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Recent research suggests the benefits of supporting a progressive understanding of concepts of inference prior to the teaching of procedures and formal calculations through the study of informal statistical inference (ISI). To contribute to the growing knowledge about the early learning and teaching of statistics, particularly regarding the development of informal inferential reasoning (IIR), we designed a learning trajectory (LT) that addresses ISI in K-4 students (ages 5 to 9 years). This article describes part of the LT in detail, in which third-grade students (n = 12) were introduced to sampling, frequency distribution, randomness and sampling variation as well as to developing a data sense in online lessons. The results of this type of teaching show that the creation and collection of authentic data in a playful context, together with an exploratory analysis of the data as a precursor to utilizing aspects specific to IIR, promoted the integration progress of IIR components in the oral and written informal inferences of students.

Purpose: This 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/approach: To 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. Findings: The 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 implications: The 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/value: The 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.

Purpose: The purpose of this study was to examine the digital competence displayed by a primary school teacher who implemented an interdisciplinary cross-border lesson that was designed with the lesson study methodology and involved two countries--Brazil and Chile. Design/methodology/approach: A qualitative methodology was adopted via the case study method through which the case of a sixth-grade Chilean teacher participating in the study was documented. The data were collected through a lesson plan, a videotape of the implemented lesson and a questionnaire. A professional digital competence framework for teachers provided an analytical perspective via data analysis. Findings: The results show that the teacher displayed digital competence in a synchronous collaborative learning environment in which she had time to reflect on the educational value of technology and appropriate teaching methods involving information and communication technologies. Certain elements of the studied case contributed to this performance, namely the cross-border context, the classroom setting and the collaborative Lesson Study methodology. Practical implications: The lesson study methodology facilitated the teacher's performance in the "Pedagogy and didactics" digital competence by enabling her to participate in planning and implementing a lesson that allowed all those who collaborated, including teachers and researchers, to reflect on teaching in a digital learning environment. Social implications: The cross-border context, which involved co-designing and implementing a lesson in two countries, allowed the teacher to display her "School in society" and "Ethics" competencies. This was achieved through connecting two classrooms with different languages and cultures digitally and synchronously, thereby providing students the opportunity to debate and participate in a global and local problem such as a country's responsibility for energy consumption. Originality/value: Modern society requires the transformation of school practices, and new teaching approaches should include the provision of collaborative spaces that incorporate digital technologies. In this sense, this paper shows that cross-border lessons involving a synchronous learning environment offer a potential alternative, as digital teaching competence enables teachers to bring together different social and cultural groups virtually, thereby contributing to the reduction of social gaps and to the promotion of positive identity among less advantaged students.

In order to study the manifestation of data sense and identify ways of thinking about variability in authentically realistic problems in a group of Chilean fifth-grade students, a lesson plan was designed and implemented, within the framework of statistical literacy and using the "lesson study" modality, in which students were urged to make inferences based on the analysis of data corresponding to the tsunami that struck the Chilean coast in 2010. This article focuses on the qualitative study of the data representations produced by two groups of students during the implementation of the lesson plan. The analysis of the behavior of the tsunami carried out by the students led them to work simultaneously with nominal qualitative, ordinal qualitative, discrete quantitative, and continuous quantitative variables; to create new variables; to construct representations of data (multiple bar graphs and frequency tables); and to make inferences based on the data. We conclude that the use of an authentic context and the construction of their own representations promoted data sense in students and facilitated the development of their statistical thinking, through which they were able to recognize, describe, and explain the variability of the phenomenon.

Among the critical components related to the improvement of mathematics learning are the design of high cognitive demand tasks and teachers' ability to maintain these cognitive demands during their implementation of lessons. We investigate the factors affecting the maintenance and decline of cognitive demand in the implementation of a statistics lesson by two teachers who participated in a Lesson Study group for third graders (8-9 years old). The results of the investigation show notable changes in the maintenance factors associated with the teachers' questions and feedback, the scaffolding provided for the students' reasoning and the modelling of high-level performance. In terms of the decline in the level of cognitive demand, the greatest changes were found in factors corresponding to the routinization of problematic aspects of the task and to problems in lesson management. Based on the results of our collaborative work with teachers in the context of Lesson Study, we conclude that it is possible to design and implement statistical tasks in primary school classrooms that maintain high cognitive demand.

