Boix Mansilla (2010) defines interdisciplinary as a coherent integration of disciplines for solving complex problems. STEM (Science, Technology, Engineering, Mathematics) education has been gaining attention for the last two decades, which can be considered as one of the effective approaches to address the implementation of interdisciplinary education. STEM education can be defined as the integration of various contexts to solve real-life problems (Mumcu et al., 2023). Considering interdisciplinary, “transparent and equitable connections” of disciplines (Nugraha et al., 2024, p. 5) are necessary. For the information age, it’s critical to incorporate interdisciplinary education in K-12 education settings especially for mathematics and science. The main element in such integration would be mathematical modeling (e.g., English, 2024).  Mathematical modeling aims to solve complex real-world problems (Garfunkel & Montgomery, 2016). The produced mathematical model would be a representation of the real-world problem to be explored and investigated. Mathematical modeling can be considered as a process of utilizing “mathematics to represent, analyze, make predictions or otherwise provide insight into real-world phenomena” (Garfunkel & Montgomery, 2016, p. 8). Based on the definition of Garfunkel and Montgomery (2016), mathematical modeling is a cyclical and iterative process with the elements: “Identify the problem, make assumptions and identify variables, do the math, analyze and assess the solution, iterate, implement the model” (pp. 12-13).

The aim of this research is to address the need for improving pre-service mathematics and science teachers’ competencies in interdisciplinary teaching. For this purpose, an undergraduate course was designed and implemented. Various research suggests implementing mathematical modeling with pre-service science and mathematics teachers to support their learning for interdisciplinary (e.g., Aminger et al., 2016; Anhalt & Cortez, 2016). Anhalt and Cortez (2016) also discussed the role of such learning with mathematical modeling opportunities to overcome some difficulties that pre-service teachers had. Aminger and his colleagues (2021) conducted a study with pre-service secondary science teachers to help them in the implementation of reform-based science with computational thinking and mathematics. The findings revealed that most of the participants implemented cognitively demanding lessons which were integrated. The researchers also discussed that these implementations included mathematical modeling in a way “to move students’ understanding of the science phenomena forward” (p. 188).

Interdisciplinarity (Boix Mansilla, 2010), mathematical modeling (Garfunkel & Montgomery, 2016), task design and pre-service teacher education (Geiger et al., 2022) were used as the theoretical framework for this study. Thus, for this study, based on the relevant literature (Boix Mansilla, 2010; Garfunkel & Montgomery, 2016; Geiger et al., 2022), an interdisciplinary mathematical problem for teaching is defined as an interdisciplinary problem that can be solved through mathematical modeling and used for pedagogical purposes.

Based on the literature on interdisciplinary education, there is a need to design learning experiences for in-service and pre-service teachers to study mathematical modeling in a way to integrate various disciplines in their teaching. This current study is a part of a larger design-based research that aims to design and implement an undergraduate course for pre-service secondary mathematics and science teachers. In this presentation, the authors will focus on the following research question:

How do the pre-service teachers who take a course on interdisciplinary mathematics and science education pose interdisciplinary mathematical modeling problems for teaching? 

The larger study is design-based research which may use various data analysis approaches (Bakker, 2019). The research question of this presentation was investigated with qualitative methods (Yin, 2016) in order to get deeper insights into participants’ posing interdisciplinary mathematical problems for teaching. The data source of this investigation were interviews (pre- and post-interview), which included items about interdisciplinarity, interdisciplinary education, interdisciplinary mathematics and science education, and how to pose interdisciplinary mathematical modeling tasks. For this presentation, the focus will be on the interview item asking how to design an interdisciplinary mathematical modeling task, write such an example, as well as how to define the context or theme of an interdisciplinary mathematical modeling task. The study took place during the seven weeks of an elective course on science and mathematics education in a state university in Türkiye. There were fifteen pre-service teachers taking the undergraduate course on interdisciplinary teaching yet nine of them actively attended the course and completed it. Four of them were science teaching majors (P1, P2, P4, P9) and five of them were mathematics teaching majors (P3, P5, P6, P7, P8). Thus, those nine pre-service teachers were taken as the participants for this presented study. The purposeful sampling was used to include actively participating pre-service mathematics and science pre-service teachers in the course. The primary data source of the study are semi-structured interviews. Transcribed interviews were read to construct initial open codes. The thematic analysis (Braun & Clarke, 2021) was used to analyze data inductively. Based on the analysis, the findings were grouped under the following themes: context, modeling, organization, and level. Context was defined as the context of the problem including real-life connection, interdisciplinarity, and connections. Modeling was defined as the mathematical modeling process and related elements in the problem. Organization was defined as the structure of the problem including content and problem type. Level was defined as the level of the task including relevant student level and mathematical level of the problem. Modeling was the dominant theme, and there were more codes about modeling in the post-interview compared to that in the pre-interview.

Concerning context, participants mentioned more on interdisciplinarity in the post-interview compared to that in the pre-interview. Interdisciplinarity necessitates to consider different disciplinary viewpoints (Brassler & Dettmers, 2017). Thus, pre-service teachers might need more support to enhance understanding interdisciplinarity. Participants prioritized modeling in posing interdisciplinary problems for teaching. This finding was parallel to the literature on utilizing modeling to enhance interdisciplinary learning, particularly in mathematics and science education (e.g., English, 2024). Concerning organization, there were more codes in the post-interview (e.g., group work, engagement) compared to those in the pre-interview. This was consistent with the literature on task design in mathematics education such as specifying goals helps to connect mathematics to other disciplines (e.g., Yang & Ball, 2024). For level, prior knowledge of students was stated in the pre-interview while student level and mathematical level of the task were emphasized in the post-interview. Cognitive demand was emphasized in the post-interviews, which was considered important in task design (e.g., Stein et al., 2000). Moreover, collaboration with another major and working in small groups, active learning experiences were found to be beneficial in this study. This is aligned with literature (e.g., Geiger et al., 2022). This study revealed that context, mathematical modeling, organization, and level were the key components in posing interdisciplinary mathematical modeling problems for teaching. These components could be investigated in further studies on posing problems, especially in interdisciplinary mathematical ones. Since posing problems is complex, this study could contribute to the literature on pre-service teachers’ designing problems in mathematics and science education. This study is limited within its context of the study, including participants. Future research might investigate the development of pre-service teachers’ skills in posing interdisciplinary mathematical problems with a longer professional development programme.

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