. We try to show the students the need for Statistics knowledge. Then they are able to establish a relation between reality and their studies and they can use Statistics as an indispensable tool to handle some data. With these objectives we start this project using real data to teach Statistics to our students. We work with students of the University of Granada, Spain, in a third course of Environment Sciences.

C202: POSING PROBLEMS AS A STATISTICS TEACHING ACTIVITY AT ENGINEERING UNDERGRADUATE AND GRADUATE LEVELS

Patricia E Balderas Cañas, Ana María Vázquez Vargas
Universidad Nacional Autónoma de México

In this work we pose some problems related with data analysis, hypothesis test, and making decisions. Our objective in posing stochastic problems is promoting connections among some important stochastic concepts; in order that students would be able to apply statistical procedures when they face real problems of data analysis. We are concerned with design of some key situations and problems for conducting statistics teaching to promote statistics learning trough case analysis and project development.

C205: A THIRD WORLD UNIVERSITY’S STUDENTS’ PERSPECTIVE OF STATISTICS

Martin M. Chanza, R.O. Ocaya
North West University, Mmabatho, South Africa

In this age of information technology vast amounts of data are generated from many different processes which necessitate the practice of statistics in some form or other. Many third world students grapple with understanding the subject of Statistics and the success of teaching statistics depends on finding a satisfactory answer to many of the questions asked by the majority of students. This paper highlights the misconceptions that students have about statistics and shows that dispelling the myths and prejudices eases the teaching of the subject matter and the acceptance of statistics as a rewarding career.

C207: PERIODIC REGRESSION

Katrina Cobanovic, Z. Lozanov-Crvenkovic, E. Nikolic-Doric
University of Novi Sad, Serbia and Montenegro

Periodic regression is seldom included in syllabus of statistical courses. However, data following periodic or cyclic behavior are often encountered, especially in agriculture. Therefore, we think that this type of regression should be taught to students of agriculture, even in basic courses of statistics. In this paper we propose the way of teaching periodic regression through examples usually encountered in practice. The analysis of data will be based on the graphical interpretation, which would provide the visual display of the investigated problems as well.

C208: TEACHING CONSTRUCTION CLASSIFICATION RULES WITH APPLICATIONS IN SOCIAL SCIENCES

Margarita Diaz, Cecilia Diaz, Patricia Caro, María Ines Stimolo
Universidad Nacional de Córdoba, Argentina

Supervised classification or pattern recognition is a method to solve decision problems in Social Sciences. It is organized on the basis of specific sets of predictor variables and the existence of classes known a priori. Based on a training sample, its main objective is to construct a classification rule in order to predict the class to which a new object belongs. Nowadays, the availability and efficacy of powerful computers have made possible many advances in this field, both in Statistics and Computer Sciences. In this section, different methods will be discussed and illustrated with the results obtained in several applications. The following topics will be dealt with: Parametric Discriminant Analysis, Non-parametric Discriminant Analysis, Logistic Discriminant Analysis, Neuronal Networks, Recursive Partitioning and Estimation of Error Rates.

C210: THE CALCULADORA ESTADISTICA FOR PRESENT AND DISTANCE LEARNING

Renata G.S. Gomes, Ronei M. De Moraes, Liliane dos S. Machado
Federal University of Paraíba, Brazil

Discussions about distance learning are not a novelty. In the last years, several systems to support learning were proposed and developed, some of them based on the Internet. For statistics teaching, as in other areas, there are many systems for distance learning in the web that only present a digital version of the traditional classes’ content. Besides of the information access, these systems do not present a function to help the student in his doubts or a function to teach step-by-step for some concepts. Systems with this approach only present the simulation of some situations, or only detect mistakes, or refuse the operation and provide information about the user mistakes. In this paper we present a system to support statistics teaching that joins all of these features: help students by pointing out his mistakes and by teaching the correct steps. The system can be used for present or distance learning and it is named Calculadora Estatística (Statistics Calculator).

C214: AN INTRODUCTORY COURSE TO STATISTICAL CONCEPTS, THEORY AND DESIGNS IN EDUCATIONAL RESEARCH METHODS: A COMBINATION OF STRENGTHS AND WEAKNESSES

Josepf Mafokozi
Universidad Complutense de Madrid, Spain

Ever since its founding, the Pedagogy Department at the Complutense University of Madrid has considered statistics to be fundamental instrument in the training of educational researchers. For this reason, the department has made every effort for the teaching of statistics to keep pace with the field itself. However, the results so far have been unsatisfactory. These negative results, combined with Pedagogy students’ initial limited ability in statistical processing, point out the need for new techniques that can be used to teach research methods in education.

C216: THE VARIATION CONCEPT: A STUDY WITH SECONDARY SCHOOL MATHEMATICS TEACHERS

Cláudia Borim da Silva
Universidade São Judas Tadeu, Brazil
Cileda de Queiroz e Silva Coutinho
Pontíficia Universidade Católica de São Paulo, Brazil

This paper aimed at identifying the invariants employed by teachers to understand the variation conception. Ten Mathematics teachers were involved in this research, in a process of continuing formation lasting 54 hours. During the early discussions with these teachers it was possible to identify the absence of such conception among them. When working with quantitative data we realized the teachers knew the algorithm for the calculation of standard deviation, although they were not able to interpret the results they obtained. At the end of the process we used an exercise to diagnose possible changes in the conceptual field of variation. Only one lady teacher was able to clearly identify data variation and the mean variation. Although we worked with such a small groups of teachers, we could notice that data variation is an intuitive conception, which does not happen in terms of standard deviation, which is extremely hard to interpret

C303: IMPROVING THE TEACHING OF STATISTICS IN EARLY GRADES THROUGH TECHNOLOGY-ENHANCED LEARNING ENVIRONMENTS

Maria Meletiou-Mavrotheris
Cyprus College, Nicosia, Cyprus
Efi Paparistodemou
University of Cyprus
Despina Stylianou
City University of New York, United States

The research discussed in the paper comes from a multifaceted program for the teaching and learning of early statistical reasoning in Cyprus. The overall aim of the program is to enhance the quality of statistics education offered in Cypriot elementary schools by facilitating professional development of teachers using exemplary technological and educational tools and resources. As part of the program, professional development seminars for the teaching of statistics with the use of Tinkerplots – a dynamic data-visualization package designed specifically for young learners – were designed and offered to elementary school teachers. The article discusses insights gained from the seminars regarding the ways in which computer visualization tools can enhance teachers’ content and pedagogical knowledge of statistics.

C305: DISCRIMINANT ANALYSIS BETWEEN TWO POPULATIONS USING THE MAXIMUM FUNCTION

Thu Pham-Gia
Université de Moncton, New Brunswick, Canada

The maximum function can be used very efficiently in discriminant analysis and hypothesis testing, and can significantly improve the comprehension of the approach presented.

