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The concept of variable and the 3UV model: A literature review Castro-Fernández, Felipe; Lop-Herrera, Reinier; Juárez-López, José Antonio
Journal of Didactic Mathematics Vol 5, No 1 (2024): April
Publisher : Mahesa Research Center

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34007/jdm.v5i1.2105

Based on a literature review covering the time period 2005-2023, the objective of this article is to present the research trends on the concept of variable and the contributions for its study made through the theoretical framework called Model of the Three Uses of the Variable (Model 3UV). For this reason, a documentary research design was developed with a qualitative approach and at a descriptive level. The instruments for the collection and analysis of information were a search log, a bibliographic matrix, and a synthesis matrix, elaborated in the Excel software. The technique used to carry out the documentary review was the content analysis, from the deductive analytical categories: objective, research method and conclusion. The advanced search was carried out in Academic Google and of the total results obtained, the 10 most relevant articles published during the period 2005-2023 were selected. One of the main findings found was the identification of three trends in research with Model 3UV: the first, related to teaching proposals; the second, concerning the understanding of difficulties in the learning of students; and the third, concerning teaching materials.

Classification of figures in primary school based on van Hiele’s model: Report of two cases De León-Zamora, Wendy Loraine; Juárez-López, José Antonio; Juárez-Ruiz, Estela de Lourdes
Unnes Journal of Mathematics Education Vol 12 No 2 (2023): Unnes Journal of Mathematics Education
Publisher : Department of Mathematics, Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujme.v12i2.66357

In this paper, the results of an investigation based on an activity on the recognition of geometric shapes are reported, where different figures were presented that must be classified in order to identify the level of reasoning of each student. The present investigation follows a qualitative method and the data collection was carried out through clinical interviews applied to two children, an 8-year-old boy and a 10-year-old girl, who at that time were in the third and fourth grades of primary school respectively, in the State of Puebla, Mexico. Among the main results, it stands out that both children were located at level 0 of reasoning according to van Hiele's classification, since they recognize geometric shapes by their physical appearance, not by their properties and relationships.

The teaching-learning process of the continuity of real variable functions: A literature review Maxil-Cardoso, G. Elizabeth; Castro-Fernández, Felipe; Juárez-Lopez, José Antonio
Journal of Didactic Mathematics Vol 5, No 3 (2024): December
Publisher : Mahesa Research Center

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34007/jdm.v5i3.2329

This article´s objective is to present the current state of research on the teaching-learning process of continuity of real variable functions. To achieve this, a documentary research design with a qualitative approach and a descriptive depth level was adopted. The instruments for data collection and analysis included a search log, a bibliographic matrix, and a synthesis matrix, created using Excel software. The technique used for the literature review was qualitative content analysis, based on deductive analytical categories: objective, theoretical framework, research method, and conclusions. Advanced searches were conducted on Google Scholar, on Scopus and Web of Science and out of the total results found, 13 relevant articles published during the period 2020-2023 were selected. Among the main findings, the use of a variety of theoretical frameworks in the foundation of the analysed studies was identified, such as the theory of semiotic representations, the MTSK model, the TPACK, and the conceptual contributions of Tall and Vinner, among others. Additionally, a growing interest in the use of technological tools, such as GeoGebra, to enhance the teaching and learning process of mathematics in general, and the continuity functions in particular. Although its limitations, it was identified that this software can be used as a tool for visualization, construction, representation and communication of mathematical knowledge.

EXPLORING DIFFICULTIES IN TEXTUAL UNDERSTANDING OF MATHEMATICAL WORD PROBLEMS FROM A PSYCHOLINGUISTIC PERSPECTIVE AND USE OF DRAWINGS Reyes-Huerta, Valentín; Juárez-López, José Antonio; Iglecias-Antonio, Reynaldo
IJIET (International Journal of Indonesian Education and Teaching) Vol 8, No 2 (2024): July 2024
Publisher : Sanata Dharma University Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24071/ijiet.v8i2.8161

Several studies have reported the importance of textual understanding in the solving of verbal mathematical problems. Therefore, the objective of the present study was to analyze the difficulties the secondary-education students presented in the textual understanding of verbal mathematical problems. An instrument was applied with three verbal problems in three different moments: comprehension of the problem, representation of the situation, and the application of a semi-structured interview. An important factor that could be seen in the responses obtained is that the context played an essential role. It was also obtained that the textual understanding and the cultural context show an important relationship when building a representation of the problem. Finally, according to the results obtained in the study, we suggest that it would be important to encourage students to do previous work to familiarize themselves with the context posed in the problem to be able to reach a solution that satisfies the statement.

Pertimbangan realistis dan non-realistis dalam soal cerita matematika dengan siswa kelas delapan Meksiko Martínez-Meléndez, Karol Mayreni; Juárez-López, José Antonio; Díaz-Espinoza, Irving Aarón
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 13 No 1 (2025)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v13i1.18651

The present exploratory study with a qualitative approach had the objective of analyzing the type of realistic and unrealistic responses, as well as the considerations of the real-world environment in second grade high school students in Mexico in the resolution of mathematical verbal problems. To this end, students were presented with several realistic and pseudorealistic verbal problems of proportionality, false proportionality, division with remainder and arithmetic operations. Two data collection instruments were created: a verbal problem sheet and a questionnaire. The responses were classified as realistic, unrealistic, and other responses. This research showed that some of the students conceived realism in the answers based on the interpretation they were able to make of the context of the problem. That is, they took realism into account in their solution, through comments or arguments from their own experiences, by analyzing their mathematical answers to link them with the existing knowledge they have of the real world. The study contributes to the understanding of how students’ cultural background and everyday life experiences influence their approach to mathematical problem-solving, highlighting the importance of context in shaping students’ problem-solving strategies. This finding emphasizes the need for educators to recognize the value of incorporating realistic contexts in mathematical instruction to enhance students’ engagement and understanding.

