Early statistics in kindergarten: analysis of an educator's pedagogical content knowledge in lessons promoting informal inferential reasoning

PurposeThis study aims to describe the pedagogical content knowledge (PCK) of a kindergarten educator who implements a lesson plan about informal inferential reasoning designed in a lesson study group.Design/methodology/approachTo this end, we analyzed teaching interventions in two kindergarten lessons focused on the playful task of tossing two coins, associated with inferential statistical reasoning. The study highlights the importance of arguing and promoting this reasoning to develop statistical thinking. It is crucial to recognize how early students can be subject to learning experiences that promote a language of uncertainty, assess the evidence provided by the data, and make generalizations.FindingsThe results reveal that while the educator demonstrated knowledge and skills relevant to the curriculum and conceptual teaching strategies, the understanding of the content by the students and the integration of the PCK components still present a challenge.Practical implicationsThe lesson study collaborative teaching practices that promote PCK have proven effective for informing the design and implementation of instructional practices supporting the development of early statistical thinking in young children.Originality/valueThe study enriches the knowledge regarding the potential of the lesson study (LS) in the professional learning of kindergarten educators. It also contributes to a comprehensive approach based on authentic playful experiences in grade K that supports the development of early statistical thinking in young children.

The Emergence of the “FlexTech” Orchestration of Inferential Reasoning on Pattern Generalization

The purpose of this study is to further our understanding of orchestrating math-talk with digital technology. The technology used is common in Swedish mathematics classrooms and involves personal computers, a projector directed towards a whiteboard at the front of the class and software programs for facilitating communication and collective exploration. We use the construct of instrumental orchestration to conceptualize a teacher’s intentional and systematic organization and use of digital technology to guide math-talk in terms of a collective instrumental genesis. We consider math-talk as a matter of inferential reasoning, taking place in the Game of Giving and Asking for Reasons (GoGAR).The combination of instrumental orchestration and inferential reasoning laid the foundation of a design experiment that addressed the research question: How can collective inferential reasoning be orchestrated in a technology-enhanced learning environment? The design experiment was conducted in lower-secondary school (students 14–16 years old) and consisted of three lessons on pattern generalization. Each lesson was tested and refined twice by the research team. The design experiment resulted in the emergence of the FlexTech orchestration, which provided teachers and students with opportunities to utilize the flexibility to construct, switch and mark in the orchestration of an instrumental math-GoGAR.

Correction format has a limited role when debunking misinformation

Given that being misinformed can have negative ramifications, finding optimal corrective techniques has become a key focus of research. In recent years, several divergent correction formats have been proposed as superior based on distinct theoretical frameworks. However, these correction formats have not been compared in controlled settings, so the suggested superiority of each format remains speculative. Across four experiments, the current paper investigated how altering the format of corrections influences people’s subsequent reliance on misinformation. We examined whether myth-first, fact-first, fact-only, or myth-only correction formats were most effective, using a range of different materials and participant pools. Experiments 1 and 2 focused on climate change misconceptions; participants were Qualtrics online panel members and students taking part in a massive open online course, respectively. Experiments 3 and 4 used misconceptions from a diverse set of topics, with Amazon Mechanical Turk crowdworkers and university student participants. We found that the impact of a correction on beliefs and inferential reasoning was largely independent of the specific format used. The clearest evidence for any potential relative superiority emerged in Experiment 4, which found that the myth-first format was more effective at myth correction than the fact-first format after a delayed retention interval. However, in general it appeared that as long as the key ingredients of a correction were presented, format did not make a considerable difference. This suggests that simply providing corrective information, regardless of format, is far more important than how the correction is presented.

Networks and Stories. Analyzing the Transmission of the Feminist Intangible Cultural Heritage on Twitter

Internet social media is a key space in which the memorial resources of social movements, including the stories and knowledge of previous generations, are organised, disseminated, and reinterpreted. This is especially important for movements such as feminism, which places great emphasis on the transmission of an intangible cultural legacy between its different generations or waves, which are conformed through these cultural transmissions. In this sense, several authors have highlighted the importance of social media and hashtivism in shaping the fourth wave of feminism that has been taking place in recent years (e.g., #metoo). The aim of this article is to present to the scientific community a hybrid methodological proposal for the network and content analysis of audiences and their interactions on Twitter: we will do so by describing and evaluating the results of different research we have carried out in the field of feminist hashtivism. Structural analysis methods such as social network analysis have demonstrated their capacity to be applied to the analysis of social media interactions as a mixed methodology, that is, both quantitative and qualitative. This article shows the potential of a specific methodological process that combines inductive and inferential reasoning with hypothetico-deductive approaches. By applying the methodology developed in the case studies included in the article, it is shown that these two modes of reasoning work best when they are used together.

