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The problem that the given paper aims to solve is associated with the need to resolve the contradiction between the requirements of the digital economy for a high level of computational thinking of specialists of the future and an insufficiently developed methodological base for training graduates that meets these requirements. The purpose of the research is to theoretically prove and experimentally verify the need for the use of gamification technology in training of specialists of the future to form computational thinking skills which are most in demand in the digital society. The research methodology includes the analysis and generalization of scientific works on the problem of determining the phenomenon of computational thinking, the use of digital gamification resources in training, and clarifying the requirements for training of highly qualified specialists of the future. The HTML 5 language was used as a software tool. The pedagogical experiment is presented on the example of the assessment of changes in the levels of skills that make up the essence of computational thinking. Results: The paper clarifies the concept of computational thinking and describes the directions of educational and cognitive activity based on the gamification principles which most effectively form computational thinking. The authors formulate didactic principles for the inclusion of computer games to foster students' cognitive activity, support professional self-determination, and develop systematic and critical thinking. Specific materials are proposed to improve the methods, tools, and organizational forms of the training focused on the formation of computational thinking as the basis for the supra-professional skills of specialists of the future. In the end, conclusions are made which confirm that the included educational and cognitive activities on game designing in the training of highly qualified specialists of the future fosters the formation of computational thinking skills.

This paper reports findings from a longitudinal qualitative study that explored the ethnographic learning processes of 10 modern languages students who spent one full academic year abroad, having first completed successfully an "Introduction to Ethnography" course in the UK. It begins from the argument that although significant attempts have been made to integrate ethnography into modern languages undergraduate degree programmes, relatively little is known about its actual impact on modern languages sojourners. Drawing on active interviews and reflective diaries that were designed to investigate this impact from shortly before participants embarked on their year abroad to the moment they returned, the thematic and critical discourse analysis of the data focuses attention on two key themes: students' perceptions of their host cultures and the impact of ethnography on students' perceptions. Findings from the first theme reveal that participants' perceptions were derogatory and that they used a number of mitigating discourse strategies to avoid creating a negative impression on the researchers. Findings from the second theme suggest that ethnography made little impact on most participants, given that their derogatory perceptions of the "foreign other" remained almost intact throughout the year abroad. The paper discusses possible reasons for these findings, arguing that the contextual nature of ethnographic inquiry does not always enable modern languages sojourners to dismantle the cultural generalisations they may make.

This paper reports an experiment that investigates interpretive distinctions between two different expressions of generalization in Spanish. In particular, our aim was to find out when the distinction between generic statements (GS) such as "Tigers have stripes" and universally quantified statements (UQS) such as "All tigers have stripes" was acquired in Spanish-speaking children of two different age groups (4/5-year-olds and 8/9-year-olds), and then compare these results with those of adults. The starting point of this research was the semantic distinction between GS and UQS in that the former admit exceptions, unlike the latter. On the other hand, several authors have observed a Generic overgeneralization effect (GOG) consisting in allowing for UQS to be felicitous in the face of exceptions, thus proposing that this "error" stems from GS being defaults (simpler, more easily learned and processed). In the current paper we aimed to test the "Generics as Default" (GaD) hypothesis by comparing GS and UQS in three different age ranges. Our data show that, overall, the accuracy of GS is greater than the accuracy of UQS. Moreover, we also confirm a hypothesized interaction between age and NP type (GS vs UQS). Further, we present several data points that are not predicted by the GaD, including an observed decline in the accuracy of GS in the older group of children as well as in adults, and that children fail at rejecting statements that are not considered to be true generalizations.

This paper extends the use of Generalizability Theory to the measurement of extemporaneous L2 speech through the lens of speech perception. Using six datasets of previous studies, it reports on "G studies"--a method of breaking down measurement variance--and "D studies"--a predictive study of the impact on reliability when modifying the number of raters, items, or other facets that assist the field in adopting measurement designs that include comprehensibility, accentedness, and intelligibility. When data from a single audio sample per learner were subjected to D-studies, we find that both semantic differential and rubric scales for comprehensibility were reliable at the 0.90 level with about 15 trained raters or 50 untrained crowdsourced raters. In order to offer generalizable and dependable evaluations, empirically informed recommendations are given, including considerations for the number of speech samples rated, or the granularity of the scales for various assessment and research purposes.

