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Visualization and argumentation are central processes in the learning of geometry, giving rise to specific lines of research in mathematics education. However, it is worth asking whether they should be developed independently or if it is possible and in what way an articulation between them can be promoted. The objective of this paper is to search for this articulation within the most recent advances in empirical research on the teaching and learning of geometry in Spain. The analysis is approached through the tasks used in research employing two theoretical frameworks which have been developed in Spain, the Onto-Semiotic Approach and Configurational Reasoning. Two main types of task were found in the selected studies: visual tasks and conjecture-and-proof tasks. The results show that in visual tasks the articulation between visualization and argumentation is only necessary in some tasks, in which argumentation aims to justify or to describe the external representation provided as a solution. However, in conjecture-and-proof tasks the articulation between visualization and argumentation must always be present to resolve the task. Analyzing this articulation helps to detect and gain a better understanding of the difficulties that students encounter in solving these types of task. In visual tasks, argumentation helps to understand difficulties associated with the use of visualization. In conjecture-and-proof tasks, visualization determines the argumentation followed, in such a way that many of the difficulties originate more from the visualization than from the process of argumentation. [ABSTRACT FROM AUTHOR]

Research in mathematics education can be understood as a system of activities addressing the basic and applied problems related to teaching and learning of mathematics. Such a system includes the activities of foundation, planning, implementation, evaluation of mathematics instruction, and teacher professional development, which are supported by different theories. This diversity of theories raises interest in their comparison, coordination, and possible integration. The paper aims to present a case of application of the Cultural Historical Activity Theory (CHAT), in its 3rd and 4th generation versions, to analyze the emergence of the Onto-semiotic Approach to mathematical knowledge and instruction as a theoretical framework that addresses the study of the five partial activities mentioned above. This use of the CHAT can be useful in studies on theory articulation by focusing not only on the subjects, the object, and the instruments but also on the community context, the ecological-normative environment in which these activities take place, and the dilemmas or contradictions between theories. [ABSTRACT FROM AUTHOR]

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students' geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the Euclidean geometry context. For this, we designed and implemented two mathematical tasks with 52 secondary education students (15–16 years old, 10th grade) during the COVID-19 emergency lockdown period in Italy. The tasks involved four phases: constructing, exploring, conjecturing, and proving. This article presents an epistemic analysis of the tasks and a cognitive analysis of the answers given by one of the students. The theoretical tools of the onto-semiotic approach supported these analyses. Cognitive analysis allows us to confront the intended meanings of the task and the meanings actually employed by a student, thus drawing specific conclusions about the roles of such artifacts in written arguments and give an interpretation of their combined use in mathematics education. [ABSTRACT FROM AUTHOR]

The development of algebraic reasoning from the earliest educational levels is an objective that has solid support both from the point of view of research and curricular development. Effectively incorporating algebraic content to enrich mathematical activity in schools requires considering the different degrees of generality of the objects and processes involved in algebraic practices. In this article, we present an expanded version of the model of levels of algebraization proposed within the framework of the onto-semiotic approach, establishing sublevels that provide a more microscopic view of the structures involved and the processes of generalization, representation, and analytical calculation at stake. We exemplify the model with mathematical activities that can be approached from primary education, classified according to the different sublevels of algebraization. The use of this expanded model can facilitate the development of didacticmathematical knowledge of teachers in training on algebraic reasoning and its teaching. [ABSTRACT FROM AUTHOR]

The mathematical connections Colombian engineering students activated when they solved vector problems were explored. The study was based on the extended theory of connections and the onto-semiotic approach. We followed a qualitative methodology that consisted of three stages: (1) selection of engineering students as participants; (2) application of a questionnaire with 15 tasks on vectors to the participating students; and (3) analysis of these data based on the theoretical articulation. The results show that students perform arithmetic operations with vectors, find the scalar and vector product, the norm of a vector, the angle between vectors, and unit vector based on mathematical connections (procedural, meaning, different representations, and implication), detail from an onto-semiotic point of view. However, some students have difficulty finding the angle between vectors because they misuse the norm. Furthermore, the new metaphorical connection based on mnemonics activated by the “law of the ear” is reported. The connections activated by engineering students to solve problems about vectors may have been influenced by the explanations provided by their calculus teacher, who promotes connections for the teaching and learning mathematical concepts. [ABSTRACT FROM AUTHOR]