C306: HOW TO TEACH SOME BASIC CONCEPTS IN TIME SERIES ANALYSIS

Clelia Toloi
University of São Paulo, Brazil
Mr Sergio Martins
IBMEC-SP, Brazil

Time series teaching needs some specific concepts that are not intuitive for most students. In this paper we consider an approach to guide the early stages of time series learning. First we introduce the time series definition and some examples of the sort of series which arise in practice. Here, we comment about their components: trend and/or seasonality. After this we talk about some useful transformations to stabilize the variance, to make the data normally distributed, to eliminate trends and/or seasonal components. These transformations are necessary to reach stationarity, which underlies an important class of stochastic models for describing time series. Finally we introduce the sample autocorrelation function, which measures the linear relationship between observations at different distances apart and provides an idea about a model for generation of the data.

C307: A DIALOGUE WITH FLORENCE NIGHTINGALE

Alice Richardson
University of Canberra, Australia
John Maindonald
Australian National University, Australia

On her death in 1910, Florence Nightingale left a vast collection of reports, letters, notes and other written material. There are numerous publications that make use of this material, often highlighting Florence’s attitude to a particular issue. In this paper we gather a set of quotations and construct a dialogue with Florence on the subject of maternity hospitals. Our dialogue draws attention to strong points of connection between Florence’s use of statistics and modern evidence-based approaches to medicine and public health. We offer our dialogue as a memorable way to draw the attention of students of both statistics and health sciences to the key role of data-based evidence in medicine and in the conduct of public affairs. These are issues that were important in Florence’s time, and remain important.

C309: A PROPOSAL FOR CHANGING EDUCATIONAL PRACTICES IN THE TEACHING OF PROBABILITY AND STATISTICS

Pedro Gerardo Rocha Salamanca
Universidad Distrital Francisco José de Caldas, Colombia

In this report we present a proposal to work in the classroom starting from some theoretical and conceptual elements that might be used for teachers when facing the problem of teaching the main probability and statistics concepts in the Colombian context. We first reflect on the knowledge that is offered in the country and then outline a didactic work approach from exploratory data analysis.

C310: COMMENTS ON THE LEARNING IN INTRODUCTORY STATISTICS COURSES

Marcos Nascimento Magalhães
University of São Paulo, Brazil

A recurrent problem in teaching is to evaluate what the students will retain from the contents discussed in class. For the students who completed two basic courses on statistics, we applied a questionnaire with a test, 3 months after the end of the course. The test was composed of 50 true-false questions. The results revealed that students could satisfactorily answer the questions directly related with definitions. However, there was no such performance when the questions required additional procedures related.

C312: ASSESSMENT OF THE PEDAGOGICAL UTILIZATION OF THE STATISTICS ONLINE COMPUTATIONAL RESOURCE IN INTRODUCTORY PROBABILITY COURSES: A QUASI-EXPERIMENT

Ivo Dinov, Juana Sanchez
University of California, Los Angeles, United States

Java-applets have proved to be effective in different settings to demonstrate statistical concepts. The NSF-funded Statistics Online Computational Resource (SOCR) provides a number of interactive tools for enhancing instruction in various undergraduate and graduate courses in probability and statistics. In this paper, we present the results of a quasi-experiment aimed at assessing the effect of moderate use of SOCR on three outcome measures: course scores, student satisfaction and choice of technology to complete the final examination. One section of an upper division “Introduction to probability” class, the treatment group, was conducted with the instructor using the probability applets and materials as assessment tools in homework. Another section, the control group, of the same class was conducted exactly the same way, but not using SOCR. We compared the three outcome measures in the two groups and discuss ways to improve the quasi-experiment. Ideas are given on how to incorporate the applets in various probability courses.

C313: STATISTICS TEACHING IN HUNGARY

Klara Lokos Toth
Szent Istvan University, Hungary

Teaching statistics in an agricultural university is not an easy work. The students usually not only are not interested in the subject but are afraid of it too. So the first step would be to turn the resistance and wake up their interest. That is a difficult task and very rarely successful. How can we break the resistance of students? To answer that question is the most important first step towards successful statistics teaching.

C314: STUDENTS’ ERRORS AND DIFFICULTIES FOR SOLVING PROBLEMS OF SAMPLING DISTRIBUTIONS BY MEANS OF COMPUTER SIMULATION

Santiago Inzunza
Autonomous University of Sinaloa, Mexico

This paper reports results the main errors and difficulties experienced by a group of eleven university students when solving problems of sampling distributions by means of computer simulation using Fathom software (Finzer et. al, 2002). The main difficulties were the formulation of the population model, the definition of the statistics to be calculated in each sample and the definition of the intervals to calculate the probabilities. It was not necessary to carry out some of the long processes of the pencil and paper environment which are the source of several mistakes and difficulties. It was also possible to facilitate the interpretation of some results such as the proportions of cases of interest out of the total of possible cases.

C315: PROGRESSIVE MASTERY TESTING: DOES IT INCREASE LEARNING AND RETENTION? YES AND NO

Dalene Stangl, David Banks, Leanna House, Jerry Reiter
Duke University, United States

Student mastery of material from an introductory statistics course was compared across courses that differed by whether a progressive mastery testing method was used. Students taught using progressive mastery methods showed increases in exam scores. The increases were small but of the same order of magnitude as increases associated with earning a course grade of A versus B+ and as increases associated with 100 points increases on the SAT math test. The increase in exam scores was about 75% of the increase associated with having taken a high school advanced placement course in addition to the college introductory course. However these increases were short lived as these students showed double rates of decline when tested in follow-up semesters. All benefit of the method vanished within two semesters.

C317: A TOOL FOR COLLABORATIVE KNOWLEDGE-BUILDING IN STATISTICS EDUCATION

Tjaart Imbos, Antoinette Vesseur, André Koehorst
Maastricht University, The Netherlands

Learning to understand statistical concepts, necessary to become a knowledgable scientist, is difficult. From learning and educational points of view it may help if students work together in groups on learning tasks. If they are stimulated to write about their understanding of relevant concepts they become active learners. The writing can be seen as a process of developing understanding. This process could be stimulated by using a computer tool. Such a tool, called POLARIS was used in our study. In this paper we describe the developmental process of POLARIS. The statistical learning environment in which we used it and how we used it is described.

C319: READING ABILITY AS A PREDICTOR OF AFRICAN-AMERICAN GRADUATE STUDENTS’ WRITING PROFICIENCY IN THE CONTEXT OF STATISTICS COURSES

Kathleen M. T. Collins
University of Arkansas at Fayetteville, United States
Anthony J. Onwuegbuzie
University of South Florida, United States

Assessing technical writing skills, such as writing results stemming from statistical analysis of real data, is considered by some statistics instructors as a viable way of providing authentic assessment. Unfortunately, many students find such technical writing extremely difficult. Because writing result sections of quantitative studies involves the ability to receive, to encode, to translate, and to reproduce material presented in statistical textbooks, it is likely that reading ability plays an important role in the technical writing process. This study’s purpose was to examine this link among 115 African-American graduate students. A canonical correlation analysis revealed that reading ability significantly predicted students’ abilities to write the results of the following four statistical analyses: correlation analysis, independent samples t-test, dependent samples t-test, and chi-square analysis.