Recent research has highlighted the role of functional relationships in introducing elementary school students to algebraic thinking. This functional approach is here considered to study essential components of algebraic thinking such as generalization and its representation, as well as the strategies used by students and their connection with generalization. This paper jointly describes the strategies and representations of generalization used by a group of 33 sixth-year elementary school students, with no former algebraic training, in two generalization tasks involving a functional relationship. The strategies applied by the students differed depending on whether they were working on specific or general cases. To answer questions on near specific cases they resorted to counting or additive operational strategies. As higher values or indeterminate quantities were considered, the strategies diversified. The correspondence strategy was the most used and the common approach when students generalized. Students were able to generalize verbally as well as symbolically and varied their strategies flexibly when changing from specific to general cases, showing a clear preference for a functional approach in the latter.

The global COVID-19 pandemic has passed. This process required greater attention and care to the specifics of the organization of distance learning and the resolution of problems that arose for participants in the educational process. By late 2021 face-to-face teaching was returning but Russian aggression against Ukraine interrupted the comparatively carefree life of children and hindered access to kindergartens and schools which required a further focus on remote education. The paper outlines the peculiarities of the organization of distance learning under martial law in Ukraine and presents the problems of the organization of training during a time of conflict as well as the challenges presented by Internet platforms for the organization of the distance learning approaches recommended by the Ministry of Education of Ukraine. The aim of the research was theoretical analysis and generalization of literature on research problems, pedagogical observations, surveys, methods of mathematical statistics. The article provides one of the first analyses of the difficulties faced during this period of immense disruption based on empirical data and explains to what extent Ukrainian teachers under martial law have the possibility to organize distance teaching, what problems they face, what is the psychological state of children.

In this study, it was aimed to determine the effects of the Simultaneous Prompting (SP) package jointly with the systematic review and corrective feedback in teaching a student with poor performance in mathematics to recall the multiplication facts. One of the single subject designs, the multiple probes design across behaviors (sets) is used in this study. The participant is an 11 years old female student at the 6th grade who has not been diagnosed with any disability but has been getting support because of her poor performance in mathematics than her peers. The dependent variable of this study is the skill of recall multiplication facts with the sets of 3, 5 and 8. The independent variable of the study is the SP package jointly with the systematic review and corrective feedback. Results show that the SP was effective in teaching the student with low mathematical performance to the skill of recall the multiplication facts. The student generalized the learned multiplication facts to another teacher and different setting and maintained her performance on the 15th and 45th days following the systematic reviews. Considering the findings of social validity, it has been determined that the teacher presented positive opinions, as she became happy with that achievement and the method is a way, which can be adopted and implemented by all teachers. These results indicate the acceptability of the SP package and results of the study are highly meaningful. Implications and future research needs are discussed. [This article was presented as an oral presentation at the "27th International Conference on Educational Sciences (ICES/UEBK-2018)" on 18-22 April 2018 in Antalya.]

This study aimed to explore how prospective middle school mathematics teachers think critically about a newspaper article that reported the findings of a statistical research. Participants of the study were four fourth-year students enrolled at the mathematics teacher education program of a public university. To investigate the research question of the study, case study method was employed. In-depth semi-structured interviews were done to examine participants' critical thinking processes. The findings of the study indicated that prospective mathematics teachers made use of a variety of critical thinking processes (comprehending, making connections, inferring ideas, critiquing, and self-reflecting) and provided clues about the interrelated nature of these processes. This study would shed light on the characterization of critical thinking in the context of statistical literacy by suggesting a blended framework. It also suggests the design of the tasks including media articles to promote both statistical literacy and critical thinking in statistics education courses for prospective mathematics teachers. [This study was presented at the Ninth Congress of the European Society for Research in Mathematics Education (CERME 9).]

A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need to also split the prior for the local inferences; these weakened priors may not provide enough regularization for each separate computation, thus eliminating one of the key advantages of Bayesian methods. To resolve this dilemma while still retaining the generalizability of the underlying local inference method, we apply the idea of expectation propagation (EP) as a framework for distributed Bayesian inference. The central idea is to iteratively update approximations to the local likelihoods given the state of the other approximations and the prior. The present paper has two roles: we review the steps that are needed to keep EP algorithms numerically stable, and we suggest a general approach, inspired by EP, for approaching data partitioning problems in a way that achieves the computational benefits of parallelism while allowing each local update to make use of relevant information from the other sites. In addition, we demonstrate how the method can be applied in a hierarchical context to make use of partitioning of both data and parameters. The paper describes a general algorithmic framework, rather than a specific algorithm, and presents an example implementation for it.

