OVERVIEW OF BRAZILIAN RESEARCH ON STATISTICS EDUCATION INVOLVING TEACHERS: METHODOLOGICAL PATHS AND TRAINING CONTEXTS

This article aims to analyze Brazilian research on statistics education involving teachers to highlight methodological trends and training contexts mobilized by such research. To this end, a survey was carried out in the Dissertation and Thesis Bank of CAPES, considering the descriptor "Statistical Education” and the 2013-2018 timeframe. A total of ninety-nine studies were found, twenty of which met the proposed objective. This is a documentary and bibliographic study, in which an interpretative approach was adopted using the technique of content analysis. The data analysis verified that nine of those studies did not lead to training processes with teachers. In addition, the analysis of the other eleven studies, which led to training, revealed an intrinsic relationship between the methodological path and the training contexts reported. This demonstrated the expressiveness of training contexts based on epistemology of collaboration, that is, those contexts that both give voice and listen to teachers, and recognize them as producers of knowledge. Conversely, we identified two research studies that shaped the training considering the paradigm of technical rationality, and designed training courses to address certain content/concepts that teachers supposedly do not master. It was evidenced that the conception of teacher training has a direct and explicit relationship with the organization of the training spaces outlined. Finally, we identified one research study based on epistemology of practice, which focuses on the understanding of knowledge mobilized in teaching practice. Abstract: Portuguese O presente artigo tem por objetivo analisar pesquisas brasileiras de Educação Estatística que envolveram professores, com vistas a evidenciar tendências metodológicas e de contextos formativos mobilizados por tais estudos. Para tanto, realizou-se um mapeamento no Banco de Dissertações e Teses da CAPES, considerando o descritor “Educação Estatística” e o período de 2013 a 2018. Foram identificadas 99 pesquisas, dentre as quais 20 dialogam com o objetivo proposto. Trata-se de um estudo documental e bibliográfico, no qual se adotou uma abordagem interpretativa que tem como técnica a análise de conteúdo. A análise dos dados permitiu identificar que nove destes estudos não desencadearam processos formativos com os docentes. Além disso, a análise das demais 11 pesquisas, que desenvolveram processos formativos, revelou uma intrínseca relação entre o percurso metodológico e os contextos formativos relatados. Nesse sentido, evidenciou-se uma expressividade de contextos formativos pautados na epistemologia da colaboração, ou seja, aqueles que dão voz aos professores e se colocam à sua escuta; que os reconhecem como produtores de conhecimento. Em contrapartida, duas pesquisas estruturaram as formações, considerando o paradigma da racionalidade técnica e concebendo cursos de capacitação para abordar determinado conteúdo/conceito que o professor supostamente não domina. Constatou-se que a concepção de formação de professores tem relação direta e explícita com a organização dos espaços de formação delineados. Por fim, identificou-se uma pesquisa alicerçada na epistemologia da prática, que se volta para a compreensão de saberes mobilizados no fazer docente.

EDITORIAL: STATISTICS EDUCATION RESEARCH FROM A LATIN AMERICAN PERSPECTIVE

Welcome to a special issue of SERJ.

Statistics Teaching Practice at Czech Universities with Emphasis on Statistical Software

This paper aims to reveal the beliefs of students and fresh university graduates about teaching statistics during their university studies with focus on using statistical software. The objective is to detect the approach of faculties to statistics education and to find out which didactic materials and teaching methods are mainly used. Students’ opinions are captured by means of a questionnaire survey and analysed both quantitatively and qualitatively. The results show the increasing importance of quantitative research and the necessity of improving statistical thinking. Unfortunately, the teaching methods used in various statistical courses are outdated and unattractive for most students. They call for an active and modern approach. Teaching statistics with the statistical software support seems to be the right way to make statistics accessible to students. The recommendation is to take students’ notions into account when preparing statistical courses.

Statistics Education in the Era of COVID-19

The present survey explores the changes in the teaching of statistics modules during the COVID-19 pandemic, including the impact of these changes on the students of the Department of Statistics and Insurance Science of the University of Piraeus. A questionnaire was prepared and administered online. The survey involved a total of 88 participants aged between 18 and 23. The main questions that were asked addressed: (i) the online structure of the statistics courses compared with the structure of the lifelong courses; (ii) the psychological adjustment of the participants to the contents and obligations of the regular courses; (iii) internet-based communication within the scope of the statistics modules and its role in developing skills relating to the use of statistical software and programming languages (i.e., SPSS, RATS, and R); and (iv) the degree of active participation in the online courses. Based on the outcomes of the survey, we concluded that the students did not notice any significant difference regarding their interest in the course or the transfer of knowledge between the online modules and the lifelong courses. Moreover, we found that courses using games and computers were more effective in terms of learning objectives, though they were more costly than conventional courses. Finally, we discovered that the students preferred the online courses over the regular ones, probably because they were richer and more versatile in structure.