C320: RELATIONSHIP BETWEEN READING ABLITY AND STATISTICS ANXIETY AMONG AFRICAN-AMERICAN GRADUATE STUDENTS: IMPLICATIONS FOR THE TEACHING AND LEARNING OF STATISTICS

Kathleen M. T. Collins
University of Arkansas at Fayetteville, United States
Anthony J. Onwuegbuzie
University of South Florida, United States

The several antecedents of statistics anxiety that have been identified, at best, identify students who are at risk for debilitative levels of statistics anxiety, thereby having only minimal implications for intervention. Further, these few interventions have tended to be teacher-centered rather than student-centered. The area of reading ability appears to offer a viable avenue for research on the antecedents of statistics anxiety. Because statistics textbooks often present complex material, students with low reading ability possibly are prone to experience high anxiety levels. To date, this link has not been formally investigated. Thus, this study examined whether reading ability predicts statistics anxiety levels among 92 African-American graduate students. A canonical correlation analysis revealed a strong multivariate relationship between reading ability and statistics anxiety. Instructional implications are discussed.

C322: A REAL DATA APPROACH TO TEACHING THE CONSEQUENCES OF NON-RANDOM SAMPLING

Michael C. Mosier
Washburn University, Kansas, United States

An important topic, which most statisticians fully understand, is that in order for many statistical inference procedures to be valid, the data must come from a random sample. However, the consequences of not meeting this assumption are seldom demonstrated. In this paper, we discuss how heart rate data collected by students may be used to demonstrate this concept. When asked to collect data from a sample of five people, the students will never follow true random selection. The resulting data then gives the instructor a large number of samples of size n=5, ready-made to estimate the coverage probability of confidence intervals for the mean heart rate. This coverage probability has never failed to be far below the stated confidence level. We then pool the data and divide the observations randomly into samples of size n=5. Once confidence intervals are constructed on each of these random samples, the coverage probability is correct.

C323: DEVELOPMENT OF STATISTICS METHODS TEACHING IN PRIMARY AND SECONDARY EDUCATION (SCHOOL)

Diana Rosana Kucukbeyaz, Mabel H. Batto, Ernesto A. Rosa
National University of Tres de Febrero, Argentina

The Federal Law of Education in Argentina has included Statistics in Primary and Secondary School into Mathematics and other areas but the teachers were not themselves competent in Statistics and were not able to explain the concepts simply enough for students to understand. Several educators groups included some points or chapters about Statistics in the books of Primary and Secondary School trying to give, to the different levels students, the principal concepts and examples of Statistics Methods. Now: How much success has this intention? Do the students of Primary and Secondary School understand teacher’s way to develop the techniques that they suggested? Do teachers and professors in charged of show these techniques capacitated to develop successfully those Statistics subjects included in the books? These are the doubts that starts this Project, which Hypothesis is: verify if the adopted methodology to develop the uses of Statistics Methods could be or not considerate successful; verify teachers enabling, of Primary and Secondary School, to transmit Statistics Methods; and finally, if those two affirmations turn out rejected, to propose contents, points of view and teaching Methods to be used to carry out the Education Federal Law statements satisfactory as far as Statistics teaching is concerned.

C324: TEACHING ESTIMATION ABOUT THE FAMILY OF SRS, PPS AND MPPS SAMPLING DESIGNS

Zhang Yong, Xie Qingquan, Niu Junjun
National Bureau of Statistics, China

This paper introduces the MPPS sampling design developed by the National Agricultural Statistics Service of Agricultural Department in the U. S. A. to solve the problems of multi-purpose survey. Then it gives a uniform estimator formula that is suitable to the family of SRS, PPS sampling and MPPS sampling designs under some conditions. The application of the MPPS sample design and how to give this course to the students are discussed also.

C325: SOFTWARE TOOLS FOR INTRODUCTORY STATISTICS: A STUDENT-BASED COMPARISON

Mark Werner
The American University in Cairo, Egypt

We investigate experiences of first-year, non-science students with three data analysis tools during a pre-Calculus, introductory statistics course at the American University in Cairo, Egypt. Students could choose between DataDesk, Excel or StatCrunch, and were required to use one of these packages to analyze data collected for a semester project. It was especially important to evaluate these software packages from the point of view of a first-time user with no previous experience in either Statistics or advanced computer usage; several students were at first somewhat apprehensive of using a computer to analyze data. Among other outcomes, this investigation led to the development of student-based comparison of three software packages, from the perspective of a large group of potential users.

C327: DEVELOPING A PROGRAMME OF STATISTICAL TRAINING TO SUPPORT A COMPETENCY FRAMEWORK IN THE ONS

Ceri Underwood
Office for National Statistics, United Kingdom

The United Kingdom Office for National Statistics (ONS) has recently committed to modernising its Learning and Development infrastructure and has introduced four 'job families' and associated competence frameworks. This new structure has raised the need for a programme of Statistical Training that develops the expertise of staff in accordance with ONS business needs. The resulting teaching programme is diverse; using a variety of teaching sources ranging from internally led statistical training modules and courses, to a collaborative MSc programme, which is delivered jointly by the ONS and University of Southampton. Links are also made within this paper to the infrastructure that has been put in place at the ONS to support staff as they progress with their statistical/methodological careers.

C328: EXPERIENCE WITH USING ELECTRONIC SURVEYS TO MEET THE SIX RECOMMENDATIONS OF THE GAISE COLLEGE REPORT

Bill Rybolt, Joe Aieta
Babson College, United States

For several years we have used web-based surveys to collect data from the students in our introduction to probability and statistics course at Babson College. We believe that the use of such surveys and the data produced from them is an ideal way to meet the recommendations of the GAISE College Report. Our surveys are designed to collect data representing all four measurement scales: categorical, ordinal, interval, and ratio. In this presentation we give examples of the questions we ask and the surveys from which they come. As we go through each of the six recommendations of the GAISE report, we demonstrate how our use of our survey data contributes to achieving that objective and indicate areas needing improvement.

C329: THE LIVING CENSUS

Bruno C. de Sousa
Universidade do Minho, Portugal

What is a Census? What purpose does a Census serve? How should a Census be conducted? What conclusions can be drawn from a Census? What consequences does a Census have for me? These are some of the questions that we intend to address in the Project entitled, The Living Census. This project will consist of the following four distinct phases: Discovering Portugal, Getting to Know the Community in which We Live, Dealing with the Data and finally, Taking Command. Each one of the phases of the project will consist of a series of activities where concepts in the area of mathematics, geography, and graphic arts, among others, will be introduced. These activities will then be put together in the form of a Guidebook of Practical Activities for The Living Census, to be distributed to all secondary schools in the country. Presenting The Living Census in the secondary career of these students will bring more awareness of the topic to the students and will encourage them to participate in civic activities, such as a census or an election.

