Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems?

Abstract

As problem posing has been shown to foster students’ problem-solving abilities, problem posing might serve as an innovative teaching approach for improving students’ modelling performance. However, there is little research on problem posing regarding real-world situations. The present paper addresses this research gap by using a modelling perspective to examine (1) what types of problems students pose (e.g., modelling vs. word problems) and (2) how students solve different types of self-generated problems. To answer these questions, we recruited 82 ninth- and tenth-graders from German high schools and middle schools to participate in this study. We presented students with different real-world situations. Then we asked them to pose problems that referred to these situations and to solve the problems they posed. We analyzed students’ self-generated problems and their solutions using criteria from research on modelling. Our analysis revealed that students posed problems that were related to reality and required the application of mathematical methods. Therefore, problem posing with respect to given real-world situations can be a beneficial approach for fostering modelling abilities. However, students showed a strong tendency to generate word problems for which important modelling activities (e.g., making assumptions) are not needed. Of the students who generated modelling problems, a few either neglected to make assumptions or made assumptions but were not able to integrate them adequately into their mathematical models, and therefore failed to solve those problems. We conclude that students should be taught to pose problems, in order to benefit more from this powerful teaching approach in the area of modelling.

Problem-posing research in mathematics education: A bibliometric analysis

“…In addition, the fact that the studies using the keywords ‗teaching mathematics through problem-posing' or ‗teaching through problem-posing' Zhang & Cai, 2021) and affect (Cai & Leikin, 2020;Guo et al, 2020;Parhizgar et al, 2021;Schindler & Bakker, 2020) were published after 2020, in the last period, indicates that these issues are the most current trends in this research area. On the other hand, keyword analysis shows that in many studies (Abramovich, 2014;Abramovich & Cho, 2008;Aytekin-Uskun et al, 2021;Chang, 2007;Chen et al, 2013;Ellerton, 2013;English, 2020;Ertane-Baş & Özturan-Sağırlı, 2021;Hartmann et al, 2021;Koichu, 2010;Kopparla et al, 2019;Leavy & Hourigan, 2020;Leavy & Hourigan, 2021;Mallart et al, 2018;Mamona-Downs & Downs, 2005;Martinez & Blanco, 2021;Özdemir & Şahal, 2018;Palmer & van Bommel, 2020;Samkova & Ticha, 2016;Samkova & Ticha, 2017;Schindler & Bakker, 2020;Van Harpen & Sriraman, 2013;Xia et al, 2007;Xie & Masingila, 2017) problem solving and problem posing are considered together with various aspects. For example, Xie and Masingila (2017) focused on discovering what actually happens in the process of preservice teachers alternately participating in problem solving and problem posing activities.…”

“…Moreover, in the articles using the density map problem posing subject, the most commonly used items are test, effect, development, work, etc., while the most current elements, such as flexibility, creativity, and mathematical creativity, among others, are used less frequently. Indeed, in recent years, some changes have occurred in the focus of problem posing studies, from studies carried out to determine problem posing skills, errors, or beliefs in certain subjects, such as fractions or operations with fractions (Chen et al, 2013;Işık & Kar, 2012;Kılıç, 2015), to studies in which problem posing is considered together with different fields of study such as modelling (Hartmann et al, 2021) and mathematical creativity (Ayvaz & Durmuş, 2021;Biçer et al, 2020;Elgrably & Leikin, 2021;Leikin & Elgrably, 2020), among others. Cai and Hwang (2020) state that one of the potential benefits of including problem posing in math classes is that it provides useful insights about students' mathematical thinking.…”

“…Cai and Hwang (2020) state that one of the potential benefits of including problem posing in math classes is that it provides useful insights about students' mathematical thinking. In this direction, it is noteworthy that in recent years, there has been a greater orientation toward studies wherein problem-setting is used as a cognitive activity to evaluate the mathematical thinking of teachers or students (Guo et al, 2021;Hartmann et al, 2021;Silber & Cai, 2021;Xu et al, 2020;Yao et al, 2021). To increase our understanding of this field, it is proposed to increase the number of studies to be conducted.…”

Python-based simulations of the probabilistic behavior of random events for secondary school students

“…This endeavor began with research on mathematical modeling in elementary (English, 2012;Kazak et al, 2018;Patel & Pfannkuch, 2018;Shahbari & Peled, 2017) and secondary schools (Balakrishnan et al, 2010;Krutikhina et al, 2018;Stillman, 2010). The objective is to develop the learners' ability to create mathematical models that solve everyday problems (Blum & Leiß, 2006;Galbraith et al, 2020;Hartmann et al, 2021;Schukajlow et al, 2015b;Wake, 2015), as well as developing student competency in creating mathematical models of various types. Such models could be deterministic (Farihah, 2019;Ortega & Puig, 2017;Yanagimoto & Yoshimura, 2013), probabilistic (Frejd & Ärlebäck, 2017;Greefrath & Siller, 2017;Kazak, 2010;Kotelawala, 2011), or dynamic (Blomhøj, 2020;Kaiser et al, 2011;Leung, 2013;.…”

Preservice Teachers in Real-world Problem-Posing: Can They Turn a Context into Mathematical Modelling Problems?

“…In this paper, we considered the openness of problems related to two main aspects, namely whether the mathematical models might be constructed by solvers are various or not and whether the initial state was clear or not as an unclear initial state is a feature of modelling challenges (Maaß 2010). The clarity of initial state is also closely related to knowledge about the real world with extraneous or missing data, in which a solver of modelling problems should rely on assumptions when there is a lack of knowledge or given information (Hartmann et al, 2021).…”