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Este trabajo pretende inferir características del conocimiento didáctico-matemático de futuros profesores de matemáticas al desarrollar tareas basadas en prácticas etnomatemáticas locales. Se identificaron las prácticas etnomatemáticas y los conocimientos matemáticos de estos futuros profesores, estudiantes de una universidad ecuatoriana y, posteriormente, se analizaron sus reflexiones con relación al llevar estas prácticas al aula de clases. Los resultados indican una contemplación positiva por parte de los futuros profesores en dos aspectos: primero, en conectar las prácticas etnomatemáticas con las actividades profesionales locales y segundo, en presentar fragilidades en las características del conocimiento tanto matemático como didáctico-matemático. Como camino a seguir, el artículo sugiere que estas percepciones deben incorporarse en la formación de los futuros profesores, además de los conocimientos didáctico-matemáticos y las perspectivas de las Etnomatemáticas.

Background: The interactions in the classroom are of particular interest to the teaching and learning processes. Objectives: This study examines nonverbal interaction in mathematics classrooms, and how different modes of nonverbal behaviour, contributed to the engagement in lessons. Design: A quantitative study. Setting and Participants: 30 randomly selected students wore mini camera-mounted eyeglasses in their mathematics and English lessons. Approximately 45 hours of video recording were made from these cameras (from a first-person’s perspective) to analyse and compare the nonverbal interaction in mathematics and English lessons. Data collection and analysis: In Google Images, we objectively searched and statistically analysed frames in which the class teachers appeared within the students’ visual field. Results: The results show that how students are visually engaged with the teacher depends on a set of proxemics. Differences were found related to visual attention both regarding the subject matter and the different proxemics of the student in relation to the teacher, pointing out that students are more visually involved with the teachers’ instructions when at a proxemic of 1.20 to 3.70 meters. Furthermore, we report differences between boys and girls and how they are visually engaged in their mathematics classrooms. Conclusions: Finally, we report how teachers pointing gestures can serve as a tool to recapture student’s visual attention in mathematics classrooms.

According to Glucksberg’s class-inclusion model of metaphor comprehension, metaphors are understood by the inclusion of the topic X into a metaphorical class of the vehicle Y. But what is the cognitive mechanisms through which X is included in the metaphorical class of Y? Drawing on previous literature on the roles of semantic features, metonymy, and relations in metaphor processing, this article presents a new proposal according to which every metaphorical class is defined by one of three categories of a concept’s characteristics: semantic features, metonymic aspects, or relational aspects. Each category may consist of a large set of such characteristics. One characteristic (or at most several characteristics) usually defines the metaphorical class of Y. Additionally, it is proposed that the metaphorical class is created by the suppression of metaphorically-irrelevant characteristics, consistent with ideas from Relevance Theory. The result of this process is a metaphorical class which has a higher degree of abstractness compared to the literal class of Y. Finally, it is proposed that the three categories of characteristics may be in interaction with each other. Therefore, in some cases, two or even three categories of characteristics may be involved in the formation of a metaphorical class, but one specific category plays the main role in the process.

This work aims to identify the criteria to design activities based on problem-solving tasks that emerge when future early childhood education teachers jointly plan their activities and reflect on them. The participants were 76 students from the Didactics of mathematics subject that was carried out in the 2nd year of the Early Childhood Education Degree of a Catalan public university. This is qualitative research in which the phases of the thematic analysis have been adapted: familiarizing with the data; systematically applying the categories to identify the student criteria emerged; triangulating the analysis with experts; reviewing and discussing the results. The Didactic Suitability Criteria (DSC), from the Ontosemiotic approach (OSA) framework to design tasks and their indicators, were used to categorise and analyse the tasks performed by future teachers. As a result, it was identified that when the future teachers adopt consensually design their activities, they are implicitly based on the Didactic Suitability Criteria (DSC). Still, not all their indicators emerge since their reflection is spontaneous and is not guided by an explicit guideline that serves them to show their didactic analysis in detail. The study concludes that it would be convenient to offer future teachers a tool, such as DSC, to have explicit criteria to guide the designs of their mathematical tasks. In this sense, a future line of research opens, much needed, to adapt the DSC to the singularities of this educational stage.

