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All Journal Union: Jurnal Ilmiah Pendidikan Matematika Journal on Mathematics Education
Díaz-Espinoza, Irving Aarón
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Education Mathematics Social Sciences Other

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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

Abstract

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

Abstract

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

Abstract

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.
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

Abstract

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.
Co-Authors Juárez-López, José Antonio Martínez-Meléndez, Karol Mayreni Miranda, Isaías