This paper presents an experimental campaign conducted next to the Condoroma dam, in Perú, at 4075 m a.s.l. The tests carried out in this paper were conducted in a 21 m long channel located at the toe of Condoroma dam. The setup consisted of a series of standard profile spillways with a vertical upstream face of up to five different dimensionless heights (P/Hd) ranging from 0.5 to 2. The experimental results indicated that, the P/Hd ratio influences the discharge coefficients in Condoroma, and P/Hd ≥ 1 values are recommended for the design of the spillway profile. In addition, for all the P/Hd ratios studied, the discharge coefficients adjusted to the Condoroma altitude were lower than those reported by classical formulations used in conventional spillway designs. Finally, a generalized equation is proposed to estimate the discharge coefficient for standard spillways located in dams at similar elevations above sea level. [ABSTRACT FROM AUTHOR]

The lack of sidewalls in a spillway leads to lateral expansion of the flow and, consequently, a non-uniform transversal flow rate distribution along the chute. The present work shows the velocity field measured in a physical model of a 1 V:0.8 H steeply sloping stepped spillway without sidewalls. An application of a Bubble Image Velocimetry (BIV) technique in the self-aerated region is shown, using air bubbles entrained into the flow downstream of the inception point as tracers. The results indicate that, for small dimensionless discharges and sufficiently downstream of the point of inception, the free-surface velocity compares relatively well with the corresponding air–water interfacial velocity previously obtained with a double-tip fiber optical probe in the same facility. In turn, the velocity profiles along the normal to the pseudo-bottom, far downstream of the inception point, are reasonably in agreement with the air–water interfacial velocity profiles in the inner part of the skimming flow, with the largest differences being verified in the upper skimming flow region near the free-surface. [ABSTRACT FROM AUTHOR]

The social distancing measures that were imposed as a result of the Covid-19 pandemic, led many countries to adopt distance education. In Chile, a group of teachers sought to support children's education, and with the combined efforts of parents, teachers and administrators took up the challenge of how to help children continue learning in such an adverse environment. To this end, an open-access television program, specifically to support daily math for grade 1 children, was created. The program, which was available on the Internet, comprised fifty-seven video clips based on the official school text and tutor-student interaction. The present paper reports on this initiative and its outcomes. [ABSTRACT FROM AUTHOR]

The article presents a study that explored teacher awareness of student statistical knowledge and the teaching of statistical content. The study used three items related to statistical education including graph comprehension, differentiation between cognitive levels, and the understanding that arises from changing representational systems, and reveals students' great difficulty to produce and read statistics in their various possibilities of presentation.

This study investigated the impact of a scaffolding system that connects theory and practice to promote the development of the ability to teach mathematics in 100 future Chilean preschool teachers. The theoretical dimension and the practical dimension of both mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) were analysed. Data were collected and analysed following a mixed approach. The results of the study reveal the effectiveness of the system in the theoretical dimension and the difficulties that arise in classroom practices. The critical role of the specialized components of MPCK in the theory-practice articulation is discussed. [ABSTRACT FROM AUTHOR]

Since there are few instruments to measure of teaching in early childhood mathematics education, it is described the construction and validation of a Scale to Measure Mathematics Teaching Capability in Practice of preservice early childhood teachers. Through of the validation by expert judgment, the scale obtained a content validity of .97 Aiken's V coefficient and a reliability of .80 Cronbach's alpha coefficient. The work contributes with an instrument for initial teacher training processes and increases the corpus of knowledge about early mathematics education. [ABSTRACT FROM AUTHOR]