Journal of Hunan University Natural Sciences

This study delves into the crucial role of metaphors in classroom communication and their impact on student learning. It followed three goals. The first was to analyze the presence of metaphorical language in teaching abstract mathematical concepts within the context of seventh-grade classes at the Pablo Sexto Educational Institution in Dosquebradas, Colombia. This objective aims to identify the type of metaphors used in the classroom language of the teacher to facilitate comprehension of abstract concepts and to understand how these metaphors influence the students’ understanding of such concepts. The second objective was to evaluate the impact of using metaphorical language on the students’ understanding of the irrational number concept. This involves examining how the teacher’s metaphoric phrases affect the understanding and retention of abstract mathematical concepts, as well as identifying their strengths and weaknesses. Third goal seeks to establish links between the presence or absence of metaphors and students’ perceptions of their own understanding, considering whether metaphorical language contributes or hinders the conceptual clarity of mathematical content. Employing qualitative research tools, the study revealed a noteworthy presence of metaphors in the teachers’ discourse. This study stands as a promising starting point for future research endeavors in this field, while concurrently serving as a valuable tool to enhance teaching practices in mathematics education. Armed with an awareness of how metaphors can shape students’ comprehension, teachers can optimize their educational approaches and thereby contribute to their students’ academic accomplishments. In conclusion, this study emphasizes the paramount importance of metaphors in educational communication and their pivotal role in shaping the teaching and learning processes. By diligently considering the influence of metaphors on students’ understanding, educators can refine their pedagogical practices and make a profound contribution to their students’ academic achievements, not only in mathematics but also in various academic disciplines.

Keywords: conceptual metaphor, incidence of language, metaphorical language, teaching irrational numbers.

https://doi.org/10.55463/issn.1674-2974.50.7.21

This unique research in our region presents the findings of a qualitative research study aimed at determining the didactic contributions in the creation of a dynamic hypermedia aid (DHA) for teaching the sine theorem. To achieve this, a pedagogical design was devised to guide the creation of the DHA, based on a conceptual map outlining its structure, as well as the development and integration of digital resources. Subsequently, a teaching sequence was designed and implemented, incorporating the DHA and its associated resources. This sequence was conducted with 10th-grade students at a school in Pereira (Risaralda). The results revealed that the creation and use of the DHA enabled educators to propose alternative instructional frameworks, complementing specialized mathematical knowledge with technological and pedagogical proficiency in using information and communication technologies (ICT). Consequently, the students discovered novel methods of learning and problem-solving. The implementation of the DHA offered educators fresh opportunities and dynamics to engage with students, fostering exchanges of ideas related to the sine theorem.

Keywords: dynamic hypermedia aid, didactic contributions, pedagogical design, information and communication technologies, sine theorem, teaching resources.

https://doi.org/10.55463/issn.1674-2974.50.7.20

This qualitative study explores the impact of a didactic sequence based on the theory of didactic situations on the learning of the van der Pol equation and its solution using the Haar wavelet method among undergraduate students in Mathematics and Physics at the Technological University of Pereira. The study objectives focus on identifying students’ strengths and challenges, assessing collaborative and individual competencies, and evaluating proficiency in applying the Haar wavelet method to solve the equation. A sample of five students actively participated in all phases of the Didactic Situation, which included action, formulation, validation, and institutionalization. The results indicate that the carefully structured didactic sequence significantly improved students’ understanding and engagement with the van der Pol equation and Haar wavelet method. The inclusion of real-world applications and interactive approaches facilitated effective learning strategies. Overall, this study highlights the effectiveness of the theory of didactic situations-based didactic sequence in fostering a deeper appreciation and comprehension of complex mathematical concepts among Mathematics and Physics undergraduates. This research contributes to the enrichment of the academic journey, creating a captivating realm of mathematical beauty and scientific wonder for both students and educators.

Keywords: didactic sequence, the van der Pol equation, the Haar wavelet method, problem-solving.

https://doi.org/10.55463/issn.1674-2974.50.7.19

This study aims to strengthen critical thinking in future engineers through mathematics by stimulating their attitudes. To achieve this, a qualitative informative study will be conducted with a characteristic cut and a deductive orientation through the analysis and synthesis of contents from scientific publications specializing in the development of critical thinking. This type of thinking can be strengthened through strategies proposed by the mathematics teacher, allowing an increase in curiosity, eagerness to learn and inquire, and especially promoting and awakening curiosity in students through contexts where mathematics is formally applied in engineering. These strategies should include concrete actions that foster attitudes of critical thinking and a better ability to argue, interpret, and make judgments independently, ultimately acquiring a set of skills, especially in problem-solving. The results show that an engineering student as a critical thinker must have a critical attitude, which is evidenced through dispositions, habits, and character traits, which, when stimulated through mathematics, would contribute to their professional formation.

Keywords: disposition, education, habit, problem-solving.

https://doi.org/10.55463/issn.1674-2974.50.7.18

This study explores the pedagogical benefits of integrating Massive Open Online Courses (MOOCs) in teaching the sine function within a specific educational setting. Drawing on a comprehensive approach, this study combines socio-constructivist principles with theories of autonomous, collaborative, and problem-based learning, along with Van Hiele’s levels theory. At the heart of the investigation lies the meticulous design and implementation of a MOOC as a pivotal element in the didactic sequence, all conducted within a virtual learning environment. To assess its effectiveness, classroom sessions were closely observed and analyzed through the lenses of prominent teaching theories such as technological pedagogical content knowledge (TPACK), mathematical knowledge for teaching (MKT), and Knowledge Quartet (QK). The findings underscore the remarkable potential of leveraging MOOCs to foster a deeper understanding and practical application of the sine function, thereby enriching the overall learning experience. By providing students with accessible and flexible learning opportunities, this approach enhances engagement and encourages active participation. The integration of MOOCs empowers students to take ownership of their learning journey while benefiting from collaborative and problem-solving activities. Ultimately, this research sheds light on the valuable contributions that MOOCs can make to mathematics education, revolutionizing the traditional teaching paradigm and paving the way for more inclusive and effective learning environments.

Keywords: Massive Open Online Courses, socio-constructivism, Van Hiele, autonomous learning, collaborative learning, problem-based learning, technological pedagogical content knowledge, mathematical knowledge for teaching, Knowledge Quartet.

https://doi.org/10.55463/issn.1674-2974.50.7.17