Motion events have been the target of many studies since their introduction by Talmy (1985). The overwhelming majority of investigations have compared languages cross-culturally with English and Spanish (see, Slobin, 1996, 2004, 2005). The literature is ultimately in need of the practice of this cognitive typology. Since motion events represent cognitive styles and conceptualizations, language teaching and learning is a controversial subject of investigation. To provide insights and contribute to the development of English Language Teaching (ELT) worldwide, we conducted this interdisciplinary study on the verge of cognitive linguistics and ELT. We compared EFL textbooks taught in Iran and Turkey, employing the context of Australia as the source of comparison as the target language. Data were collected from two corpora; one consisting of three English textbooks taught at high schools and one consisting of three novels in each language. Having analyzed the motion components in the corpora, we discovered the discrepancies and diversity of patterns in the languages and the corresponding English textbooks. A detailed comparison of Mannerin these languages revealed that Talmy's typology needs further investigations for a more robust classification of languages. The EFL textbooks in Iran and Turkey do not fully picture English cognitive structures.

I would like to start this editorial commentary with a quote I read: “The youth of today is spoiled to the root. They are mean, ungodly, and lazy. They will never be like the youth of before and they will never ever be able to hold on to our values”. This quote does not come from an article I read in a conservative province newspaper published 2 days ago nor it is part of a political discourse of a right-wing Chilean presidential candidate. This sentence rather is displayed on a Babylonian stone, which has been written more than 3000 years ago. Through the course of time, there has been a phenomenon known as the generation gap. This phenomenon is a popular term used to describe differences in cultural norms between members of a younger generation and their elders.

Gestures have been shown to reflect speakers’ embodied thinking about mathematical concepts and play a role in conveying understandings in teaching/learning interactions. However little research has been done to consider the similarities and differences in the functions that a particular gesture might have in mathematics classrooms in different parts of the world. In this paper, the occurrence of a metaphorical gesture to do with addition in a bilingual mathematics classroom in the UK and two Spanish-speaking classrooms in Chile is investigated. To do this, we elaborate on Systemic Functional Linguistics to consider how the gesture is integrated with other modes of communication to reflect the immediate context of situation as well as a wider mathematics education context of culture. An analysis of the interactions in three classrooms illustrates how the gesture seemed to convey extra meanings, sometimes complementary and sometimes contradictory, to what was expressed through other modes. Besides adding meaning to the mathematical ideas conveyed verbally, the gesture could potentially convey meanings to participants in the interactions about interpersonal relationships which were not as evident in the verbal communication.

This study aimed to examine the gestural embodiment of intensifiers in iconic and metaphoric gestures when these words are used with literal and metaphoric statements. We asked a group of Persian native speakers to listen to and then retell a set of Persian stories. In these stories, a number of intensifiers were used with literal and metaphoric sentences. The results showed that when an intensifier was used with a literal sentence, there was a higher probability of using an iconic or beat gesture than when there was no intensifier in the sentence. Also, when an intensifier was used with a metaphoric sentence, there was a higher probability of using a metaphoric or beat gesture than when the sentence contained no intensifier. These results suggested that an intensifier in a literal or metaphoric sentence can strengthen the mental simulation and the embodiment of objects, ideas, or situations. When an intensifier is used with a literal or metaphoric sentence, the strength of activation in the premotor areas may be amplified and spread to motor areas. In contrast, when no such intensifier is used in a literal or metaphoric sentence, there is a higher probability of simulation in premotor areas without spreading to the primary motor areas. The production of an internal force and expressing emphasis are two other possibilities that may explain the higher use of gestures with intensifiers.

The social, scientific and technological development of recent years has encouraged the incorporation of computational thinking in the school curriculum of various countries progressively, starting from early childhood education. This research aims to characterize future kindergarten teachers’ traits of didactic-mathematical and computational knowledge presented when solving and posing robotics problems. Firstly, aspects of the mathematical and computational knowledge of the participants (97 students of the subject of Didactics of Mathematics of the Degree in Early Childhood Education at a Spanish university) were identified when they solved problems as users of the Blue-Bot didactic robot. Secondly, we analyzed their justifications for reflecting on the design of robotics problems. The results indicate that future teachers present characteristics of didactic-mathematical knowledge when solving and designing robotics problems, although errors and ambiguities are evident, especially in the procedures and representations of the programming. These shortcomings significantly influence the didactic suitability of the robotics problems they design. From a future perspective, in the training of future teachers, it is considered relevant to incorporate didactic-mathematical and computational knowledge that allows them to develop logical, spatial and computational thinking.