Promoting conceptual change regarding infinity in high school mathematics teachers through a workshop Díaz-Espinoza, Irving Aarón; Juárez-López, José Antonio; Miranda, Isaías
Journal on Mathematics Education Vol. 15 No. 2 (2024): Journal on Mathematics Education
Publisher : Universitas Sriwijaya in collaboration with Indonesian Mathematical Society (IndoMS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jme.v15i2.pp473-494

This report delineates the outcomes of an intervention conducted with in-service high school educators, focusing on elucidating three distinct scenarios within geometric and arithmetic domains: the infinitely large, infinitely numerous, and infinitesimally close. Grounded in the theoretical framework of conceptual change, it is posited that when an individual exhibits entrenched conceptions, it signifies a misclassification of the pertinent concept, necessitating a categorical shift to effectuate a transformation in their cognitive schema, particularly concerning the notion of infinity. Thus, the principal objective of this investigation was to ameliorate the entrenched conceptions held by educators pertaining to infinity through a workshop-based intervention. Preceding the workshop, educators predominantly exhibited conceptions aligned with natural and potential infinities. However, after the workshop, a discernible transition was observed, with educators engendering an actual conception of infinity or an omega-epsilon position, exemplified by their acceptance of equivalences such as 0.999…=1 and the parity in the cardinality of sets comprising natural numbers, even numbers, and perfect squares. Nonetheless, notwithstanding this progress, confident educators evinced resistance to embracing the concept of actual infinity, particularly in instances such as the hypothetical scenario depicted in Hilbert's Grand Hotel. Consequently, drawing upon the framework of conceptual change theory, it can be postulated that a complete categorical shift was not universally realized among educators due to their reluctance to revise entrenched beliefs concerning natural or potential infinity.

Pertimbangan realistis dan non-realistis dalam soal cerita matematika dengan siswa kelas delapan Meksiko Martínez-Meléndez, Karol Mayreni; Juárez-López, José Antonio; Díaz-Espinoza, Irving Aarón
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 13 No 1 (2025)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v13i1.18651

The present exploratory study with a qualitative approach had the objective of analyzing the type of realistic and unrealistic responses, as well as the considerations of the real-world environment in second grade high school students in Mexico in the resolution of mathematical verbal problems. To this end, students were presented with several realistic and pseudorealistic verbal problems of proportionality, false proportionality, division with remainder and arithmetic operations. Two data collection instruments were created: a verbal problem sheet and a questionnaire. The responses were classified as realistic, unrealistic, and other responses. This research showed that some of the students conceived realism in the answers based on the interpretation they were able to make of the context of the problem. That is, they took realism into account in their solution, through comments or arguments from their own experiences, by analyzing their mathematical answers to link them with the existing knowledge they have of the real world. The study contributes to the understanding of how students’ cultural background and everyday life experiences influence their approach to mathematical problem-solving, highlighting the importance of context in shaping students’ problem-solving strategies. This finding emphasizes the need for educators to recognize the value of incorporating realistic contexts in mathematical instruction to enhance students’ engagement and understanding.

The Impact of augmented reality on the learning of polyhedral: an approach based on didactical engineering and instrumental genesis Sies, Alberto Apreza; Román, Guillermina Sánchez; Juárez-López, José Antonio
Polyhedron International Journal in Mathematics Education Vol. 3 No. 2 (2025): pijme
Publisher : Nashir Al-Kutub Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59965/pijme.v3i2.263

Despite the relevance of spatial skills in mathematics education, upper-secondary students face persistent difficulties, especially in the manipulation and conceptual understanding of three-dimensional objects. This study aims to design, implement, and analyze a didactic sequence mediated by Augmented Reality (AR) for the learning of polyhedral. The novelty lies in the analysis of the underlying cognitive processes through the framework of Instrumental Genesis, basing the design on the principles of Didactic Engineering. The research adopts a mixed-method and quasi-experimental approach. A pre-test and post-test were administered to a sample of fourth-semester upper-secondary students (n=12), complemented by an exhaustive qualitative analysis of the interaction with the GeoGebra 3D AR tool. Pre-test findings confirmed student weaknesses, showing only 25% success on measurement and dimensioning tasks. The post-intervention analysis demonstrated a significant and positive impact of the didactic sequence, evidenced by the total adaptation and instrumentalization of the AR tool. This resulted in a favorable evolution of cognitive schemes and a noticeable improvement in spatial visualization skills. The findings suggest that successful technological integration in 3D geometry must be guided by rigorous theoretical design and a detailed analysis of knowledge construction mediated by the instrument, providing empirical evidence for the implementation of AR in the mathematics classroom.

Mathematics teachers’ conceptions about infinity: A preliminary study at the secondary and high school level Díaz-Espinoza, Irving Aarón; Juárez-López, José Antonio
UNION : Jurnal Ilmiah Pendidikan Matematika Vol 11 No 3 (2023)
Publisher : Universitas Sarjanawiyata Tamansiswa

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30738/union.v11i3.16006

The literature indicates that students consistently exhibit limited conceptions of infinity in various contexts. Furthermore, it is more resistant in geometric than arithmetic contexts. On the other hand, there is a smaller amount of literature that explores teachers' conceptions and how these conceptions may be similar to those of their students. Therefore, this work presents the results obtained from applying a five-item instrument with secondary and high school mathematics teachers who are in public or private service in the state of Puebla, Mexico. This study had a dual purpose: to show that teachers also possess limited conceptions of infinity, as students do, thereby expanding the existing literature on this topic; and secondly, to emphasize that the results shown here will enable subsequent work to design an intervention for a profound conceptual change regarding infinity among teachers.

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