Copyright of Avances de Investigación en Educación Matemática is the property of Sociedad Espanola de Investigacion en Educacion Matematica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Literature review in Mathematics Education on connections makes evident the necessity of delving into extra-mathematical connections. In this line, we answer the question: What types of mathematical connections are required to develop the modelling process? To this end, we consider three theoretical references: Onto-Semiotic Approach, Extended Theory of Connections, and Mathematical Modelling Cycle from a Cognitive Perspective, following a methodology used in two theoretical articulations previously developed by the authors between these frameworks, based on the use of models for the analysis of mathematical activity proposed by the Onto-Semiotic Approach for connections and the modelling process. The results of this analysis consist of, on one hand, the evidence of the types of intra- and extra-mathematical connections intervening in the different phases of the modelling cycle and, on the other hand, the proposal of a more detailed classification of mathematical connections.

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the Onto-semiotic Approach. The methodology was qualitative-descriptive where data was collected through interviews based on a task. Subsequently, following the joint analysis method of both theories, the mathematical activity of the participants when they solved the task was analyzed. The results show that, teacher and students established a system of connections of feature type, different representations, meanings, part-whole, procedural and implications in terms of practices, processes, objects, and semiotic functions that relate them. However, some students presented difficulties caused by some incorrect mathematical connection such as stating that the maximum height of the projectile is the time obtained with the critical number, errors in performing arithmetic calculations when evaluating the function, graphically representing the quadratic function as a straight line and use the general formula in an inappropriate way that prevents the procedural connection from being made.

Representations are key to mathematical activities and meaning-making processes as they are part of modeling, connecting, communicating, and understanding mathematical ideas and concepts. The current study sought to examine a group of novice algebra learners' interactions with different representations from an onto-semiotic approach. A case study method was employed to understand how different algebraic practices (abstracting, generalizing, justifying, and operating on symbols) and functional thinking types (recursive, covariational, and correspondence) were facilitated through working with multiple representations. Three 6th graders participated in the study by completing 12 algebra tasks and taking part in two interviews. The onto-semiotic approach guided the data analysis process that involved the identification of mathematical objects that emerged in the participating students' mathematical practices. Then, the configuration of objects and semiotic functions established by the students in the functional situations was examined to understand the role of representations in the students' development of algebraic thinking and practices. Findings showed that abstraction is an essential process for generalization. Thinking about far figures facilitated abstraction and generalization through helping students construct non-ostensive concrete/pictorial representations. Verbal representations interacted with all representations and preceded symbolic representations. Working with near figures promoted recursive and covariational thinking while examining the far figures usually resulted in correspondence thinking. Implications for the school curriculum are discussed in the paper. [ABSTRACT FROM AUTHOR]

The literature reports that students have difficulties connecting different meanings, multiple representations of the derivative, and performing reversibility processes between representations of f and f'. The research goal is to analyze the mathematical connections that university students establish when solving tasks that involve the graphs of f and f' when the two functions do not have associated symbolic expressions. Seven students from the first year of undergraduate studies in mathematics from a university in southern Mexico participated. For data collection, two tasks involving the graphical context of the derivative were applied. An analysis of the mathematical activity was carried out by the participants with the analysis model proposed by the onto-semiotic approach, and thematic analysis with types of mathematical connections from the extended theory of connections was carried out to infer the connections made in that mathematical activity, which allowed us to consider the reversibility connection between the graphs of f and f' as the encapsulation of a portion of the mathematical activity. Four students establish the reversibility relationship between the graph of f and the graph of f'. It has been concluded that some students can establish the reversibility connection between the graphs of f and f', but the complexity of the mathematical activity that encapsulates the connection explains (by showing everything that the student must do) why some students are not able to establish it. [ABSTRACT FROM AUTHOR]

The theoretical reflection on the nature of school algebra and the development of algebraic thinking from the first educational levels is a relevant topic in mathematics education. In this paper, we first summarize and clarify the positions held on this topic by two theoretical frameworks: the Theory of Objectification and the Onto-semiotic Approach. We identify concordances and complementarities in the respective conceptions of algebra and of the processes of developing algebraic thinking, as a result of applying these frameworks to analyse some students' responses to a task on numerical patterns. We also analyse and compare the didactic models proposed in both theoretical frameworks for developing algebraic thinking. The analysis of the algebraic thinking and learning episodes is also used to illustrate a general discussion on the identity and boundaries of these theoretical frameworks and the possibilities of coordination and integration. [ABSTRACT FROM AUTHOR]