This study aimed to examine the embodied conceptualization of hope through metaphors. We asked a group of participants to discuss their hopes in a semi-structured interview. We examined the types of hand, head, and eyebrow gestures produced when they were talking about their future hopes. The obtained results showed that when participants talked about their future hopes, they mainly used forward hand gestures, rightward head gestures, and upward eyebrow gestures. Based on these results, it is suggested that various semantic components and emotional associations of hope are metaphorically embodied in different manners in various parts of the body. The future aspect of hope is conceptualized as a forward movement and is embodied as a forward hand gesture. The good or positive emotional aspect associated with future hopes is metaphorically conceptualized as a rightward head gesture or an upward eyebrow gesture. We call this process distributed embodiment of a metaphorical concept. Our proposal is supported by the findings of past studies that have found future is metaphorically embodied as something in front of us (or forward movement), and good is metaphorically embodied as upper space (or upward movement) or right side (or rightward movement). Refereed/Peer-reviewed

TIME is a highly abstract concept and prevalent in languages worldwide. Cross-cultural and cross-linguistic research suggests that TIME is embodied dissimilarly in different languages. Still the literature has not received sufficient attention in examining the differences. This study aimed to identify and compare how TIME is metaphorically represented and embodied worldwide. We investigated 14 languages; Arabic, Assamese, Chinese, English, Finnish, French, German, Japanese, Kikuyu, Persian, Polish, Russian, Spanish, and Swedish, which represent nine language families. The metaphors were categorized conceptually as TIME IS AN ORGANISM, TIME IS MOTION, TIME IS SPACE, and TIME IS A VALUABLE COMMODITY. We employed a two-part paper-based task. The first part consisted of generation of metaphor items and the second part consisted of a valence rating task. The key variables considered were 'metaphor category' and 'language family' while controlling for demographic variables such as gender, age and handedness. Data from 513 participants were collected. Results showed a significant association between language categories and the valences of time metaphors. The data of this study suggest that within the languages of a certain category, there might be some similarity between the valences of words that are used to realize a given conceptual metaphor. Refereed/Peer-reviewed

This study aimed to investigate how priming a metaphor by the gestural representation of its schema affects the understanding of that metaphor. In each of the two tests, different groups of participants were invited to judge the sensibility of the same 20 metaphors preceded by congruent versus incongruent gesture primes as compared to no prime. In the congruent gesture-prime conditions, each metaphor was preceded by a gesture that represented the schema of the subsequent metaphor whereas this gesture was not compatible with the schema of the subsequent metaphor in the incongruent gesture-prime conditions. Results showed that a higher proportion of sentences were judged to be sensible in the congruent gesture-prime conditions compared to no-prime and incongruent gesture-prime conditions. Also, response times of sensibility judgements were shorter in congruent gesture-prime conditions compared to no-prime and incongruent gesture-prime conditions. These results suggest that metaphor schema affects metaphor comprehension through the activation of metaphorically-relevant information and suppressing irrelevant information.

Understanding how humans acquire or learn a language has been controversial in various disciplines. Most vigorously, psychologists and linguists have been struggling with models that would represent the processing and development of language. The current literature carries many models, making it formidable for the researchers to heed the appropriate approach. A review of the most salient models could provide enlightenment on such bewildering concerns. To this aim, this systematic review paper compares the most reliable and practical models and discusses their salience. By highlighting the requirements of a functional model to be partially universal, we raise issues for a more compelling model that would encompass areas of first and second language acquisition.

Refereed/Peer-reviewed The role of gestural schematization in enhancing thinking processes has been the subject of a large body of works. In this process, contextually unimportant or irrelevant information related to a concept (or a system of concepts) is deleted or ignored, while relevant spatial information is maintained. This process is a special type of inhibition, which is one of the key components of executive functions. In this short paper, it is suggested that gestural schematization is a special type of symbolic schematization, a much more general process through which irrelevant information related to features of a concept (or a system of concepts) is suppressed, while relevant information (spatial and non-spatial) is maintained. Through symbolic schematization, abstract structural similarity between two concepts or between two systems of concepts can be discovered. In this way, an individual’s knowledge about the first situation can be generalized to the second situation. Symbolic schematization is the basis of abstraction, knowledge generalization, and knowledge development. This is particularly the case with abstract mathematical thinking. This proposal offers a picture of cognitive mechanisms through which knowledge of abstract mathematical concepts is created and developed in the mind.