Early algebraic thinking is the reasoning engaged in by 5- to 12-year-olds as they build meaning for the objects and ways of thinking to be encountered within the later study of secondary school algebra. Ever since the 1990s when interest in developing algebraic thinking in the earlier grades began to emerge, there has been a steady growth in the research devoted to exploring ways of fostering this thinking. While in its early days this research had to grapple with the question of what kinds of algebraic thinking might be feasible for the younger student, the evolution of the field over the past 30 years has led to an ever-increasing range of activity that is truly multi-dimensional. In this survey paper, I have framed the multi-dimensionality of early algebraic thinking according to three overarching types, namely, that of analytic thinking, structural thinking, and functional thinking, with generalizing being the scarlet thread that runs through all three. The first part of the paper looks back to the history of the notion of early algebra and the initial research efforts aimed at characterizing early algebraic thinking. The second part delineates the three overarching theoretical dimensions of early algebraic thinking, presents a sampling of past empirical findings, and points to some of the more recent work in the field, including the contributions to this Special Issue. The paper concludes by highlighting the new directions of this domain of research and offering suggestions for further research.

This paper presents data from the first of three iterations of teaching experiments conducted with secondary teachers. The purpose of the experiments was to investigate how teachers' combinatorial reasoning could support their development of algebraic structure, specifically structural relationships between the roots and coefficients of polynomials. The data in this paper examines the learning that occurred as one teacher transitioned from making a generalization from a sequence of contextualized combinatorics problems to applying her combinatorial reasoning to symbolic problems common in algebra curricula. The findings from the study include the identification of three planes of learning that can be used to differentiate among ways that combinatorial reasoning can be used to engage in binomial expansion. The highest plane involved constructing a "combinatorial scheme for binomial expansion," a scheme that supported the teacher to produce the equivalence, (x + a)(x + b)(x + c)=x[subscript 3] + (a + b + c)x[subscript 2] + (ab + ac + bc) x + abc), and to see important algebraic structure in it. The contributions of the study include: (a) expanding earlier arguments about the ways that combinatorics can be integrated into goals of extant curricula (e.g., Maher et al. in Combinatorics and reasoning: Representing, justifying and building isomorphisms. Springer, 2011); and (b) proposing how reflecting abstraction can be used to study the transition between generalizations learners make from contextualized problem situations to operating with and on generalizations expressed with conventional algebraic symbols. This second contribution is an under-researched area in the algebra literature (Dörfler in ZDM - Int J Math Educ 40(1):143-160, 2008), and points to an important role that combinatorial reasoning can play in algebra learning.

Using electronic tablets to present flash cards for teaching skills is becoming common among practitioners. However, no published study compared the effectiveness of the electronic tablet-based flash cards to paper flash cards for teaching receptive labeling skills. The purpose of this study was to compare the efficacy of the iPad-based and paper flash cards for teaching receptive labeling to learners with autism. An adapted alternating treatments design was used. Participants included one preschool student with autism and one elementary school student with autism. Findings indicated that iPad-assisted instruction resulted in a slightly faster acquisition and slightly lower levels of prompts for both participants. No differences were found in the generalization and maintenance of the skills between the two instructional mediums. Mixed results were found for challenging behaviors associated with each intervention. Implications and suggestions for future research are discussed.

Argues that the rural development policy for Australia proposed by Jonathan and Katrina Sher in a previous issue of this journal is inadequate because the analysis on which it is based is generally unsubstantiated, supportive arguments have been found invalid, the richness of Australian society is overlooked, and economic arguments are flawed. (Author/LP)

Social stories play a significant part in the teaching skills and behaviors to children with ASD who lack social skills. The purpose of this study is to analyze studies in which social stories were used for teaching social skills to individuals with Autism Spectrum Disorders (ASD). The present study includes a descriptive review and meta-analysis of single-subject studies that met the criteria. In all studies, social validity, maintenance, and generalization data were collected in 56.25%, 50%, and 31.25% of the respective studies. Although most studies showed that social stories were effective in teaching social skills to children with ASD in the descriptive study, in the meta-analytic study, the mean of Percantage of Non-overlapping Data (PND) scores for all studies was 63.43%, with a range of 0% to 100%. Results suggest that social stories should not yet be considered as evidence based practice for teaching social skills to individuals with ASD. However, social stories seem to be a promising practice that warrants future research. Results will be discussed extensively and future directions for research and practice will be addressed. [This paper was presented at 1st International Early Childhood Intervention Conference & EURLYAID Annual Conference 2012, Braga, Portugal. This paper was presented at 22nd International Conference on Special Education, Trabzon, Turkey.]

