cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.14304748
title: Didactical paradoxes observed in the management of Euclid's theorems

description: Abstract Geometry teaching and learning processes have allowed us to pose several problems that have been intensively studied by the Mathematics Education research community in recent decades, focusing on aspects such as software use, student knowledge, mathematical complexity, teacher knowledge etc. However, today, there is still interest in understanding the difficulties associated with the teachers' practices, in particular, regarding the management of the classes they carry out, since this directly impacts geometry learning by the students. In this sense, we present a study that consists on the observation of the management of two teachers who have faced the teaching of Euclid's Theorems in their second-year courses in Middle Education in Chile. To this end, direct observation of the classes was carried out and both teachers were subsequently interviewed. For the analysis of pedagogical management, we used Guy Brousseau's Theory of Didactical Situations (TSD), specifically focusing on the notions of didactical contract, didactical milieu, and the processes of devolution and institutionalization. The methodology used in the study is qualitative, descriptive, and interpretive, where extracts of episodes from a class are retrieved. The analysis reveals numerous didactical paradoxes that do not favor the learning of the students in relation to the foreseen objectives, nor to the mathematical objects treated in class. Among the paradoxes, phenomena such as the topaze and resonance effects are observed, detected in the teacher-student interaction. The need to analyze in depth the professional practices of teachers is evident, since this work revealed the rupture between the institutional discourse and the pedagogical management in practice.
DOI: 10.6084/m9.figshare.14304746
title: Experimental Activities with Technologies in Mathematical Modeling Scenarios

description: Abstract This article analyses the realization of experimental activities carried out by groups of second-year students from a secondary school in Córdoba (Argentina), within the framework of open modelling projects with the free use of technologies. The students developed these projects in modeling scenarios created in their mathematics classes. Our research seeks to investigate: 1) the learning of students participating in active mathematical modeling scenarios with experimental activities and digital technologies and, 2) the role that digital technologies play in modeling processes that involve experimental activities. In theoretical terms, the perspective of situated learning and the epistemological vision embedded in the humans-with-media construct are adopted. Learning is evidenced by the participation of students in different phases of mathematical modeling processes developed in local communities of practice in the educational context.The digital technologies most used by the students were their cell phones and cameras, to record experiments and take measurements, and mathematical software to represent graphs and communicate results. These uses were related to the experimentation and resolution phases. The in-depth analysis of a particular project shows the potential and creative use of various digital technologies in these phases. It is important to note that the study provides an example that responds to curricular recommendations around the inclusion of modeling and the use of technologies in mathematics classes. Finally, we reflect on the importance, for teacher education, of living experiences such as the one reported in this study.
DOI: 10.6084/m9.figshare.14304740
title: The relationship between Math Anxiety, Working Memory, and Inhibitory Control: A meta-analysis

description: Abstract Numerical processing demands functions that may show interference from anxiogenic reactions. The relationship between mathematics and threatening situations is called math anxiety (MA), which is a feeling of tension and mental disorganization when number manipulation is required. It is a consequence of genetic and environmental predictors, but may also be associated with poor working memory (WM) performance and inhibitory control (IC). The aim of this study was to demonstrate the size effect of MA on performance in WM tasks, and to investigate the strength and significance of correlations between MA, WM, and IC. A new hypothesis test was performed with data from articles that have the same pattern of statistical information, comparing groups with high and low MA. The software R, version 3.6.4, and the packages Revmeta, Metafor, and Forest were used. The size of the effect of MA on WM was SMD = -0.22, CI = 100%, [-0.38; -0.07]; p = 0.01, demonstrating that there is a significant difference between the WM means for groups with high and low MA. However, a high heterogeneity index (I2 = 81%) was found, which shows little robustness about the variety of our data. Groups with high levels of MA have been shown to have higher error rate and reaction time in irrelevant stimulus inhibition tasks, which shows difficulties in resisting interference while performing mathematical tasks presented by these individuals.
DOI: 10.6084/m9.figshare.14304737
title: Emerging Obstacles of Teaching Practice with Mathematical Research

description: Abstract From the qualitative-phenomenological-hermeneutic perspective, we researched in this article, the factors that limited the Mathematical Research task, as reported in the productions of teachers who worked under this perspective in the Educational Development Program of Paraná (EDP). The research movement is that of perception as a conscious experience, exemplified by Sokolowski's cube metaphor. We articulated the data in four categories to be able to affirm that the obstacles stem from the actions of the subjects involved in the work (teachers and students), from the dynamics and epistemological characteristics of Mathematical Research itself, from the school's structure and organization, and from the insertion of the Information and Communication Technologies (ICT), which find more explanations in the conceptions and beliefs of teachers, students, school management, pedagogical team, family, and state, coming from the prevailing culture.
DOI: 10.6084/m9.figshare.14304734
title: Cognitive biases and their implications for financial education: the “Brumadinho effect” case in graphs construction

