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All Journal Union: Jurnal Ilmiah Pendidikan Matematika Indonesian Journal of Mathematics Education
José Antonio Juárez-López
Benemérita Universidad Autónoma de Puebla
Education Mathematics

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Exploring a Mathematics Teacher’s Conceptions of Infinity: The Case of Louise Irving Aaron Diaz-Espinoza; José Antonio Juárez-López; Estela Juárez-Ruiz
Indonesian Journal of Mathematics Education Vol. 6 No. 1 (2023): Indonesian Journal of Mathematics Education
Publisher : Universitas Tidar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31002/ijome.v6i1.560

Abstract

Several papers studied infinity from the difficulties that students and teachers show in developing the concept. For this study, it was considered the analysis of the equality 0.999 … = 1. Mainly, this research aims to show that a mathematics teacher presents erroneous conceptions just like a student; that is, both students and teachers have the same difficulties in the concept of infinity. To this aim, a semi-structured interview was conducted with an in-service mathematics teacher in Tlaxcala, Mexico. The purpose of this research is to exhibit a high school math teacher’s misconceptions about the concept of infinity. In general, misconceptions found here can be divided into four groups: without a clear picture of the concept of infinity, an infinite periodic decimal number cannot be a representation of a finite number, a decreasing infinite sum cannot lead to a finite number and an infinite process is limited in real life is finite and has ended. The results obtained were compared with those already available in references about the difficulties with students and teachers, finding that the results shown here are like those reported in the literature. This highlights the need to overcome the teacher’s conceptions of infinity in future research.
Konsepsi guru matematika tentang ketidakterbatasan: studi pendahuluan di tingkat sekolah menengah dan atas Irving Aarón Díaz-Espinoza; José Antonio Juárez-López
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.
Mathematics teachers’ conceptions about infinity: A preliminary study at the secondary and high school level Irving Aarón Díaz-Espinoza; José Antonio Juárez-López
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.
Pertimbangan realistis dan non-realistis dalam soal cerita matematika dengan siswa kelas delapan Meksiko Karol Mayreni Martínez-Meléndez; José Antonio Juárez-López; Irving Aarón Díaz-Espinoza
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.
Co-Authors Estela Juárez-Ruiz Irving Aaron Diaz-Espinoza Karol Mayreni Martínez-Meléndez