C330: ON AVERAGE AND OPEN-ENDED QUESTIONS

J.A. García Cruz, Alexander J. Garret
Universidad de La Laguna, Tenerife, Canary Islands

This paper reports on our ongoing research on the teaching and learning of averages in secondary mathematics education based on a questionnaire that combine open-ended and multiple-choice questions. Analysis has led us to note that many students who choose the correct answers in multiple-choice questions were completely unable to demonstrate any reasonable method of solving related open questions.

C331: A UNIFIED APPROACH TO TESTING HYPOTHESES ABOUT PARAMETERS OF A NORMAL POPULATION

Nikolai Kolev, Delhi Paiva
University of São Paulo, Brazil

We discuss our practice related to classical hypothesis testing about unknown parameters of a normal population offered to undergraduates in the University of São Paulo. We consider the tests for the population mean and variance when the sample size is "large" and "small" as well as the well-known tests comparing the means and variances for independent samples. We suggest an algorithmic approach, which our students appreciate.

C332: AN INVESTIGATION ABOUT TRANSLATION AND INTERPRETATION OF STATISTICAL GRAPHS AND TABLES BY STUDENTS OF PRIMARY EDUCATION

José Carlos Carrión Pérez
University of Las Palmas de Gran Canaria, Spain
María Candelaria Espinel Febles
University of La Laguna, Spain

This work used a test to explore capacities, limitations and errors that students may have during processes of learning statistical graphs in Primary Education. We display some results of a test given to groups of students from schools in New Zealand and Spain, to investigate how they make translations between different types of graphic representation.

C333: ANALYSIS OF DIDACTIC SITUATIONS SUGGESTED TO DISTINGUISH DISJUNCTIVE EVENTS AND INDEPENDENT EVENTS

Adriana D'Amelio de Tari, Angela Diblasi
Universidad Nacional de Cuyo, Mendoza, Argentina

The concepts of disjunctive events and independent events are didactic ideas that are daily used in the classroom. Previous observations of attitudes and assessment given to students at university level who attend the introductory Statistics course have helped detect the confusion between disjunctive events and independent events, and indicate the spontaneous ideas that students tend to elaborate about both concepts in the different situations in which these notions have to be considered. However the relation between these ideas and their formal definitions is not known in detail. In this work, we use Didactic Engineering as methodology to analyze students’ misconceptions, their persistence, and the process by which the student confronts his misconceptions by applying theoretical concepts. The aim is to improve the teaching of these topics.

C335: DOES VIEWING VIDEO OF STATISTICS IN ACTION AFFECT STUDENT ATTITUDES?

J. Richard Alldredge, H. Dean Johnson, Jose J. Sanchez
Washington State University, United States

Recent studies have indicated that student attitudes can assist or impede learning and that students tend to have negative attitudes towards mathematics and statistics. We used a treatment-control experimental design to explore the effects of using video clips, showing applications of statistics in real world settings, on student attitudes toward statistics. Students with higher scores on standardized tests of mathematical and verbal ability, who were exposed to the video treatment, had more positive attitudes toward statistics than video exposed students with lower ability scores and more than students who were not exposed to the video treatment.

C336: INTEGRATING STATISTICS AND INFORMATION TECHNOLOGY INTO AN INVESTMENT RISK COURSE

Philip L.H. Yu
The University of Hong Kong

Dated back to the academic year 1990-91, our statistics department has offered the course named “Statistics of Investment Risk”, the first investment course in our university. It is rather unusual but we understand that investment risk is making use of many statistical methods. With an explosion in information technology (IT) in the past decade, more IT elements have been integrated into the course so that students can learn through an interactive approach to understand various concepts in modern investment theory. This paper will introduce how to integrate statistics and information technology into an investment risk course.

C337: THE TOTAL PROBABILITY THEOREM, THE “DEPENDS” ARGUMENT AND SIMULATION

Gabriel Yáñez Canal
Universidad Industrial de Santander, Bucaramanga, Colombia

As an alternative to the Total Probability Theorem, the “depends” argument that students use to calculate marginal probabilities is studied. We discuss an experience with undergraduate engineering students who took a computed aided basic probability course based on the frequency approach. The result of this experience shows that an adequate interpretation of the outcomes of simulated random experiments allows conjecturing and arguing algebraic results of the theory of probability.

C339: LEARNING OBJECTS AND BLENDED LEARNING: AN EXAMPLE OF A CONTINUING EDUCATION COURSE

Helle Rootzén
Technical University of Denmark

Faced with a new generation of students who are used to exploiting the possibilities of the computer, we need a new type of education that will reflect a rethinking of content, form and duration. In the future, education will be in the form of ‘voucher systems’. You get a set of vouchers and use them to attend the specific chunk of a study programme you need whenever and wherever it suits you. If the providers are to meet these requirements, the task of developing new courses and tailoring these to new students must be manageable. We therefore propose a new type of research-based courses. These are structured around ‘Learning Objects’, short complete education sessions, which may be combined in various ways according to the student’s interests and levels. We combine the Learning Objects with ‘blended learning’ and the ideas are tried out in research-based continuing education in applied statistics.

C340: A WEB-BASED EXERCISE TOOL USING RANDOMIZED DATASETS FOR STATISTICAL EDUCATION

Peter Pipelers, Olivier Thas, Dries De Vleeschauwer, Jean-Pierre Ottoy
Ghent University, Belgium

A learning environment for statistical education aims at providing on-line course material for distance learning. It typically also includes practical exercise material, providing the student the ability to test his/her statistical knowledge in a real-life situation. A desirable aspect of a self-test module is that students cannot cheat and copy the answers from their colleagues. The Elestat project maintains this scenario with the construction of a web-based self-test module that contains many realistic datasets of which the observations are randomized before they are presented to a student, obliging the student to analyze a different dataset each time an exercise is started. The student is guided through the exercises in a step-by-step manner. The open source statistical software package R takes care of calculating the correct solution in real-time and offering immediate feedback. The web-technology is based on a collaboration between Java and the Rserve-interface. The Elestat project is accessible via the website www.elestat.be.

C341: TEACHING LINEAR MODELS BASED ON OPERATIONS RESEARCH IN STATISTICAL EDUCATION

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

Teaching the topic of linear models is a complex process. A new teaching process will be investigated which we will consider in two different ways: on one hand linear models and quadratic programming problems are formulated and solved by statistical methods; on the other hand the solution of the linear regression model with constraints makes use of the simplex methods of linear and quadratic programming.

C401: SEMIOTICS FUNCTION AND LEARNING OF ARITHMETICS MEAN

Marcos Pinho
Universidade do Sudoeste da Bahia, Brazil

This paper continues earlier studies about the teaching and learning of the arithmetic average and it is part of a broader research in progress at Santiago of Compostela University (Spain). We have analyzed a sample of six teaching manuals (textbooks) used for teaching mathematics at high schools in Salvador, Bahia. The study is based on theoretical ideas by Godino and Batanero (1994; 1998) and Godino and Recio (1997) who propose a semiotics perspective based on the functions of signs by Hjelmslev (1943), later known as “semiotic function”.( Eco, 1979).

