We investigated how high school students formulate and refine investigative questions when conducting a statistical investigation with secondary data. The data consisted of students’ written activity reports and email-based, post-interview responses collected after a seven-session instructional sequence in which CODAP served as the primary tool for multivariate data analysis. We distinguished initiating investigative questions (IIQs) from analysis-phase investigative questions (AIQs) implied in students’ analysis plans and characterized both sets across five analytical components: variables, clarity of population, intent, feasibility of drawing conclusions from the data, and global view of data. We then used thematic analysis to examine how data visualization appeared to be involved at points where IIQ-to-AIQ refinement was evident. Compared with IIQs, AIQs more often included a greater number of clearer variables and took forms that were more feasible for drawing conclusions from the given dataset. Across the three episodes analyzed, the representational and exploratory functions of data visualizations appeared to support refinement by helping students operationalize everyday terms, narrow populations, anticipate interpretable relationships, and set aside uninformative variables. This study offers classroom-based empirical insights into investigative questions in the context of secondary data and into the potential role of data visualization in their refinement.
This systematic review investigates measures of statistical ability in published literature to understand how statistical ability has been conceptualised and assessed. The review examines the components, reliability, validity, and correlations of these measures with cognitive (e.g., intelligence) and non-cognitive (e.g., attitude towards statistics) factors. From 51 papers, 25 unique measures were identified, with 60% assessing knowledge-based competencies. The validity evidence suggests that these measures assess their intended learning outcomes. Correlations between the measures and cognitive factors were stronger when closely aligned with the assessed ability. Research reporting correlations between statistical ability measures and non-cognitive factors is relatively limited. The review aims to inform educators and provide direction for future measurement development to address the identified gaps in the literature.
Using the commognitive construct of routine—repetitive rules or patterns observed in statistical discourse—we aimed to investigate how students use inconsistent routines when engaging in statistical reasoning about mode in the context of comparing modes across several data groups. The study data was collected by distributing mode-related questions to students through a Google Form, followed by interviews. Four mode-related questions were given to 43 undergraduate students participating in the study. The results showed that routine plays a significant role in statistical reasoning. The study identified two factors that contributed to the occurrence of inconsistent routines among students: (a) the way students described the data display and (b) the disconnection between routine and endorsed narrative. The results of this research highlight the importance of providing students with opportunities to work with diverse forms and conditions of data associated with mode.
The knowledge needed to teach statistics overlaps with, but is not limited to, the knowledge needed to do statistics. Hence, research on statistical knowledge for teaching should not be limited to the study of teachers’ subject matter knowledge. This article outlines a taxonomy describing multiple foci for research on statistical knowledge for teaching. The theoretical structure for the taxonomy is sketched and then stress-tested using a collection of articles from the Statistics Education Research Journal. Challenges of using the taxonomy to categorize research are made explicit, and ideas for navigating them are provided. It is shown how the taxonomy can serve as a framework to track the prevalence of various research foci in the field and plan future studies. Directions for future scholarship to refine the taxonomy itself are also proposed.
Proficient handling of data is a skill gaining importance with the increasing amount and availability of data. Therefore, promoting data literacy should begin in everyday school life. The foundation for this is formed by competence models for data literacy, which include the sub-skill of data collection that has so far been inadequately considered in K–12 education. This study investigates the relevance of data collection through pedagogical intervention research with learners aged 14 to 17 years. The evaluation highlights the benefits of personal data collection—data collection in one’s own environment and in virtual reality—as part of a holistic approach to teaching data literacy. This work extends existing approaches regarding the importance of data collected by students for their own use through sensors for a reflective and critical understanding of data.
A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ). For this Special Issue we were interested in scholarly articles addressing the aspects of inclusion and digital resources in statistics education.