Correction Format has a Limited Role when Debunking Misinformation

Given that being misinformed can have negative ramifications, finding optimal corrective techniques has become a key focus of research. In recent years, several divergent correction formats have been proposed as superior corrective methods based on distinct theoretical frameworks. However, these correction formats have not been compared in controlled settings, so the suggested superiority of each format remains speculative. Across four experiments, the current paper investigated how altering the format of corrections influences peoples’ subsequent reliance on misinformation. We examined whether myth-first, fact-first, fact-only, or myth-only correction formats were most effective, using a range of different materials and participant pools. Experiments 1 and 2 focused on climate change misconceptions; participants were Qualtrics online panel members and students taking part in a massive open online course, respectively. Experiments 3 and 4 used misconceptions from a diverse set of topics, with Amazon Mechanical Turk crowdworkers and university student participants. We found that the impact of a correction on beliefs and inferential reasoning was largely independent of the specific format used. The clearest evidence for any potential relative superiority emerged in Experiment 4, which found that with a delayed retention interval, the myth-first format was more effective at myth correction than the fact-first format. However, in general it appeared that as long as the key ingredients of a correction were presented, format did not appear to make a considerable difference. This suggests that simply providing corrective information, regardless of format, is far more important than how the correction is presented.

Sensitivity to misinformation retractions in the continued influence paradigm: Evidence for stability

Research has consistently shown that misinformation can continue to affect inferential reasoning after a correction. This phenomenon is known as the continued influence effect (CIE). Recent studies have demonstrated that CIE susceptibility can be predicted by individual differences in stable cognitive abilities. Based on this, it was reasoned that CIE susceptibility ought to have some degree of stability itself; however, this has never been tested. The current study aimed to investigate the temporal stability of retraction sensitivity, arguably a major determinant of CIE susceptibility. Participants were given parallel forms of a standard CIE task 4 weeks apart, and the association between testing points was assessed with an intra-class correlation coefficient and confirmatory factor analysis. Results suggested that retraction sensitivity is relatively stable and can be predicted as an individual-differences variable. These results encourage continued individual-differences research on the CIE and have implications for real-world CIE intervention.

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.

Narrative Inference with and without Statistics

This article investigates the role played by narrative in drawing inferences from statistics before the adoption of formal inference regimes in economics. Two well-known, and exemplary, cases of informal inference provide the materials. Nikolai Kondratiev’s struggles to make inferences about the existence of his “long waves” from heaps of statistics in the 1920s contrast sharply with Thomas Robert Malthus’s confident account of demographic-economic oscillations made on the basis of the limited numbers available in the late eighteenth century. Comparison of their inferential reasoning, using detailed textual analysis, casts attention on the important role of narrative. These cases prompt the notion of “narrative inference”: where informal statistical inference depends on narrative accounts—used to make sense of the numbers by Malthus or to add sense onto the numbers by Kondratiev.

Research at a Distance: Replicating Semantic Differentiation Effects Using Remote Data Collection With Children Participants

Remote data collection procedures can strengthen developmental science by addressing current limitations to in-person data collection and helping recruit more diverse and larger samples of participants. Thus, remote data collection opens an opportunity for more equitable and more replicable developmental science. However, it remains an open question whether remote data collection procedures with children participants produce results comparable to those obtained using in-person data collection. This knowledge is critical to integrate results across studies using different data collection procedures. We developed novel web-based versions of two tasks that have been used in prior work with 4-6-year-old children and recruited children who were participating in a virtual enrichment program. We report the first successful remote replication of two key experimental effects that speak to the emergence of structured semantic representations (N = 52) and their role in inferential reasoning (N = 40). We discuss the implications of these findings for using remote data collection with children participants, for maintaining research collaborations with community settings, and for strengthening methodological practices in developmental science.

Inferential Statistical Reasoning of Math Teachers: Experiences in Virtual Contexts Generated by the COVID-19 Pandemic

The COVID-19 pandemic generated a new scenario in education, where technological resources mediate teaching and learning processes. This paper presents the development of a virtual teacher training experience aimed at promoting inferential reasoning in practicing and prospective mathematics teachers using inference problems on the Chi-square statistic. The objective of this article is to assess the implemented or intended institutional meanings and the degree of availability and adequacy of the material and temporal resources necessary for the development of the training experience. For this purpose, we use theoretical and methodological notions introduced by the Ontosemiotic Approach to Mathematical Knowledge and Instruction (OSA), among which are the notions of practice and suitability criteria. The participants of this experience were divided into three groups; one of them was comprised of practicing teachers and the other two of prospective teachers. The intervention used different virtual modalities that enabled the development of the participants’ inferential reasoning in a similar way.