This article discusses perspective and frame of reference in the metaphorical description of mathematical concepts in terms of motions, gestures, and embodied actions. When a mathematical concept is described metaphorically in terms of gestures, embodied actions, or fictive motions, the motor system comes into play to ground and understand that concept. Every motion, gesture, or embodied action involves a perspective and a frame of reference. The flexibility in taking perspective and frame of reference allows people to embody a mathematical concept or idea in various ways. Based on the findings of past studies, it is suggested that the graphical representation of a mathematical concept may activate those areas of the motor system that are involved in the production of that graphical representation. This is supported by studies showing that when observers look at a painting or handwritten letters, they simulate the painter's or writer's hand movements during painting or writing. Likewise, the motor system can contribute to the grounding of abstract mathematical concepts, such as functions, numbers, and arithmetic operations. Refereed/Peer-reviewed

Contexto: “A cultura esconde mais do que revela e, por mais estranho que pareça se esconder, esconde-se mais efetivamente de seus próprios participantes” (Hall, 1959, p. 39). Esta citação se enquadra muito bem com um provérbio persa, também, um aforismo bem conhecido que tem sido bastante citado em muitos artigos etnográficos, o qual se apresenta como “um peixe é a última criatura a descobrir a água”. Estar imerso na água, cercado por ela, torna invisível e quase impossível percebê-la. Em outras palavras, muitas vezes desconhecemos nosso comportamento interacional, enquanto professores de matemática, quando o realizamos em nossa prática profissional habitual e localizada. Objetivo: Discutir como se mostra a linguagem corpórea do professor de matemática ao ensinar equações e, assim, perceber essa linguagem em termos de ação educacional profícua ao se ensinar equações em sala de aula, por exemplo. Metodologia: Metodologia qualitativa. Coleta de dados e análise: A partir de referenciais teóricos que tratam de linguagem corpórea, corporeidade e percepção, analisamos as aulas de dois professores de matemática que ensinavam equações, em Birmingham (Reino Unido) e em Rolante (Brasil), individualmente e comparativamente. Assim, prestando atenção especial à cultura matemática em sala de aula e analisando os gestos localmente situados no ensino de equações e o comportamento não-verbal dos professores, podemos compreender o ensino de matemática por meio do movimento do corpo, o qual muitas vezes passa despercebido. Resultados: Compreendemos com os resultados dessa pesquisa que perceber a linguagem corpórea dos professores de matemática, a qual é produzida-coma-fala, nos dá indicativos da materialização do sentidos atribuídos à equação e como isso possivelmente afetará a própria constituição do conhecimento matemático do estudante, em termos de possíveis sentidos atribuídos a cada gesto. Conclusões: Consideramos que conhecer a linguagem corpórea pode favorecer o próprio ensinar do professor, ou seja, metaforicamente, conhecer o mar pode favorecer o peixe a nadar. Background: “Culture hides much more than it reveals and, strangely enough, what it hides, it hides more effectively from its own participants” (Hall, 1959, p. 39). This quote corresponds well to a Persian proverb, also a well-known aphorism that has been widely cited in many ethnographic articles: “a fish will be the last to discover water.” Being immersed in water, surrounded by it, makes it invisible and almost impossible to perceive. In other words, we often do not know our interactional behaviour as mathematics teachers when we perform it in our usual and localised professional practice. Objective: To discuss mathematics teacher’s body language when teaching equations and thus perceive this language in terms of possible fruitful educational action when teaching equations in the classroom. Design: Qualitative methodology. Data collection and analysis: Based on theoretical references that deal with body language, corporeality, and perception, we analysed individually and comparatively the classes of two mathematics teachers who taught equations in Birmingham (United Kingdom) and Rolante (Brazil). Thus, particularly attentive to mathematical culture in the classroom and analysing the localised gestures in the teachers’ teaching of equations and the non-verbal behaviour, we can understand mathematics teaching through body movement, which often goes unnoticed. Results: We understand from the results of this research that perceiving the body language of mathematics teachers, which is produced with speech, gives us indications of the materialisation of the meanings attributed to the equation and how this will possibly affect the very constitution of the student’s mathematical knowledge, in terms of possible meanings attributed to each gesture. Conclusions: We consider that knowing the body language can favour the teacher’s teaching, i.e., metaphorically, knowing the sea can favour the fish to swim.