Recently, the importance of statistical literacy has been stressed, and three central concepts in statistical literacy are the measures of central tendency: mean, median, and mode. This study explores aspects of statistical literacy expressed by 12–13-year-old students, focusing on mean, median, and mode. Their responses were analysed using a framework of statistical literacy that includes knowledge and dispositional elements. The results showed that students’ descriptions of the measures were mainly based on mathematical and vocabulary knowledge. When discussing what measure was easiest or hardest to explain, a variety of conceptions were expressed. Some explanations about the usefulness of the measures were related to context knowledge. Here, the median was an exception as students gave neither examples of contexts nor found the median useful outside the classroom.
To ensure the learning of mathematics, teachers must be able to analyse their students’ mathematical practices when solving tasks, interpret the difficulties that students encounter, and decide how to manage students’ difficulties. This competence in didactic analysis and intervention allows teachers to adapt their teaching to meet individual student needs. In this paper, we analyse how preservice teachers interpreted students’ responses to a task involving the proportional determination of probabilities and understanding the sample space. We propose didactic strategies that help students overcome difficulties. The results revealed the difficulties some preservice teachers experienced in adequately interpreting student responses and making informed decisions to improve learning.
Probability literacy has gained importance in educational curricula. The aim of this research was to analyse secondary education teachers’ attitudes towards probability and its teaching and to examine differences across the factors of gender, academic training, and work experience. From a positivist paradigm, a quantitative methodology was used. The sample consisted of 185 in-service teachers, and the instrument used was the Attitudes Towards Probability and Its Teaching questionnaire. The results suggested that gender had no effect on teachers’ attitudes, but having a mathematics background was associated with a relevant weight on teachers’ attitudes. Work experience presented a medium effect on the behavioural aspect of the teaching probability dimension, with better attitudes among teachers who had more work experience. This led us to acknowledge the importance of disciplinary knowledge in both initial and continuing training.
Functional models of anxiety based on dispositional variables have gained scientific acceptance. Their application to investigate constructs such as statistical anxiety can facilitate understanding and intervention. This study aimed to estimate whether dispositional variables such as worry and its negative consequences mediated the relationship between negative problem orientation and statistical anxiety among university students. We evaluated survey responses from a sample of 532 students and tested a multiple mediation model. Negative problem orientation indirectly influenced statistical anxiety through the negative consequences of worry. Negative problem orientation predicted worry but did not mediate the effect on statistical anxiety. Cognitive appraisal of the adverse sequelae of worry is a key variable in the manifestations of statistical anxiety in university students.
This paper reports on a study concerning the social nature of young students’ informal inferential reasoning. Employing inferentialism as a background theory, we examine cognitive and sociocultural aspects of reasoning that arose during group discussions as well as trace relations between those aspects. Following a design experiment approach, we analyzed the discussion that emerged while a group of second-grade students was working on a carefully constructed inferential task. The results illustrate the dynamic interplay between cognitive and sociocultural aspects of informal inferential reasoning during students’ attempts to reach a conclusion while working in a group.
Language, culture, and conceptions of uncertainty can impact the way that students respond to a statistical investigation. The aim of this small exploratory study was to gain insight into how two groups of children (aged 9-12) speaking different home dialects adopted expressions of uncertainty in a standard dialect used in school, specifically the use of the Marathi word for “about.” One group of children went to a government school where the home dialect differed from the standard dialect, while a second group attended a relatively elite private school where children spoke the standard dialect at home. Our findings suggest that children from both groups did not spontaneously use the word “about” while describing data even when nudged by the researcher to do so, though the children from the second group were more quickly able to adopt the word and use it in the way the researchers expected. The findings have the potential of exploring and impacting the influences of language on the learning of statistics in a non-Western culture.