C402: TEACHING AND LEARNING OF THE POISSON’S MODEL: A MODEL BUILDING EXPERIENCE

Maria Inez R. Miguel
Pontifícia Universidade Católica de São Paulo, Brazil

In this article, we describe an experience with the teaching and learning of the Poisson´s Model, directed to university students. We used the Anthropological Theory of the Didactic and the principles of the Mathematical Modeling Process for the elaboration of the teaching sequence, showing that it is possible to build the model without resorting to the Binomial limit, making use of the notions of calculus. In the development of the learning activities, the computer was used as a didactic tool. The analysis of results was based on the Theory of the Semiotic Functions and proved that the students learned many significant elements considered in the teaching. On the other hand, the study allowed for the identification of difficulties throughout the process: for example, the interpretation of expressions such as “at least” and “at most”, the representation used, the analysis of the results of hypothesis tests and the manipulation of the software

C403: IMPROVING THE TEACHING OF STATISTICS IN BUSINESS EDUCATION: LESSONS AND REFLECTIONS

Bodapati V. R. Gandhi
University of Puerto Rico, Mayagüez, Puerto Rico

Undergraduate business students in the United States and U.S.-modeled educational institutions, often take a course in research methodology or a research seminar during their final year which requires basic statistics courses as prerequisites. This paper speaks about improving the teaching of statistics in business schools to serve the final year research methodology course. It identifies the need for a change in the methodology of teaching statistics so as to enable the students to better identify the appropriate statistical procedures and synthesize statistical results in their real world research project. Revisions in the syllabi and philosophy of teaching of statistics are suggested.

C404: DESIGNING A STUDY PROCESS OF THE CENTRAL LIMIT THEOREM FOR ENGINEERS

Hugo Alvarado
Universidad Católica de la Santísima Concepción, Chile
Carmen Batanero
University of Granada, Spain

In this paper we analyse the meaning planned by a teacher to introduce the Central Limit Theorem to engineers. This meaning takes into account the nature of variables and different approaches to the distribution of the sum or random variables. The planning of teaching is based on the mathematical knowledge about the theorem and the theoretical framework about semiotic functions, which is currently been developed at the University of Granada, Spain. The different elements of meaning for this theorem were characterised after the analysis of a sample of University statistics textbooks, the study of the theorem evolution along history and previous research related to its understanding. The didactic proposal incorporates simulation with manipulative materials and the @Risk Software (Risk analyser for Microsoft Excel). Results from this work will serve to improve the correct application of different elements of meaning for central limit theorem when solving engineering problems and to prepare new didactic proposals to teach statistics to engineers.

C405: STATISTICS EDUCATION APPLIED TO AGROFORESTRY AREA (2005)

Esperanza Ayuga Téllez, Concepción González García, José M. Moral Medina
Universidad Politécnica de Madrid, Spain

Basic subjects play an important role in engineering education. Applied Statistics may be regarded as a basic subject as well as a technical subject, and occupies therefore a central place in agro-forestry engineer professional curriculum. Statistics is present in some proportion in our whole life. With the purpose of implementing new methods for statistical learning, in the framework of European Higher Education Area, an experimental proof has been started during a quarter of academic year 2004/05 of the third class in the Faculty of Forestry Engineers from Polytechnic University of Madrid. Methodology was oriented for students to improve capacities of oral expression, information search, use of recent technologies and experience in knowledge analysis and synthesis, together with acquisition of minimum knowledge required in the subject.

C406: DESIGNING STATISTICAL LEARNING OPPORTUNITIES FOR INDUSTRY

Arthur Bakker, Phillip Kent, Richard Noss, Celia Hoyles
University of London, England

Our interest in the techno-mathematical literacies employees need in their jobs has led us to do case studies in different industrial sectors and to design learning opportunities for improving employees’ techno-mathematical literacies. We conceptualise the learning opportunities not as training or transfer, but as forms of “boundary crossing” between employees from a company and us as researchers. Two examples are given in which packaging managers explore and discuss a realistic problem using TinkerPlots, an educational software tool. The results emphasise how important it is to allow managers to bring their ideas and concerns to the problem situation so they can connect these to statistical theory that is relevant in statistical process control (SPC). This approach is contrasted with SPC training we have observed in two industrial sectors.

C408: PROMOTING POSITIVE ATTITUDES TOWARDS STATISTICS IN PEDAGOGY MAJORS THROUGH PROJECT WORK

Jefferson Biajone
State University of Campinas, Brazil

Unsatisfied with the negative attitudes towards a statistics course that are common among Pedagogy majors, the author of this article and instructor of this course believes that these attitudes are very likely to be the result of traditional teaching approaches that emphasizes the mathematical and computational aspect of the statistical knowledge. Eager to change these negative attitudes to positive ones, the author decides to utilize the project work under a student cooperative environment and, as the course goes on under this new approach, this option not only demonstrated the possibility of changing these attitudes, but it proved to be a valid professional development experience for the instructor himself as well.

C409: A DIDACTIC PROPOSAL FOR THE INTEGRATION OF STATISTICS AND BASIC INFORMATICS IN AN UNDERGRADUATE PRE-DEGREE PROGRAM: ADMINISTRATION AND ECONOMY OF SMALL AND MEDIUM-SIZED BUSINESSES

Norma Patricia Caro, Cecilia Díaz, Margarita Díaz, María Stimolo
Universidad Nacional de Córdoba, Argentina

In 2004 the School of Economics and Business Administration at the National University of Córdoba opened an undergraduate pre-degree program, Small and Medium-Sized Business Administration and Economy. The first-year curriculum includes Statistics and Basic Informatics, which can complement each other in the teaching of their contents and in tests. Therefore, a test was written which makes possible the integration of both subjects. It is an Integrating Assignment which must be submitted after the theory and practical applications in both subjects have been learned. This test is published on the Educational Platform with a series of guidelines. The result of the experience was positive, since it fostered students’ learning and proved a collaborative form of work between the professors in both subjects.

C410: POSTGRADUATE TEACHING PERFORMANCE EVALUATION SYSTEM

Francisco Casanova del Angel
Unidad ALM del IPN, Mexico

A postgraduate teaching performance evaluation methodology is presented starting with the design of a questionnaire applied to enrolled in the Master’s in Sciences program. The evaluation instrument was divided into four sections and programmed in informatics language. Regular students answered 543 questionnaires, one per course taken during 2003 and 2004. The information was studied statistically course-by-course from a point of view both educational and psychological. The results were analyzed course-by-course taught and on an overall basis.

C412: SHE WILL BE LOVED: COLLABORATIVE PROJECT WORK AND STATISTICS LEARNING

Margarida César, Edgar Dias
Universidade de Lisboa, Portugal

In a knowledge-based society in which quantitative data play a major role, namely in the media, statistical literacy is becoming more and more essential in order to be a critical and active citizen. Although this is usually recognised in literature and in policy documents, statistics learning has not changed much and still needs further evolution in terms of daily practices. Research data underlines the role played by project work and by collaborative work as mediators and facilitators of transitions from students’ previous knowledge and life experiences, and academic knowledge. Interaction and Knowledge is a research project aimed at studying and implementing peer interactions to promote students’ academic achievement. Results illuminate that project work associated to collaborative work is a powerful tool for statistics learning. A critical analysis of some cases also show the challenges associated to this kind of work.