In this paper, six mathematics curriculum changes in Iran will be reviewed, spanning from 1900 until the present time. At first, change forces, barriers, and the main features of each curriculum reform will be represented. The first five curriculum changes are described briefly and the sixth and most recent curriculum reform will be elaborated. In this paper, we call the last reform as contemporary school mathematics curriculum change. This recent (contemporary) curriculum reform will be explained in more detail, followed by a discussion of the effect of globalization and research finding in the field of mathematics and mathematics education (in the Iranian mathematics curriculum). In total, three key ideas are distinguished as an effect of globalization which is “New Math”, “International Comparative Studies”, and “Computational Thinking”. Finally, the paper comments on the necessity of paying more attention to information and communication technology as part of globalization; in particular, recall policy-makers to consider “Computational Thinking” as an important component of future curriculum design.

In this article, we extend our previously suggested categorization of metaphors to literal statements, and categorize metaphorical and literal statements into four pairs of corresponding metaphorical and literal statements: (1) motion-based metaphorical/literal statements; (2) static space-based metaphorical/literal statements; (3) static object-based metaphorical/literal statements; (4) static event-based metaphorical/literal statements. Then, we report a study that investigated the use of metaphoric and iconic gestures with these corresponding categories during the retelling of a set of stories by a group of thirty participants. The participants listened to five audio short stories. Each story contained one statement of each metaphoric category and one statement of each literal category. After listening to each story, they retold it in their own language in front of a camera. The results showed that event-based metaphors and event-based literal statements were accompanied by the smallest number of metaphoric and iconic gestures. Furthermore, there was a significant similarity between each metaphorical category and its corresponding literal category in the number of gestures that were used with these categories. This similarity supports the idea that the mechanisms underlying the embodiment of metaphorical and literal statements are essentially similar.

This study explores university students’ perceptions of factors that hinder student learning with particular attention to students’ discipline (STEM vs non-STEM) and ethnicity. A sample of 1684 uni...

Learning mathematics in grade 1 as the formal starting point for learning mathematics in many countries can significantly impact students’ subsequent learnings. One of the most critical factors influencing teacher teaching and student learning is the written intended curriculum materials (official curricula). Despite the importance of this topic, there is little research on how many mathematics topics should be taught in grade 1 and to what depth students should learn these topics until the end of the first grade. In this study, we investigated and compared the grade 1 intended mathematics curriculum of Australia, Iran, Singapore, the Province of Ontario in Canada, and New York State in the USA. Indeed, we sought to examine how curriculum developers and decision-makers in education in these jurisdictions prepared the content of the first-grade mathematics in the curriculum writing materials. To do this, by examining the official curricula for grade 1 of these countries and using a procedure called general topic trace mapping, we found a list of 14 topics. The findings of the current paper showed similarities and differences in the topics intended in the mathematics curriculum of these countries. Ontario, Australia, Singapore, New York, and Iran curricula cover 13, 11, 9, 9, and 7 topics of 14 topics, respectively. We also considered five content strands and examined and compared the progress of each intended curriculum in these strands at the end of grade 1. We found that the learning progression in some content strands is different among countries. The results demonstrate the nuanced complexity of these comparisons and the importance of cross-national comparisons. We concluded this article with suggestions for curriculum developers, textbook writers, and teachers.

Language learners struggle with achieving their highest reading competence, particularly when they sit standardized tests with authentic advanced passages. The related literature shows a significant gap in suggesting specific techniques or strategies for individuals to develop a reading competence. To fill this gap, this study investigated the potential relationship between EFL learners' reading performance and their learning styles. One hundred thirty-seven participants were administered the TOEFL PBT for their recruitment test, at which the reading scores were evaluated and analyzed. Ehrman and Leaver’s Questionnaire (2003) was used to classify participants’ learning styles in an ectenic-synoptic continuum. We used the Pearson Product Moment Correlation Coefficient to find any potential correlation between learners' performance and their scores as an ectenic or a synoptic learner. The results revealed a positive correlation between synoptic learners and success in the reading tasks. Consequently, a regression model provided the classification of successful learners at reading tests. Knowing that teachers have a variety of learners in their classes and their preferred learning styles can help course instructors to design activities that will exercise a range of cognitive processes and perspectives.

