The role of generating questions in mathematical modeling

Abstract

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process. Generating questions requires noticing the unknown and cognitive steps to elucidate the unknown and solve the problem. The process and outcome of generating questions were explored using an open-ended problem. This study demonstrates (1) the role in advancing mathematical modeling from various points of view, (2) the role of fostering mathematical modeling competencies, and (3) the role in facilitating the extension of the applicability of the mathematical model. Having established these roles, the principle of teaching and learning was constructed, which is expected to foster the ability to generate questions. This study demonstrates that, in mathematical modeling, generating questions is crucial for developing a clear sense of direction for modeling real-world problems. Furthermore, generating questions reflects on the structures of mathematical models, allowing the execution of the mathematical modeling process.

Bridging Gaps: Pre-Service Mathematics Teachers’ Handling the Difficulties in Posing Real-World Mathematical Problems

“…These problems involve specific criteria and can be interpreted in various ways, such as modelling problems, application problems, and contextualized problems (Brown, 2019;McGrane, 2020). Therefore, the teacher and preservice teacher must be able to solve and pose the real-world mathematical problems (also known as the modelling problem), which is a necessary tool to enhance students' mathematical learning in the present and future (Blum, 2015;Sevinc & Lesh, 2018;Fukushima, 2021;Brady, Ramírez, & Lesh, 2024). Although the preservice teachers' abilities to pose meaningful problems were impacted by the students' own abilities, research has shown that preservice teachers encountered difficulties when attempting to combine mathematical modeling and problem posing in the classroom, particularly when starting with real-world contexts.…”

descortinar da noção de situação em modelagem matemática escolar

“…Embora diferentes pesquisas sobre a MM, na perspectiva da Educação Matemática, apontem para dificuldades reveladas por alunos e professores em sala de aula, em particular, no estudo de problemas sobre contextos reais como encaminham Sodré e Guerra (2018), Sodré (2019) e Fukushima (2021), a literatura da área (Borromeo Ferri, 2006;Blum & Borromeo Ferri, 2009, Perrenet & Zwaneveld, 2012, Blum, 2015, Greefrath & Vorhölter, 2016, Vorhölter et al, 2019, Barquero & Jessen, 2020 propõe o uso do ciclo de MM como uma ferramenta didática para minimizar parte da complexidade provedora de dificuldades para alunos e professores.…”