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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.

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.

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.

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.

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.

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.

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.