Gestures play a role in perception, production, and comprehension of language and have been shown to differ cross-linguistically and cross-culturally in aspects of performance and form-meaning relationships. Furthermore, gestures can serve as analytical tools to access tacit embodied-imagistic mathematical meanings that add to verbal-linguistic dimensions of meaning. At the same time, language plays important roles in interaction and cognition, influencing bilinguals’ learning of mathematics. Still, there is only very little research attending to the use of gestures of multilinguals as means to better understand the relationships between their language use and their mathematical thinking. This paper builds on research on multilingualism and on gestures—related and unrelated to mathematics education—to motivate and develop a framework for understanding better mathematics thinking and learning of multilinguals through integrating gesture analysis as related to languages, culture, and the use of registers. The application of this framework will be illustrated through two case studies in which we analyse interview data of a bilingual student and a bilingual mathematics teacher—focusing on gestures and language use while talking about the mathematical concept of ‘power’—or exponents—in Farsi (Persian) and in English. From analyzing the gestures’ form-meaning relations and their functions as related to hybrid language practices, we hypothesize on the vernacular and mathematical context as activated in both speech and gesture and on how it relates to mathematical meaning. From this, we draw practical implications for multilingual mathematical learning contexts and discuss implications for research on multilinguals’ mathematical thinking and learning.

Results of the studies on the way language and body coordinate in communication (through language and gesture) have significant implications for language, education, and cognitive studies. However, there is a lack of convenient research in this area analyzing perceptual changes within individuals. To fill this gap, we investigated the embodied realizations of literal sentences representing perceptual changes and metaphorical sentences describing the phenomena in terms of perceptual changes. We classified sentences that referred to a visual, auditory, haptic, gustatory, or olfactory change. Participants listened to four narratives that contained five literal sentences describing a real perceptual change and five metaphorical sentences that described a phenomenon in terms of a perceptual change. We analyzed the recorded videos of the participants. The total number of literal sentences that described a real perceptual change was obtained for each modality (visual, auditory, haptic, gustatory, olfactory) separately. Also, the total number of gestures used with each category of these literal statements was obtained. Only iconic and non-iconic gestures that described such perceptual changes as the movement of an object in the space were counted. The results revealed that gestures accompanied at least 53% of literal and 56% of metaphorical sentences. These results suggest that literal and metaphorical perceptual change sentences could be understood as movements at a conceptual level. The similarity between embodied realizations of literal and metaphorical sentences supports one of the main assumptions of the strong version of embodied cognition.

The aim of this study was to examine the impact of manner adverbs on the gestural embodiment of actions that are described by literal and metaphoric sentences. We asked a group of participants to read and then orally retell four stories. Each story had two versions. In one version, literal and metaphoric sentences describing literal and metaphorical actions did not include manner adverbs. In the other version of each story, the same sentences included a manner adverb that provided more information about literal or metaphoric actions. Participants’ reproductions of stories were recorded with a camera and were analyzed to make a comparison between gestures that accompanied sentences that included a manner adverb and sentences that did not include a manner adverb. The results showed that when literal and metaphoric sentences included a manner adverb, there was a higher probability of using a gesture than when these sentences were used without a manner adverb. In other words, using a manner adverb increases the probability of using a gesture with literal and metaphorical sentences. Therefore, it is suggested that adding a manner adverb to a literal or metaphoric sentence can strengthen the process of embodiment of the action described in that sentence. We present two explanations for this observation.

RESUMO Este artigo relata um estudo realizado sobre a interação professor-aluno em uma escola pública dos anos iniciais, na cidade de Santiago, Chile. O estudo realizou uma análise quantitativa dos quadros das imagens capturadas por uma minicâmera montada em óculos de um grupo de 18 estudantes. Os quadros selecionados foram os que a professora aparece no campo visual dos alunos. A análise foi desenvolvida a partir do conceito de proxêmica e os resultados mostram que há momentos em que a professora da sala de aula interage com os alunos em um nível mais próximo e, em outros, há um distanciamento maior. Além disso, foi possível identificar diferenças entre meninos e meninas quanto aos padrões proxêmicos de envolvimento visual na interação. Os resultados deste estudo sinalizam novos sentidos para a análise da interação professor-aluno com foco em aspectos não verbais na construção das relações de ensino e aprendizagem. RESUMEN En este artículo se relata un estudio realizado sobre la interacción profesor-alumno en una escuela pública de los años iniciales, en la ciudad de Santiago, Chile. En el estudio se realizó un análisis cuantitativo de los cuadros de las imágenes capturadas por una minicámara montada en gafas de un grupo de 18 estudiantes. Los cuadros seleccionados fueron los que la profesora aparece en el campo visual de los alumnos. El análisis se desarrolló a partir del concepto de proxémica y los resultados apuntan que hay momentos en que la profesora de la sala de clase interactúa con los alumnos en un nivel más cercano, en otros, hay un alejamiento mayor. Además de eso, fue posible identificar diferencias entre niños y niñas cuanto a los patrones proxémicos de involucramiento visual en la interacción. Los resultados de este estudio señalizan nuevos sentidos para el análisis de la interacción profesor-alumno con enfoque en aspectos no verbales en la construcción de las relaciones de enseñanza y aprendizaje. ABSTRACT This article reports a study carried out about teacher-student interaction in a public school in the early years, in the city of Santiago, Chile. The study performed a quantitative analysis of the frames of images captured by a mini camera mounted on eyeglasses of a group of 18 students. The selected frames were those that the teacher appears in the students’ visual field. The analysis was developed from the concept of proxemics and the results show that there are times when the classroom teacher interacts with students at a closer level and, in others, there is a greater distance. Furthermore, it was possible to identify differences between boys and girls regarding the proxemic patterns of visual involvement in the interaction. The results of this study indicate new directions for the analysis of teacher-student interaction, focusing on non-verbal aspects in the construction of teaching and learning relationships.