Copyright of Profesorado: Revista de Currículum y Formación del Profesorado is the property of Profesorado: Revista de Curriculum y Formacion del Profesorado and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Characterizing and measuring the quality of instruction is a matter of growing interest in mathematics education. Based on the notion of didactic suitability and the theoretical assumptions of the onto-semiotic approach, we develop an instrument to systematically analyze the different facets involved in a mathematics instruction process. We also explore the concordances and complementarities with instruments for measuring the quality of instruction. Thus, quantitative quality measurement efforts are complemented by another qualitative approach, focusing on the initiative and responsibility of teachers when they have to make decisions about their teaching practices. This reflective activity must be supported by specific instruments that reveal the complexity of the processes and the difficulty of achieving a balance between sometimes conflicting didactic principles. [ABSTRACT FROM AUTHOR]

Copyright of JMD: Journal für Mathematik-Didaktik is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Bordón: Journal of Education / Revista de Pedagogía is the property of Sociedad Espanola de Pedagogia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This article presents a networking of two theories, the Extended Theory of Mathematical Connections (ETC) and the Onto-semiotic Approach (OSA). In particular, concordances and complementarities are identified in the respective conceptions of mathematical connections, as a result of applying these theoretical frameworks to a student's response protocol when solving a task on the derivative. First the mathematical connections were identified from the perspective of the ETC and, second, an onto-semiotic analysis was carried out where the mathematical practices, the primary mathematical objects activated in them and the semiotic functions established between these objects were analysed. The main conclusion is that both theories complement each other to make a more detailed analysis of the mathematical connections. In particular, the more detailed analysis carried out with the OSA tools, visualizes a mathematical connection like the tip of an iceberg of a conglomerate of practices, processes, primary objects activated in these practices and semiotic functions that relate them, which enables a thorough analysis that details the structure and function of the connection. [ABSTRACT FROM AUTHOR]

Copyright of Alteridad: Revista de Educación is the property of Universidad Politecnica Salesiana and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Abstract: This research is conducted to obtain a description of students’ difficulties in understanding and applying Pythagorean theorem based on the onto-semiotic approach. This research applies a qualitative approach with phenomenology interpretation design. Research data were collected using test and interview methods. The research result was deducted from students' answer sheets and interviews. Participants involved in this study were as many as 25 students of UPI Lab School Junior High School Bandung, who had learned Pythagorean theorem, 4 of which also participated in the interview. It showed that students found it complicated to comprehend definition, describe symbols or notations of mathematical objects, and interpret mathematical objects. Meanwhile, in solving problems related to the application of the Pythagorean theorem, students could describe procedure, algorithm, and technique in solving questions well. Abstrak: Penelitian ini bertujuan untuk mendapatkan gambaran kesulitan siswa dalam memahami dan menerapkan Teorema Pythagoras menggunakan pendekatan onto-semiotika. Penelitian ini menggunakan pendekatan kualitatif dengan desain interpretasi fenomenologi. Metode pengumpulan data, yaitu tes dan wawancara. Partisipan penelitian yang dilibatkan dalam uji kemampuan siswa adalah 25 orang siswa SMP Lab School UPI Bandung yang pernah belajar materi teorema Pythagoras, 4 orang dari 25 orang siswa tersebut dilibatkan dalam wawancara. Hasil penelitian menunjukkan bahwa siswa mengalami kesulitan dalam memahami definisi, mendeskripsikan simbol atau notasi dari objek matematika, serta kesulitan dalam memaknai objek matematika, sedangkan dalam menyelesaikan permasalahan penerapan teorema Pythagoras, siswa mampu mendeskripsikan prosedur, algoritma, dan teknik penyelesaikan masalah dengan baik.

TRAINING ON THE IMPLEMENTATION OF ONTO-SEMIOTIC APPROACH IN CLASS LEARNING FOR TEACHERS AT JUNIOR HIGH SCHOOL AL-BAHJAH TULUNGAGUNG. The purpose of this community service activity is the teachers training by implementing an onto-semiotic approach in classroom learning and produce a lesson plan. This activity done at Junior High School Al-Bahjah Tulungagung. The participants are teachers in Junior High School Al-Bahjah Tulungagung. The method used is theory method and practice. The results obtained throught this training are knowldge of innovative learning with an onto-semiotic approach for teachers and their ability to create and implement the lesson plan with an onto-semiotic approach.