description: Abstract This paper discusses the cognitive biases identified from the analysis of 21 graphic and textual records produced individually by 47 university students during an Economics class. The records were the result of an activity in which students were required to complete Cartesian charts in which part of the stock price trajectory of some companies was present, and part was hidden. Students should draw the trajectory that the stock price would have taken in a past period. In this sense, it was a “retrospective projection” activity. More than 80% of the 21 graphical and textual records included chronological distortions that exemplified the cognitive challenges involved in teaching and learning financial topics. The identified phenomenon consisted of a synthesis of cognitive biases that jeopardized the perception of event chronology that are part of the students' prior knowledge, being an example of the challenges to be considered in the initiatives for the promotion of Financial Education in Mathematical Education.
DOI: 10.6084/m9.figshare.14304731
title: Mathematical objects linked to statistics and probability in Early Childhood Education: an analysis from textbooks

description: Abstract This article analyzes how the contents of statistics and probability are addressed in the textbooks of Early Childhood Education in Chile. For this, we used theoretical tools of the Ontosemiotic Approach to Mathematical Knowledge and Instruction, which have allowed us to investigate mathematical objects (problem situations, language, concepts, and procedures) linked to the study of statistics and probability in textbooks for Early Childhood Education. The results show, first, the absence of activities associated with the study of probability and, secondly, an adequate and gradual approach towards the construction of certain basic notions of statistics. These results provide valuable information to improve the presentation of these contents in textbooks for Early Childhood Education.
DOI: 10.6084/m9.figshare.14304729
title: Pre-service Teacher Self-Efficacy in the Use of Technology for Teaching Mathematics

description: Abstract Self-efficacy has proved to be a powerful predictor of performances that people plan to attain a specific goal. The purpose of this article is report to what extent self-efficacy of pre-service teachers in the use of technology for teaching mathematics is transformed, during a 64-hour course designed to promote self-efficacy. The sample consisted of sixteen teachers in training who self-completed the self-efficacy measurement instrument “Preparation in the use of technology to teach mathematics” which consists of a battery of 6 dimensions and 23 ordinal variables in the scale of 0 to 10. Two measurements were carried out, the first one at the beginning and the second one right after the course. Nonparametric tests were performed for data analysis: Spearman's rank correlation coefficient, the Kruskal-Wallis test, the Mann-Whitney U test, and the Wilcoxon test. The results indicate age, professional experience, and gender as non-significant variables on pre-service teacher self-efficacy in the use of technology for teaching mathematics. Statistically, there were significant differences between self-efficacy ranges before and after course implementation. Pre-service teachers reported feeling prepared to use technology for teaching. However, they consider necessary to have more training experiences.
DOI: 10.6084/m9.figshare.14304728
title: Mathematics Education and Distance Learning: a systematic literature review

description: Abstract The article presents the development and results of a systematic review of the literature on Mathematics Education and Distance Learning. This review is part of a doctoral research in development on e-learning and b-learning practices in Brazilian Mathematics Teacher Education Programs. The main objective of the review was to identify in Mathematics Education how previous researches (January 2011 and December 2017) defined the e-learning and b-learning teaching models. In addition, it is possible to understand at what levels of education these investigations are situated: basic education, initial or continuing teacher education. Although focusing on a doctoral undergraduate research, it is believed that the previous research, reproduced at other school levels, can also add elements and reflections to understand these models of courses in Distance Education. We carried out a systematic review based on orientations from different organizations and researchers dedicated to this area of research. In this sense, we followed different phases in the process to make the review: definition of objectives/questions, research equations and databases; determination of inclusion, exclusion, and methodological validity criteria; presentation and discussion of results; and data. As supporting software, both Google spreadsheets and NVivo11 were herein used. In addition to a higher incidence of work that occur in the teacher training context, the review results show great dispersion about the concept of e-learning and a lower occurrence of studies on b-learning models. Also, a significant number of works refer to the need to create conditions, in Distance Teacher Education Programs, for the constitution of (virtual) learning communities.
DOI: 10.6084/m9.figshare.14304727
title: Aspects of University Students' Graph Sense in a Virtual Learning Environment