ANID/PIA/Basal Funds for Centers of Excellence FB0003 Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT) CONICYT FONDECYT 3170062

In this paper, we classify metaphors into four categories: motion-based metaphors, static space-based metaphors, static object-based metaphors, and static event-based metaphors. Then, a study that investigated the use of gestures with these types of metaphors is reported. The aim was to examine how these types of metaphors are used with metaphoric and beat gestures during the process of re-telling stories. The participants of the study listened to three audio stories. Each story contained two motion-based metaphors, two static space-based metaphors, two static object-based metaphors, and two static event-based metaphors. After listening to each story, they had to retell the stories in front of a camera. The videos were analyzed to determine the number of metaphoric gestures and beat gestures that had been used by participants during the retelling of the stories. The results showed that the highest number of metaphoric gestures had been used with static space-based metaphors. This was followed by motion-based metaphors, static object-based metaphors, and static event-based metaphors, respectively. On the other hand, the highest number of beat gestures was used with static event-based metaphors. These findings indicate that the use of metaphoric gestures and beat gestures accompanying metaphors is highly dependent on the spatial and motoric properties of the base of the metaphors, which supports the idea of embodied metaphor comprehension.

En este artículo se discuten los problemas y las cuestiones que se plantean en Educación, en particular, en Educación Matemática a partir de la problematización de los efectos de la pandemia de COVID-19. Para ello, tres investigadores en Educación Matemática de Brasil, Chile y España se han reunido virtualmente. Con base en estas discusiones, el grupo proporcionó el contexto para cada uno de los tres países en términos de cómo han estado gestionando las acciones relacionadas al contexto de la pandemia y seleccionó tres historias vivenciadas, por ellos, en este contexto, las cuales las utilizaron como elementos materiales para una discusión conjunta de forma no localizada. Por medio de esecamino, como resultado, se muestra una visión general de los efectos de COVID-19 en diferentes países relacionados con la educación, que se clasificaron en tres dimensiones: técnica, política y pedagógica. Además de eso, se presentan cuestionamientos a la Educación Matemática producidos a partir de la problematización de los efectos de la pandemia., This article discusses the problems and questions that are raised in Education and specifically in Mathematics Education from the problematization of the effects of the pandemic of COVID-19. For this, it was brought together three researchers in Mathematics Education from Brazil, Chile and Spain, who started to meet virtually. Based on these discussions, the group provided the context for each of the three countries in terms of how they have been dealing with the pandemic and selected three tales they lived related to the pandemic, that were used as material elements for a joint discussion in a non localized way. With this path, as results, it is shown an overview of the effects of COVID-19 in different countries related to education, that were categorized in Technical, Political and Pedagogical dimensions. Besides that, questions are presented to Mathematics Education produced from the problematization of the effects of the pandemic., Este artigo discute os problemas e questões que surgem na Educação, em particular na Educação Matemática, a partir da problematização dos efeitos da pandemia COVID-19. Para isso, três pesquisadores em Educação Matemática do Brasil, Chile e Espanha se encontraram virtualmente. Com base nas discussões, o grupo forneceu o contexto para cada um dos três países em termos de como eles vêm gerenciando as ações relacionadas ao contexto da pandemia e selecionou três histórias que vivenciaram nesse contexto, que utilizaram como elementos materiais para uma discussão conjunta de forma não localizada. Por esse caminho, tem-se como resultado um panorama dos efeitos do COVID-19 na educação em diferentes países, os quais foram classificados em três dimensões: técnica, política e pedagógica. Além disso, são apresentadas questões à Educação Matemática produzidas a partir da problematização dos efeitos da pandemia.