C413: COMPUTING PROBABILITIES FROM TWO WAY TABLES: AN EXPLORATORY STUDY WITH FUTURE TEACHERS

Assumpta Estrada Roca
University of Lleida, Spain
Carmen Díaz
University of Granada, Spain

Being able of correctly read and interpret two ways tables is a basic component of statistical literacy for every citizen. Therefore, future teachers who will be responsible to teach statistics to children at school level should acquire these abilities along their training. However, this capacity is taken for granted in Spain and its teaching is not usually included in the curriculum for training teachers. In this study present the results of a small exploratory study that describe the future teachers’ semiotic conflicts in solving elementary probability problems when data re given in a two-way table.

C414: AN APPROXIMATION TO THE STATE OF THE ART OF STATISTICS EDUCATION IN COLOMBIAN SCHOOLS

Felipe Fernández, Nubia Soler
Universidad Pedagógica Nacional, Colombia

Results obtained from a project carried out with the aim of studying the state of the art of statistics education in Colombian schools are reported. The methodology used was based on collecting, summarizing and analyzing more than forty written productions of Colombian authors, all of them related to statistics or probability education. These included monographs, research projects and lectures presented during Mathematics Education events, and school textbooks. It can be pointed out, as a finding, that it does not exist a consolidated vision of what statistics and probability concepts and methods should be taught and how they should be taught in schools. Further, very few of the reviewed written productions address the relationship between the teaching and learning of statistics and the use of technology.

C416: COLLABORATIVE WORK IN STATISTICS AMONG PRE-SERVICE MATH TEACHERS: AN EXAMPLE FROM PORTUGAL

Sílvia Alves Rodrigues Antunes
Escola Básica dos 2º e 3º Ciclos de Marrazes, Leiria, Portugal
Carolina Carvalho
Universidade de Lisboa, Portugal

Collaboration is an important feature of today’s teacher education. According to several researchers, teachers are open to work collaboratively, although they often work in an individual and solitary manner. Since the nineties statistics education includes the need for children to be able to pose questions, collect, organize and represent data in a spirit of investigation and exploration. This is enhanced by implementing student projects. The main research question in this paper is to clarify how three pre-service math teachers planned and prepared classes and reflected afterwards upon them. A qualitative methodology was adopted. It is shown with empirical evidence that collaborative work between teachers is an important approach to solve difficulties in statistical and didactical knowledge. Our results also show that these are the areas teachers have to improve in order to become more confident teachers of Statistics.

C417: THE DEVELOPMENT AND FUTURE OF THE PRE-UNIVERSITY STATISTICAL EDUCATION IN EGYPT: A CASE STUDY

Fayez M. Mina
Ain Shams University, Egypt

This paper is an attempt to study the development and future of the pre-university statistical education in Egypt, where it seems that the findings of the present study is applicable to many developing countries. The study starts with summing up the present state of art in the pre-university statistical education in Egypt and having a global view in the area. Paradigm shifts in science, mathematics and mathematics education were examined and their implications on statistical education were identified and classified into long, intermediate and short terms. The future of the pre-university statistical education in Egypt was described in terms of almost the scenarios; progressive, reformatory and conservative ones.

C418: PROJECT WORK IN STATISTICS: STATISTICS LEARNING AS A TOOL TO HELP STUDENTS’ KNOWLEDGE ABOUT THEIR EDUCATIONAL COMMUNITY

Nuno Santos, Margarida César
Universidade de Lisboa, Portugal

The development of students’ competencies expressed in current curricular documents is a complex task that teachers have to perform (Brocardo, 2005). Project work is a practice that can allow for this development (Abrantes, 1994). According to the Portuguese Department of Basic Education (2001), project work, namely in statistics, is one of the learning experiences that all students should have the opportunity to engage in. This study is a part of the research project Interaction and Knowledge, whose main goal is to study and implement collaborative work within classrooms. We discuss how students from two 7th grade classes (compulsory education, 12/13 years old) used project work in statistics to learn more about statistical contents, about their colleagues, and to develop social, cognitive and affective competencies.

C419: TWO BATTLES . . . TWO VICTORIES: HOW TO LEARN PROBABILITIES THROUGH A FAMILIAR GAME

Lucília Teles, Margarida César
Universidade de Lisboa, Portugal

The beginning of the school year is a crucial time for grasping students’ interest and attention regarding class work. This research took place in two 9th grade classes (n=38 students) from two different schools and realities. The task, which was the same in both cases, was the first of the school year. This task also marked the beginning of a new working methodology: collaborative work. Students played the Warship game in order to learn certain concepts related to the probability of an event. The game was followed by some questions about it, connecting intuitive and formal notions. Students were deeply engaged in the task because they love to play games. This way of beginning the school year was very stimulating for them. They felt comfortable learning Mathematics. We also observed that students did not reject the task and they did not experience any difficulty in these mathematical contents.

C421: DEMONSTRATIONS IN PROBABILITY AND STATISTICS USING EXCEL

Giuseppe Cicchitelli
University of Perugia, Italy

The list of technologies available in the teaching of statistics has been expanded in the last decade. It includes free internet-based analysis tools, multimedia textbooks, Java applets and software designed to help students learn and understand statistics. This paper presents some learning objects, developed in Excel, dealing with the following topics: Student’s T as the ratio of two appropriate independent random variables. Empirical comparison of the efficiency of different estimators of the population mean. Graphical presentation of the idea of consistency. Proper use of these tools and advantages of the Excel-based software are discussed.

C422: A NOTE ABOUT A NEW INDEX TO EVALUATE TEACHING QUALITY

M. Civardi, E. Zavarrone
University of Milano Biccocca, Italy
C. Crocetta, L. De Cesare
University of Foggia, Italy

Aim of this paper is to study a new index, called CI that has been proposed to measure the teaching quality in University courses. The questionnaire adopted by many Italian Universities to evaluate teaching quality of courses, has many items surveyed on a four points ordinal scale. This solution has many advantages and some limitations. Civardi (2002) has proposed a new index that summarizes results on each item for a single course on an interval [-1, 1]. The CI index is the algebraic sum of two indexes: an index expressing the score obtained on the half-plane of positive assessments and another corresponding to the half-plane of negative ones. In order to study the main characteristic of the CI index we have considered its sample space under different situations.

C423: USING PERCEPTIONS OF RANDOMNESS TO TEACH STATISTICS TO FIRST YEAR STATISTCS STUDENTS IN SOUTH AFRICA

Kobus de Wet
Free State University, South Africa

The perception of randomness is very important in the statistical science. It is therefore of critical importance that statistics students master the concept of randomness. It is usually difficult to change deep rooted perceptions of randomness. Many statistics students in South Africa are so-called historically disadvantaged students. They are classified as such because they generally received poor mathematics teaching at school level compared to other statistics students. The lottery game can be regarded as an ideal opportunity to teach randomness and other statistical concepts. Three data sets are compared: The lotto winning numbers, random numbers generated and the random numbers generated by two groups of first year statistics students.