As ideas from data science become more prevalent in secondary curricula, it is important to understand secondary teachers’ content knowledge and reasoning about complex data structures and modern visualizations. The purpose of this case study is to explore how secondary teachers make sense of mappings between data and visualizations, especially depictions of multivariate relationships. The participants were 14 in-service secondary teachers who were video recorded as they worked through three sets of activities. In these activities, participants created a visualization (network graph) from multivariate data, encoded raw data for several attributes from visualizations depicting multivariate relationships, and structured data into a tidy format. With minimal instruction, participants were able to create visualizations when given data representing multivariate relationships. They were also able to structure non-tidy data into a tidy format with some scaffolding and discussion. Notably, creating data tables from visualizations, especially relational tables, seemed more challenging for them. These results provide insight into secondary teachers’ reasoning about connections between multivariate data and visualization.
Statistics education researchers have been challenged to consider the theory of inferentialism in understanding concept formation in students. A critique of inferentialism is that no comprehensive method has been formulated to use the theory in practice. In this paper an inferentialism-based framework is presented that appears to be capable of explicating the development of statistical concepts during learning. By following six 11-year-olds’ learning over several statistical modelling cycles using TinkerPlots, the framework was used to capture their interrogative cycles of noticing and wondering, giving and asking for reasons, and sanctioning and censuring, as well as oscillations between concretising language about actions and conceptualising language towards concept formation. Five teaching episodes occurring near the beginning of a 12-week learning sequence are used to illustrate how the framework might be able to capture student concept formation over time.
To evaluate the evolution of statistical education research aimed at the inclusion of technological resources in the initial and continuing education of teachers in Brazil, a systematic literature review (SLR) was conducted on 25 works published in the Scientific Proceedings of the National Meeting of Mathematics Education and on 7 papers from the International Seminar on Research in Mathematics Education. This research was exploratory using both a qualitative and quantitative approach in which a descending hierarchical classification (DHC) was carried out. We consider that the inclusion of technological resources in the classroom still faces challenges stemming from the elaboration and execution of public policies that should guarantee a minimum of infrastructure for teaching institutions and teacher training.
This study examines, with focus on statistical education, how intersectionality appears in didactic tasks for Brazilian school education, developed by IBGEeduca, an educational platform organized by IBGE (Brazilian Institute of Geography and Statistics). In this study, intersectionality was used as an analytical tool to help understand and explain the complexities of the world that impose social injustices through interrelationships of power categories. The documentary methodological approach adopted in this research is part of a doctoral research project. The criteria for choosing the analyzed tasks were based on the authors' perception of the intersectional categories in the examined pedagogical proposals. We present an interpretative analysis of an IBGEeduca proposal from the theoretical perspective of critical statistics education. This investigation revealed several themes related to contemporary problems present sporadically in the proposed activities, requiring greater scrutiny of the hidden intersections among the categories exposed in the proposals. The findings of this Brazilian case study could spark conversations about how statistics teachers can use tasks to help students understand concepts of inequity and social injustice.
To address diversity-sensitive higher education, we provide the first results exhibiting the importance of the use of German Sign Language (Deutsche Gebärdensprache, DGS) in lecture videos of elementary statistics courses. We examined whether deaf individuals preferred lecture videos in DGS over those with captions. Results from quantitative and qualitative analyses on the basis of survey data and interview material in DGS indicate a clear preference for teaching materials in DGS. While the limited sample size (n = 10) did not allow for detailed modeling of the underlying reasoning, this study puts forward some indicative results and directions for future research, like assessing objective learning outcomes by employing pre- and post?tests and employing eye-tracking for more in-depth analysis of learning behaviors.
One of the most important goals in a statistics class is to develop students who are statistically literate and can reason with statistical concepts. The REALI instrument was designed to concurrently assess statistical literacy and reasoning in introductory statistics students. This paper reports a measurement analysis of the statistical literacy and reasoning subscores from the REALI assessment and the extent to which they are reliable and distinct. Investigation of these subscores is used clarify the relationship between the constructs of statistical literacy and statistical reasoning and to what extent they overlap. The results of this analysis, under a Multidimensional Item Response Theory framework, show that the statistical literacy and reasoning subscores provide no added value over a single general statistical knowledge score. This indicates the two constructs might be indistinguishable from one another.