Interaccionar con los estudiantes y construir una buena relación es fundamental para que los maestros enseñen, comuniquen conceptos básicos y se conecten emocionalmente con sus estudiantes. Este artículo reporta un estudio que se llevó a cabo en una escuela de educación primaria en Santiago de Chile, donde una muestra de 33 estudiantes (niñas), seleccionadas al azar, llevaban una minicámara de vídeo anexada en sus gafas en el momento que participaban en las clases de matemáticas. Usando imágenes de Google, se buscaron, de forma automática y objetiva, registros de las grabaciones en las que el profesor de la clase aparecía en el campo visual de las estudiantes. Los resultados muestran que las estudiantes prestaron mucha más atención visual en las clases de matemáticas cuando el discurso de los profesores iba acompañado de gestos. Además, hubo diferencias entre las niñas con alto y bajo rendimiento y en cómo se involucraron visualmente durante la instrucción de los maestros en diferentes momentos de la lección. También, se presentaron diferencias en relación con cómo las alumnas introvertidas y las extrovertidas se involucraban visualmente mientras el maestro hacía gestos. Los resultados de este estudio son muy importantes para poder construir una buena relación interaccional entre profesor-alumno y mejorar las prácticas profesionales de enseñanza.

Providing teachers with detailed feedback about their gesticulation in class requires either one-on-one expert coaching, or highly trained observers to hand code classroom recordings. These methods are time consuming, expensive and require considerable human expertise, making them very difficult to scale to large numbers of teachers. Applying Machine Learning and Image processing we develop a non-invasive detector of teachers’ gestures. We use a multi-stage approach for the spotting task. Lessons recorded with a standard camera are processed offline with the OpenPose software. Next, using a gesture classifier trained on a previous training set with Machine Learning, we found that on new lessons the precision rate is between 54 and 78%. The accuracy depends on the training and testing datasets that are used. Thus, we found that using an accessible, non-invasive and inexpensive automatic gesture recognition methodology, an automatic lesson observation tool can be implemented that will detect possible teachers’ gestures. Combined with other technologies, like speech recognition and text mining of the teacher discourse, a powerful and practical tool can be offered to provide private and timely feedback to teachers about communication features of their teaching practices.

Normally teachers can consciously control to a great extent the behaviors of their students in the classroom. But additionally, there are unconscious teacher behaviors that also impact the collective behavior of their students. To study this phenomenon, we gather data obtained from mini video cameras mounted on eyeglasses worn by fourth graders. We found that the proportion of scenes where the teacher is pointing his body toward the student is higher than the proportion of scenes when there is mutual gaze, and that this effect is slight pronounced in STEM classes. We also found that this effect is greater among boys than girls, and that is particularly evident at certain distances. More precisely, we found that in STEM classes when a male student is observing the teacher, the teacher is generally pointing their body toward the student (67% of cases). However, with female students, this number is just 46%. However, there is no such difference in non-STEM classes. Moreover, the distance between the student and the teacher also has a significant effect. This is a powerful tool for teachers as it can help them reflect on their strategies, as well as the impact of their unconscious nonverbal behavior in classroom behavior.

Attracting students’ visual attention is critical in order for teachers to teach classes, communicate core concepts and emotionally connect with their students. In this paper we analyze two months of video recordings taken from a fourth grade class in a vulnerable school, where, every day, a sample of 3 students wore a mini video camera mounted on eyeglasses. We looked for scenes from the recordings where the teacher appears in the students’ visual field, and computed the average duration of each event. We found that the student’s gaze on the teacher lasted 44.9 % longer when the teacher gestured than when he did not, with an effect size (Cohen’s d) of 0.69. The data also reveals different effects for gender, subject matter, and student Grade Point Average (GPA). The effect of teacher gesturing on students with a low GPA is higher than on students’ with a high GPA. These findings may have broad significance for improving teaching practices.

Mathematics is believed by some to be a universal language that all human beings share (Singh, 1997; Guedj, 2000). In this school of thought, mathematics has its own particular syntax, genre and ways of argumentation. For example it is commonly believed doing arithmetic is the same regardless of whether one is performing arithmetic in Chinese, Farsi or in English. However although the result is the same, the linguistic support that is behind the arithmetic process is not necessarily identical.