description: Abstract To break with the traditional model of Basic Statistics classes in Higher Education, we sought on Statistical Literacy and Critical Education to develop an activity about graphic interpretation, which took place in a Virtual Learning Environment (VLE), as a complement to classroom meetings. Twenty-three engineering students from a public higher education institution in Rio de Janeiro took part in the research. Our objective was to analyze elements of graphic comprehension in an activity that consisted of identifying incorrect statistical graphs, conveyed by the media, followed by argumentation and interaction among students about these errors. The main results evidenced that elements of the Graphic Sense were present in the discussions and were the goal of the students' critical analysis. The VLE was responsible for facilitating communication, fostering student participation, and linguistic writing, so the use of digital technologies and activities favored by collaboration and interaction are important for statistical development, but such construction is a gradual process.
DOI: 10.6084/m9.figshare.14304726
title: Score on a mathematics diagnostic assessment and its dependence on affective aspects due to making mistakes

description: Abstract Affective aspects related to making mistakes in mathematics influence learning the subject throughout school life. This study was carried out among incoming students at a private university in Guadalajara, Mexico. They are all in the field of administration. The objective of the study was to find the underlying constructs, as well as items in Ibarra-González and Eccius-Wellmann's Affectivity towards and due to Mathematical Errors questionnaire that correlate significantly with the score on a diagnostic assessment of mathematics. Regarding the constructs, the study found that evaluation scores depended on attitudes towards errors as a learning tool and negative beliefs and emotions towards mathematics due to making mistakes. The items corresponding to the aforementioned constructs revealed that the students grade decreases according to the intensity of the student's belief that he is not by nature good at mathematics. This belief lead to making more mistakes and a lack of interest in correcting them, influencing scores negatively. Based on the results, we see the need to promote a change in the pejorative connotation of error to reduce negative beliefs towards mathematics due to making mistakes and to use errors efficiently for pedagogical purposes.
DOI: 10.6084/m9.figshare.14304723
title: Statements that Constitute Mathematics Teaching in the Initial Years of Elementary Education

description: Abstract The article problematizes statements that make up the discourse of Mathematics Education and its truth effects on the pedagogical practices of teachers who work in the Early Years of Elementary Education. The theoretical contributions that underpin the investigation are the theories of Michel Foucault, especially the concepts of discourse and statement. The research material is composed of interviews with teachers of the 3rd or 4th year in the private school network of Porto Alegre. The analytical strategy used to examine the material was guided by the discourse analysis from Michel Foucault's perspective. The material examination evidenced the presence of two statements constituting the discourse of Mathematical Education in the Early Years: “the importance of the use of concrete material and digital resources in Mathematics classes” and “the relevance of the registration and formalization of mathematical knowledge as a guarantee of learning”. Thus, it can be concluded based on the interviews carried out, that mathematics teaching in the Early Years is supported by statements that are part of different discursive fields, but predominate those based on Platonic constructivism and ideals, leading the pedagogical processes in an ascending way: concrete materials for systematization and formalization, making this final stage as the most relevant and capable of ensuring learning.
DOI: 10.6084/m9.figshare.14304721
title: Promoting Geometric Reasoning in Students with Autism Spectrum Disorder through a Digital Environment

description: Abstract Reasoning and sense-making are essential capabilities in all mathematical learning and understanding processes, in children with typical development. In children with Autism Spectrum Disorder (ASD), these capabilities become much more significant, considering their importance for a successful independent living. The use of technology is considered an effective way to work academic content with children with ASD enabling the creation of creative and constructive environments where we can be develop differentiated, meaningful, and qualitative activities. However, the development of technological applications for children and youth with ASD continues to attract little attention, namely the ones regarding the development of geometric thinking. The purpose of this paper is to report the main results obtained with children with ASD using the digital Learning Environment on Mathematics for Autistic Children developed, particularly regarding the promotion of their fundamental mathematical capabilities in geometry. The “PISA 2015 Mathematics Framework” was the theoretical basis for the data collection. Its analysis allowed to place the geometric thought of the participating students between partially-structured and structured and has also pointed to the redesign of some of the activities implemented in the digital environment, in view of the promotion of geometric thinking.
DOI: 10.6084/m9.figshare.14304720
title: Spatial Structuring in 1st Grade: from local structuring to global structuring

