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Effective strategies for formulating and articulating a well-defined research problem: context in the field of mathematics education Rodríguez-Nieto, Camilo Andrés; Rodríguez-Vásquez, Flor Monserrat; Cantillo-Rudas, Benilda María; Font Moll, Vicenç; Sudirman, Sudirman
International Journal of Didactic Mathematics in Distance Education Vol. 2 No. 1 (2025): ijdmde
Publisher : LPPM Universitas Terbuka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33830/ijdmde.v2i1.10344

This research offers an answer to the question: How to pose and write a research problem in Mathematics Education? To do so, a qualitative descriptive methodology was implemented, developed in four stages: first, it presents a general overview of the Theories in Mathematics Education and some articles where relevant studies have been reported; in the second stage, the means by which research can be disseminated or published are presented; in the third, meanings and ways to pose a research problem are shown and, finally, in the fourth stage, some theoretical reflections on the problem statement are presented. The results show that the writing and statement of the problem does not necessarily follow a structure, that depends on the type of research and the way in which the author reports his ideas or in which theoretical framework he frames his work, for example, research questions from the Onto-semiotic Approach and the Extended Theory of Connections are presented. However, a special path is suggested that has worked very well to be implemented in future research. In conclusion, for research to be successful, the problem and the issue must be well constructed and supported by the literature, which guides and invites reflection on the choice of theory (if possible), the methodology and the presentation of the results that can be theoretical and practical.

The potential of ethnomathematical and mathematical connections in the pre-service mathematics teachers’ meaningful learning when problems-solving about brick-making Rodríguez-Nieto, Camilo Andrés; Pabón-Navarro, María Luisa; Cantillo-Rudas, Benilda María; Sudirman; Font Moll, Vicenç
Jurnal Infinity Vol 14 No 2 (2025): VOLUME 14, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i2.p419-444

This research explores the potential of ethnomathematical and mathematical connections in fostering meaningful learning through problem-solving in brick-making. Despite the importance of such connections in mathematics education, students often struggle with contextualized verbal problems related to daily life. A qualitative ethnographic methodology involved a workshop divided into three stages. Fourteen pre-service mathematics teachers in northern Colombia enrolled in an ethnomathematics course participated. Participant observation was used during the workshop to document how students solved problems and engaged with the material. Data analysis was guided by the Extended Theory of Connections and the Onto-semiotic Approach. The study examined the mathematics emerging from brick production, focusing on problems involving area, volume, and proportional reasoning. Ethnomathematical connections were emphasized, providing a foundation for pre-service teachers to solve problems related to the area and volume of bricks. Various mathematical connections were identified, such as representation, procedural understanding, meaning, and modelling. The research concluded with feedback from researchers, highlighting the educational potential of integrating mathematics with real-world tasks like brick-making. This study provides valuable insights for pre-service teachers in designing contextualized, meaningful math problems.

Exploring neuro-mathematical connections in the resolution of a contextualized geometric problem Cantillo-Rudas, Benilda Maria
International Journal of Didactic Mathematics in Distance Education Vol. 2 No. 1 (2025): ijdmde
Publisher : LPPM Universitas Terbuka

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.33830/ijdmde.v2i1.11821

This study aims to explore the neuro-mathematical connections activated by high school and university students when solving a contextualized geometric problem. The urgency of this research lies in the need to deepen our understanding of the cognitive and neurological processes involved in mathematical problem-solving, particularly in spatial reasoning tasks. The theoretical framework combines Connections Theory and the Onto-semiotic Approach, focusing on the typology of neuro-mathematical connections. The qualitative, descriptive methodology was carried out in three phases: (1) selection of volunteer participants from high school and university levels; (2) data collection through the application of a geometric problem involving the volume of two boxes, with video recordings capturing students’ problem-solving processes; and (3) analysis using the theoretical framework to identify and interpret the neuro-mathematical connections activated during the task. The results revealed a rich network of cognitive processes encompassing mathematical practices, objects, processes, and semiotic functions. Specifically, students demonstrated: recognition of mathematical terms and symbols; activation of visual perception, spatial reasoning, and motor coordination; association of concepts and formulas; execution of intermediate calculations and unit conversions; sequential problem-solving; and reflective verification of results. These findings support the claim of the Extended Theory of Connections that connections are inherently cognitive processes. This research contributes to the field of mathematics education and cognitive science by providing an in-depth analysis of how students engage with mathematical problems through neuro-mathematical pathways. Future research should expand this work by incorporating neuroimaging or eye-tracking technologies to further validate and visualize the cognitive mechanisms underlying mathematical reasoning.

The potential of ethnomathematical and mathematical connections in the pre-service mathematics teachers’ meaningful learning when problems-solving about brick-making Rodríguez-Nieto, Camilo Andrés; Pabón-Navarro, María Luisa; Cantillo-Rudas, Benilda María; Sudirman; Font Moll, Vicenç
Jurnal Infinity Vol 14 No 2 (2025): VOLUME 14, NUMBER 2, INFINITY
Publisher : IKIP Siliwangi and I-MES

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22460/infinity.v14i2.p419-444

This research explores the potential of ethnomathematical and mathematical connections in fostering meaningful learning through problem-solving in brick-making. Despite the importance of such connections in mathematics education, students often struggle with contextualized verbal problems related to daily life. A qualitative ethnographic methodology involved a workshop divided into three stages. Fourteen pre-service mathematics teachers in northern Colombia enrolled in an ethnomathematics course participated. Participant observation was used during the workshop to document how students solved problems and engaged with the material. Data analysis was guided by the Extended Theory of Connections and the Onto-semiotic Approach. The study examined the mathematics emerging from brick production, focusing on problems involving area, volume, and proportional reasoning. Ethnomathematical connections were emphasized, providing a foundation for pre-service teachers to solve problems related to the area and volume of bricks. Various mathematical connections were identified, such as representation, procedural understanding, meaning, and modelling. The research concluded with feedback from researchers, highlighting the educational potential of integrating mathematics with real-world tasks like brick-making. This study provides valuable insights for pre-service teachers in designing contextualized, meaningful math problems.

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