The analysis of statistical graphs constructed by primary school teachers

Background: Statistical graphs are widely used in society and are important in presenting data related to different topics. Statistics education aims improve the teaching and learning of statistics, which include the approaches to statistics graphs. Objectives: This article analyses the construction of statistical graphs by in-service teachers and their reasons for choosing these graphs. Design: It was conducted an empirical study from a qualitative perspective which investigated teachers’ choices and constructions of statistical graphs. Setting and Participants: The participants were 22 primary school teachers from public schools located in Recife Metropolitan Area, Brazil. They expressed their intention to be interviewed when they responded to a questionnaire applied among a larger number of teachers. Data collection and analysis: The interviews were composed of two tasks comprised of statistical data in which participants had to choose a type of graph, justify the choice, and construct a graph of a chosen type. It was carried out a content analysis of speech protocols. Results: The reasons for participants’ choices seemed to be related to their familiarity with the type of graph, and they constructed graphs with high levels of complexity. Conclusions: The results of this study emphasised the importance of primary school teachers developing specific knowledge about graphs through pre-service and in-service elementary school teacher education. The results from this research study offer new questions concerning the construction and the choice for statistical graphs, which include the influence of new technologies and the use of textbooks.

Introducing Statistical Inference: Design of a Theoretically and Empirically Based Learning Trajectory

This paper comprises the results of a design study that aims at developing a theoretically and empirically based learning trajectory on statistical inference for 9th-grade students. Based on theories of informal statistical inference, an 8-step learning trajectory was designed. The trajectory consisted of two similar four step sequences: (1) experimenting with a physical black box, (2) visualizing distributions, (3) examining sampling distributions using simulation software, and (4) interpreting sampling distributions to make inferences in real -life contexts. Sequence I included only categorical data and Sequence II regarded numerical data. The learning trajectory was implemented in an intervention among 267 students. To examine the effects of the trajectory on students’ understanding of statistical inference, we analyzed their posttest results after the intervention. To investigate how the stepwise trajectory fostered the learning process, students’ worksheets during each learning step were analyzed. The posttest results showed that students who followed the learning trajectory scored significantly higher on statistical inference and on concepts related to each step than students of a comparison group (n = 217) who followed the regular curriculum. Worksheet analysis demonstrated that the 8-step trajectory was beneficial to students’ learning processes. We conclude that ideas of repeated sampling with a black box and statistical modeling seem fruitful for introducing statistical inference. Both ideas invite more advanced follow-up activities, such as hypothesis testing and comparing groups. This suggests that statistics curricula with a descriptive focus can be transformed to a more inferential focus, to anticipate on subsequent steps in students’ statistics education.

Inferential Reasoning of Secondary School Mathematics Teachers on the Chi-Square Statistic

Statistics education has investigated how to promote formal inferential reasoning from informal inferential reasoning. Nevertheless, there is still a need for proposals that explore and progressively develop inferential reasoning of students and teachers. Concerning this, the objective of this article is to characterize the inferential reasoning that secondary school mathematics teachers show in the practices that they develop to solve problems regarding the Chi-square statistic. To achieve this, we use theoretical and methodological notions introduced by the onto-semiotic approach of mathematics knowledge and instruction. In particular, we have taken a theoretical proposal of levels of inferential reasoning for the Chi-square statistic. Based on the results, the main conclusion was that the proposal above effectively predicted the teachers’ practices, allowing us to distinguish characteristic elements of the levels of inferential reasoning.

Measuring Opportunity Cost in Statistics Using Evaluative Space Grid Items

Challenges to measuring students’ attitudes toward statistics remain despite decades of focused research. Measuring the expectancy-value theory (EVT) Cost construct has been especially challenging owing in part to the historical lack of research about it. To measure the EVT Cost construct better, this study asked university students to respond to items using both a Likert-type response and an Evaluative Space Grid (ESG)-type response. ESG items enable bivariate responses in a single item and permit distinguishing among two different types of neutral attitudes: indifferent and ambivalent. This pilot study evaluates the appropriateness of ESG-type items for measuring the EVT Cost construct by analyzing student response patterns to ESG-type items and comparing them with Likert-type items. Validity evidence is documented using descriptive statistics and graphs, correlations among items, and a trinomial hypothesis test. Internal consistency reliability indices are also reported. Friedman’s Test is used to compare the average response times for items of different types. Results indicate that students can meaningfully respond to ESG-type items in ways that are similar to their Likert-type responses, that students respond to ESG-type items quicker with more practice, and that distinguishing among indifferent and ambivalent attitudes seems appropriate for the EVT Cost construct. These findings suggest that ESG-type items may provide new insights not possible with Likert-type items but also that more research should be conducted to better understand their advantages and disadvantages within statistics education.