The present paper examines a type of abstract domain-general knowledge required for the process of constructing useable domain-specific causal knowledge, the evident goal of causal learning. It tests the hypothesis that analytic knowledge of "causal-invariance decomposition functions" is essential for this process. Such knowledge specifies the decomposition of an observed outcome into contributions from constituent causes under the default assumption that the empirical knowledge acquired is "invariant" across contextual/background causes. The paper reports two psychological experiments (and replication studies) with pre-school-age children on generalization across contexts involving binary cause and effect variables. The critical role of causal invariance for constructing useable causal knowledge predicts that even young children should (tacitly) use the causal-invariance decomposition function for such variables rather than a non-causal-invariance decomposition function common in statistical practice in research involving binary outcomes. The findings support the rational shaping of empirical causal knowledge by the causal-invariance constraint, ruling out alternative explanations in terms of non-causal-invariance decomposition functions, heuristics, and biases. For the same causal structure involving candidate causes and outcomes that are binary variables with a "present" value and an "absent" value, the paper argues against the possibility of multiple rational characterizations of the "sameness of causal influence" that justifies generalization across contexts.

This paper presents information from a comprehensive review of 28 experimental studies that investigated the effectiveness and efficiency of the simultaneous prompting procedure with individuals with autism. Twenty of the 25 variables examined across the 28 studies are reported on in this paper. The results reported across the studies indicated that the procedure was effective with all but one of the 71 participants with autism who were included in the investigations. A particular emphasis of this comprehensive review was information about the variants involved in the use of simultaneous prompting. An analysis of this information resulted in the identification of seven guidelines for teachers' use of simultaneous prompting with students with autism, which are presented at the end of this paper.

The aim of this study is to determine the 7th grade students' achievements in mathematical patterns presented by figures, tables, number sequences, and word problems. This research is a situation determination study where quantitative methodology is used. The sample of the study consisted of 47 female and 50 male students, totally 97 students from 7th grades in Giresun city on 2015-2016 academic year. Pattern topic oriented 7 questions were used as the data gathering tool. The questions which focused on the attainments of pattern topic were prepared by the researcher. It was determined that students could perform specialization in figural patterns but they couldn't reach a generalization. In other words, it was observed that students could find the required steps according to a given rule and so they could easily reach the situation which involved operational knowledge. Also, it was seen that although students found the number of figures in the next step of the pattern, they couldn't find the general rule that represented the pattern. Another result of the study was that students could recognize patterns of number sequences but they couldn't find the general term of the pattern. Lastly, it was determined that students couldn't understand patterns which were represented as word problems and they failed at these kind of pattern questions but they had success in pattern questions represented by tables. In this context, it can be offered to give much place to representation forms of patterns by figures, tables, number sequences, and word problems while students are given experiences of patterns. [Paper presented at the International Conference on Education in Mathematics, Science & Technology (ICEMST) (Bodrum, Turkey, May 19-22, 2016).]

The purpose of this paper is to analyze the use of the exemplar methodology (ExM) as a method for selecting exemplars in education research. ExM is a systematic approach to selecting outliers that can be used to education researchers who investigate outliers to better understand phenomena among students, teachers, schools, and communities. While ExM is prevalent in development psychology and its use is growing in other social science fields, it is not yet frequently used in education. Selecting outliers while maintaining validity requires a methodological approach. When there are not established standards for exemplarity, ExM provides a step-by-step approach to choosing exemplars to study. While there are great opportunities in using ExM, investigating outliers comes with inherent challenges; this paper examines those challenges and describes how education researchers using ExM can mitigate them.

The present paper examines a patterning activity that was organised within a teaching experiment in order to analyse the different uses of variables by secondary school students. The activity presented in the paper can be categorised as a pictorial/geometric linear pattern. We adopted a student-oriented perspective for our analysis, in order to grasp how students perceive their own generalising actions. The analysis of our data led us to two broad categories for variable use, according to whether the variable is viewed as a generalised number or not. Our results also show that students sometimes treat the variable as closely linked to a referred object, as a superfluous entity or as a constant. Finally, the notion of equivalence, which is an important step towards understanding variables, proved difficult for our students to grasp.

An introduction is provided which discusses articles in the special issue on generalizations in marketing with topics, including consumers' willingness to pay (WTP), consumers' brand relationships and customer satisfaction.