C424: A CONSTRUCTIVIST APPROACH TO COURSE DESIGN IN A GRADUATE STATISTICS COURSE

Paul J. Fields, Aubrey Baxter, Larry Seawright
Brigham Young University, Utah, United States

Too often students leave their first statistics course with at best a fuzzy understanding of basic statistical concepts and procedures. A disconcertingly high proportion cannot adequately describe or perform a t-test, for example, when taking subsequent courses. This suggests that a different approach to teaching and learning is necessary, particularly for graduate students who will need statistical tools in their research. Rote memorization of facts does not provide the preparation requisite for graduate research. A constructivist approach in course design could provide a learning environment in which students move beyond lower level cognitive skill development. Initial implementation of this approach has produced encouragingly positive results.

C426: CONCEPTIONS ABOUT PROBABILITY AND ACCURACY IN ARGENTINE STUDENTS WHO START A CAREER IN ENGINEERING

Mónica Giuliano, Ignacio Nemirovsky, Sonia Concari, Silvia Pérez,
Marcelo Alvarez, Aldo Sacerdoti, Mónica Pereziano
Universidad Nacional de la Matanza, Argentina

Previous misconceptions about science may cause difficulties in the interpretation of scientific models. A Likert scale test was made and presented to part of the population in order to find out beliefs about science and technology that students who wanted to have a degree in engineering at Universidad Nacional de La Matanza had. Principal components analysis was performed to identify the testees’ profile. We show the results referring to the beliefs and conceptions about probability, margin for error, accuracy, certainty, truth and validity. Although most of the people who answered the survey acknowledged the presence of probability in the results of a physical experiment, they also gave it accuracy and truth values which are not inherent. It is also remarkable that only a very low percentage has a posture that is coherent with the scientific vision of the terms.

C427: FORMAL ASSESSMENT OF AN INNOVATIVE WEB-BASED TOOL DESIGNED TO IMPROVE STUDENT PERFORMANCE IN STATISTICS

José Antonio González, Erik Cobo, Pilar Muñoz
Technical University of Catalonia, Spain
Lluis Jover,
University of Barcelona, Spain

We have developed a web-based tool, called e-status, that is able to generate individually different statistical or mathematical problems and to correct the students´ answers. The tool is well appreciated by the students since it is available anywhere and anytime. This ability allows the weaker students to practice the concepts as needed, without obstructing the progress of the more advanced students. Although the use of Information and Communication Technologies (ICTs) is widely extended in undergraduate education, there are few studies evaluating the effectiveness of learning methods based on ICTs. In this work, the authors propose a blinded randomized trial to assess the e-status effects on improving average exam rating on dentistry students. The data results will be available by February 2006.

C428: THE RESULTS OF A PERFORMANCE TEST: A MULTILEVEL ANALYSIS

O. Giambalvo, A. M. Milito, A. M. Oliveri
Università degli Studi di Palermo, Italy

The aim of the paper is to analyse the results of a performance test, created to evaluate how well a group of middle school pupils learned statistics, using multilevel analysis. The results show the importance of the classroom/teacher and the school on the learning process.

C431: SOTSS: A SYSTEM FOR ONLINE TESTING OF STATISTICAL SKILLS

Derk Jan Kiewiet, Natacha Borgers
University of Groningen, The Netherlands

This paper introduces the system SOTTS for online testing of statistical skills that involve software packages as SPSS. The emphasis of the system is on the interpretation of statistical output, and drawing conclusions based on these interpretations. Basic characteristics of the system are: 1) individual, 2) flexible, and 3) interactive. The system can examine statistical skills efficiently. The efficiency is achieved by the possibility to give exams at different time slots, without increasing the teacher’s workload unacceptably. Besides, the system also avoids the possibility for students to pass on answers or questions to each other.

C432: USING MATHEMATICS AND STATISTICS TO ANALYZE WHO ARE THE GREAT SLUGGERS IN BASEBALL

Randy Taylor
Las Positas College, United States
Steve Krevisky
Middlesex Community College, United States

In this presentation, we share the results of statistical work that we have done over several years, in order to determine who are the best sluggers in the game of baseball in the US. Using z scores, we examined yearly home run and slugging average figures, so as to analyze which batters were the most SD’s above the mean. We used cutoffs of 200 at bats or 250 plate appearances before expansion, and increased this by about 5%, to account for the increased number of games played after the expansion in the early 1960’s. Since real data are involved, we feel that this would be a very good application for students in a basic statistics class, and we will present various charts in the following discussion, and summarize our findings. This is a shortened version of what we have presented at numerous conferences in the US. Please let us know if you wish to see the full version of our paper!

C433: AN INTERACTIVE CD-ROM TO TEACH STATISTICS APPLIED TO HEALTH NOTIONS TO STUDENTS IN THE FUNDAMENTAL SCHOOLING

Maria Lucia Marçal Mazza Sundefeld, Ariane Vieira Guimarães, Cleide dos Anjos Santos,
Gustavo Kendi Kavano, Adriana Beatriz S. P. Fernandes, Isabel Cristina Lui Poi
São Paulo State University, Brazil

The Brazilian students of about 12 years old, in two Fundamental Schooling 6th grade classes of each of the three public schools willing to participate of the project of testing CD-Rom, to be used by all students of this grade in Araçatuba, SP, Brazil. The main of this paper is to offer a tool, a CD-Rom, to help the 6th grade students to learn about statistics and health. The assessment test and questionnaire were applied before and after the use of the CD-Rom, in order to have the results compared. Means, percentage, and graphs are included in the 6th grade curriculum, thus these were the topics explored in the interactive software program. Developed using the software Macromedia Flash MX 2004 and illustrated in a cheerful way, it presented using positive motivation. Comparing the results of the questionnaires we conclude the efficiency of this tool to help students to learn notions on basic statistics based in health subjects.

C435: AN ITEM RESPONSE ANALYSIS OF STATISTICS USE IN THE WORKPLACE

John A Harraway
University of Otago, New Zealand
Dalton F Andrade
Federal University of Santa Catarina, Brazil

Training in statistics at university should be informed at least in part by what graduates will have to do with acquired statistical knowledge after graduation. A sample of 977 employed graduates with PhD and Masters degrees in seven specialties with statistics pre-requisites at university identifies which of 46 statistics based techniques (the items) they use in their work. A two parameter item response model uses 32 of the 46 items to build a scale measuring the extent of statistics use in the workplace and creates a value for each graduate which is used to summarize differences between the use of statistics in the seven specialties. Implications for syllabus construction to better prepare graduates for the workplace are discussed.