In this article, are presented the results of a questionnaire designed to evaluate college students’ understanding of the antiderivative. Specifically, by civil engineering students when answering the questionnaire tasks, in order to identify and characterize the meanings on the antiderivative that are developed by them. In order to analyse the answers given, were used some theoretical and methodological notions provided by the theoretical model known as the Onto-Semiotic Approach (OSA) of mathematics cognition and instruction. The results show the knowledge of antiderivative by the Civil Engineering students. Furthermore, the comparison between the mathematical activity of students provides information that allows concluding that the meanings that they mobilized might be shared among their communities

Copyright of Paradigma is the property of Universidad Pedagogica Experimental Libertador and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista Praxis & Saber is the property of Universidad Pedagogica y Tecnologica de Colombia and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A subject of growing interest in mathematics education is the affective domain and its effects on the teaching and learning processes, giving rise to different models of its components and conditioning factors. In this paper, we apply the ontological and semiotic categories from the Onto-Semiotic Approach (OSA) to research in mathematics education, to build an inclusive and systematic model to consider affective situations, practices, objects and processes, as well as the corresponding dualities: personal – institutional, ostensive – non-ostensive, extensive – intensive, unitary – systemic, expression – content. The dynamic character of affects (emotions, attitudes, beliefs and values) and their relations with the epistemic, cognitive, interactional and resources is modelled by the didactical configuration and didactical trajectory notions, theoretical tools which include the affective sub-configuration and sub-trajectory as key components. Another result obtained from this work is the revision of the indicators of affective suitability proposed in previous works. [ABSTRACT FROM AUTHOR]

The number of educational videos available on the internet on the most varied topics is rapidly increasing. These include mathematics videos that cover virtually any type of curriculum content. However, their quality as a learning resource varies greatly. As a result, it is necessary to provide teachers with tools to enable them to analyse the appropriateness of using educational videos, considering the various aspects involved. This paper describes the design, implementation and results of an educational intervention with 93 prospective primary school teachers, focussed on developing their ability to analyse the educational suitability of videos about proportionality. Preliminary analysis of the video revealed significant errors and inaccuracies in the definitions, propositions, and procedures, as well as shortcomings and inaccuracies in the arguments, and so its level of epistemic suitability is rated as medium. However, the majority of the prospective teachers rated its degree of suitability as high in almost all components. Students regard studying didactic suitability and implementing it through components and indicators as positive, believing that this activity facilitates professional reflection. However, mastering this tool requires analysing a greater number and variety of videos and further collective discussion of the results of the analyses performed by the students. [ABSTRACT FROM AUTHOR]

Copyright of Visión Electrónica is the property of Fondo de Universidad Distrital Francisco Jose de Caldas and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Comparing and networking theoretical frameworks is a topic treated by various authors and discussion forums, as a source of enrichment and starting point for advancing theory development. In this paper we present a study about this topic, establishing a relationship between ethnomathematics and the onto-semiotic approach (OSA) to mathematical knowledge and instruction. Ethnomathematics is a research program with a consolidated international presence that proposes an expanded vision of mathematics and mathematics education. The OSA is a theoretical framework, which is widespread and valued in the community of scholars in mathematics education. A reciprocal glance of both theoretical frameworks can provide mutual enrichment. Specifically the basic features and the paradigmatic issues addressed by both theoretical frameworks are presented and compared. Some commonalities and complementarities are also identified.

Copyright of Estudios Pedagogicos (Valdivia) is the property of Estudios Pedagogicos and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents a study of networking of theories between the theory of registers of semiotic representation (TRSR) and the onto-semiotic approach of mathematical cognition and instruction (OSA). The results obtained show complementarities between these two theoretical perspectives, which might allow more detailed analysis of the students' performance. [ABSTRACT FROM AUTHOR]

This paper presents a networking of two theories, the APOS Theory and the ontosemiotic approach (OSA), to compare and contrast how they conceptualize the notion of a mathematical object. As context of reflection, we designed an APOS genetic decomposition for the derivative and analyzed it from the point of view of OSA. Results of this study show some commonalities and some links between these theories and signal the complementary nature of their constructs. [ABSTRACT FROM AUTHOR]