description: Abstract In this paper, we aim to understand how 1st grade students develop their spatial structuring of 2D figures composed by squares (pentominoes) by analyzing students' strategies to compose pentominoes, to determine the congruency between pentominoes and to anticipate composites, and the importance of drawing the constructions. Data was collected during the implementation of the first sequence of tasks, from cycle two, of a design-based research. Results show that, at first, students build pentominoes by manipulating squares individually and by trial and error, which is a strategy associated to local structuring. Gradually, students evolve in their capacity of coordinating components and composites, stimulated by the relationships they stablish and reflect upon between manipulatives and drawings. As they stablish more complex relationships, based on the coordination of components and composites, they start to be able to build with anticipation. Building with anticipation, based on mental images, suggests the use of integration operation, which is associated with global structuring. Students use movements as rotating and flipping, at first, with manipulatives and later mentally to determine the congruency between two pentominoes and to anticipate the result of pentominoes manipulation.
DOI: 10.6084/m9.figshare.14304716
title: History of Mathematical Analysis and Cognitive Development

description: Abstract This research discusses the historical construction of mathematical analysis concepts in the light of genetic epistemology, to obtain conclusions about the learning in this area. According to the research problem “How is structured knowledge related to mathematical analysis?”, we aim to understand the process of constructing real knowledge analysis, in history and comparing the cognitive subject development, according to the genetic epistemology perspective. For this, we studied the history of mathematics from its main references, and Piaget's theory. As a result, it was observed that the course that culminated in the current formalization of the analysis occurred in four stages: development of differential and integral calculus; organization of this calculus; analysis of this calculus; arithmetization of this analysis. Each of these stades parallels the notion of developmental stage, and the main difference between these stages would be the level of conceptualization. It is concluded that the learning of analysis takes place through successive moments of taking the awareness process that culminate in conceptualization. This implies that to present axioms and establish properties and theorems from them does not consist of a potential teaching activity, except for those students who already have reached the cognitive level necessary to carry out these assimilations and, therefore, the answer was already in the subject before. For those who have not reached that level, it is necessary to act on mathematical objects so that, from this action, the process of taking awareness of the concerned actions may occur. The aim was to contribute to broadening the debate about mathematics education in higher education, favoring a democratization of learning mathematics at all levels, including the most formal ones.
DOI: 10.6084/m9.figshare.14304713
title: How do Teachers and Pre-service Teachers Interpret the Errors Made by Students when Solving Problems of Multiplicative Structure?

description: Abstract This study investigates how in-service and pre-service teachers interpret the errors made by students when solving problems of multiplicative structure. Participants were 12 pre-service and 12 Mathematics Elementary School teachers. In a semi-structured interview, each participant was presented six cards, each one containing a mathematical problem (three product of measures and three isomorphism of measures problems) which incorrect solutions should be interpreted. According to the participants, the errors were procedural, linguistic and conceptual in nature. Pre-service and in-service teachers considered the errors in the product of measures problems mostly as conceptual in nature, while errors in isomorphism of measures problems were mostly linguistic in nature. As the two groups showed the same pattern of quantitative results, was concluded that in Mathematics teaching, more than professional training and experience, the nature of the problem has a relevant role in the way that errors are interpreted.
DOI: 10.6084/m9.figshare.14304710
title: Cognitive Monitoring Practices in Mathematical Modeling Activities

description: Abstract This article refers to a research that aims to identify, about student manifestations while developing Mathematical Modeling activities, forms of cognitive monitoring and characterizing elements of Modeling activities that promote this monitoring of students. The data analyzed consist of students speeches saved into audio during the development of activities, of the produced records to do the resolutions and of the researcher's field diary notes. What can be concluded is that in Mathematical Modeling the monitoring practices are held collectively, are learned in the interactions among the different things involved with the activities and raised by them, in this article, we named as uniqueness of modeling activities, which refers to the constant practice of analyzing the development of the activity, considering it in its totality.
DOI: 10.6084/m9.figshare.14304709
title: THE INSTITUTIONAL DIDACTIC PHENOMENON OF RIGIDITY AND THE ATOMIZATION OF SCHOOL MATHEMATICS ORGANIZATIONS

description: In this research, we studied a complex didactic phenomenon manifested on the disconnection of mathematical contents that constitute the official program of secondary education and that relates strongly to the rigidity and atomization of school mathematics. For this study, we used the theoretical and methodological tools that the Anthropological Theory of Didactic (ATD) provides us, which primary object of research is the analysis of the institutional school mathematics activity. Thus, we carry out exploratory studies in mathematics textbooks in Portugal and Spain secondary education, contrasting and proving five conjectures related, for example, with the absence of questioning and justification of the used techniques. We conclude that in these countries, the mathematical praxeologies are often disjointed, rigid and, consequently, there are isolated activities of mathematical modelling in educational institutions.