C436: MICROECONOMICS FORECAST: LEARNING BY DOING; A TEN YEARS GRADUATE LEVEL EXPERIENCE

Jean-Hugues Chauchat
Université Lumière Lyon, France

For the past twenty years, we have been using an original technique to teach statistics and Microeconomics Forecast Methods to postgraduates studying economics, computer sciences and statistics. After the usual lectures and practical exercises in the lab, students, by groups of two, have to find a shop, a company, a community organization, etc., which provide them time series of sales or activities in order to modelize them and calculate forecast for the next days, weeks or months. They find their “client” by themselves. The professor works with them as a consultant. More than 100 different times series forecasts have already been carried out by students on this program over the last 20 years. This year 2005-2006, we use the same teaching method in our double diploma program with the National Economics University in Kharkov, Ukraine.

C437: PROBLEMS WHEN INTERPRETING RESEARCH RESULTS USING ONLY P-VALUE AND SAMPLE SIZE

Rink Hoekstra, Henk A.L. Kiers, Addie Johnson, Marleen Groenier
University of Groningen, The Netherlands

The following three probabilities seem crucial when interpreting data, especially in the behavioral sciences:1) the probability that an effect is present in the population, 2) the probability that a replication is significant; and 3) the probability that the effect for a single individual in the population is in the expected direction. In our study, we asked 51 subjects (university students and lecturers in psychology) to estimate these probabilities after reading a short description of a hypothetical experiment with as outcomes only p-value and sample size given. Large variations in estimated probabilities were found. However estimates of the probabilities tended to increase as a positive function of sample size for a fixed p-value. Simulation studies show that , assuming a uniform prior distribution for the parameter, this turns out to be incorrect for all three probabilities.

C438: CONTRIBUTION OF LEARNING STATISTICS AT SECONDARY SCHOOL TO STUDENTS’ RESULTS AT UNIVERSITY

Jaime R. S. Fonseca
Pólo Universitário do Alto da Ajuda, Portugal
Carla A. L. Martinho
Universidade Aberta, Portugal

This study concentrates on the analysis of responses to a questionnaire given to a sample of University Students in Portugal that concerns the teaching/learning of Statistics and Data Analysis. We first focus on the effectiveness of teaching Quantitative Methods at secondary level as regards increasing performance in the Introductory Statistical Course (ISC) at University level. The second question is related to the students’ feelings towards Mathematics and whether these feelings imply a difference in students’ performance on statistics. Even when results cannot be generalised, since the study is limited to our context, the data analysed suggest the need to rethink the goals of teaching statistics at secondary school level, at least in our context.

C439: TEACHING OF BAYESIAN ESTIMATION OF “P” PROBABILITY IN A BERNOULLI PROCESS

María Teresa Gil
Universidad Nacional Buenos Aires, Argentina

Both at the School of Engineering of Universidad Nacional de La Matanza and Universidad de Buenos Aires, the teaching of statistics is considered to be highly important. The aim of this presentation is to show the advantages and disadvantages of the Bayesian estimation of the “p” parameter in a Bernoulli Process, in particular in a binomial distribution (n ; p). The similarities and differences between the classical estimation of such parameter and the Bayesian estimation will be established. The predictions which can be carried out as a result of the obtained estimations will also be developed. In order to teach both Bayesian and classical estimation of population parameters, mathematical and statistics software is used as a tool to help the understanding of the concepts. In this presentation Matlab and Excel have been used.

C440: NEW PATHS IN THE TEACHING OF STATISTICS - WITH THE HELP OF SPREADSHEETS

Manfred Borovcnik
University of Klagenfurt, Austria

Situations, in which data form the basis of decisions, are abundant. The paper illustrates some concepts involved like “the correlation coefficient” and how it measures the degree of connections between several variables, or “remaining risk” and how it is possible to draw general statements from restricted data. To embed such notions in concrete manipulations of data and easily accessible diagrams facilitates understanding of statistics. The ideas may be worked out with the help of any spreadsheet, here EXCEL is used.

C441: STATISTICS APPLIED TO EDUCATION: AN ANALYSIS OF TEACHING PLANS

Maria Cláudia Cabrini Grácio
State University of São Paulo, Brazil
Érica Aparecida Garrutti
Federal University of São Carlos, Brazil

The aim of this paper is to treat questions that are connected with the selection of contents, procedures of classroom and evaluation of the Statistics applied to Education subject. For such, it investigates sixteen teaching plans of Statistics in Education in nine institutions of graduate schools, public and private in São Paulo state. It is compared to the statistical tools present in such plans with the statistical tools used in papers, in dissertations and thesis from Education area, pointed out in preceding surveys. The results point out that the emphasis in organization of contents of Statistics in the teaching plans in this area, as well as already observed in Education scientific production, is in development of Description Statistic.

C442: AN INSTRUMENTAL OBSTACLE EXAMPLE

Catherine-Marie Chiocca
Ecole Nationale de Formation Agronomique, Castanet, France

The aim of this paper is to present the concept of an 'instrumental' obstacle. In French agricultural education, the spreadsheet is often used as a tool or “artefact” in statistics teaching. Some obstacles to learning appear due to the use of this instrument. Difficulties appear during the learning of analysis of variance by students, who are not trained mathematicians. The concept of average however, which might have been regarded as unproblematic, caused surprising difficulties during one step in the algorithm for analysis of variance. The notion of 'instrumental' obstacle seems to be pertinent in order to analyse this phenomenon. This kind of obstacle is different from those presented by the internal constraints of the artefact. This study confirms that students have yet some problems with the notion of average, but that with spreadsheet use they become aware of this difficulty.

C443: EDUCATING CHILDREN IN STOCHASTIC MODELING: GAMES WITH STOCHASTIC URNS AND COLORED TINKER-CUBES

Laura Martignon, Elke Kurz-Milcke
University of Education, Ludwigsburg, Germany

It is an established opinion that young children have good probabilistic intuitions although their mental framework for reasoning probabilistically may be fragmentary and even contain inconsistencies. We join the camp of mathematics educators who advocate an early training in stochastic thinking. We recognize, however, that such early training can only be based on a heuristic approach to stochastics. The heuristic approach that we propose here is implemented by guiding children to enactively construct stochastic situations by means of plastic tinker-cubes and stochastic urns. The aim of this enactive training is to foster the development of a dynamic mental imagery for representing stochastic situations.

C444: MATHEMATICS WITH SENSE: A DIDACTIC APPROACH FOR TEACHING STATISTICS AND PROBABILITY FROM EARLY AGES ON

Gabriela Pilar Cabrera, Ana Beatriz Sosa
Jardín de Infantes Marqués de Sobremonte, Argentina

Between 2000 and 2005 a didactic research project has taken place in kindergarten with five-year old. The starting point of such research consisted of finding out if children were able to start learning some statistics and probability notions, thus determining which notions were feasible to be learnt The research was connected to the feasibility of implementing the “CONTRATO DIDÁCTICO APROXIMATIVO” (approximate didactical contract) proposed by Brousseau-Chevallard and the organization of classes into phases, in the framework of a Dialectics Tool-Object defined by Regine Douady. During this project a chain of didactic macrosituations was designed, implemented, analysed and restructured.