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Interest and performance in solving open modelling problems and closed real-world problems
Abstract
Modelling is an important part of mathematical learning. One characteristic feature of modelling problems is their openness. In this study, we investigated the relationship between interest and performance in solving open modelling problems and closed real-
world problems. We used questionnaires and tests to assess the interest and performance of 143 ninth- and 10th-grade students at different achievement levels. We found that low-achieving students were more interested in solving open modelling problems than closed real-world problems. Also, prior individual interest in mathematics and performance were positively related to situational (task-specific) interest. These results contribute to interest theories by underlining the importance of types of real-world problems and achievement levels for situational interest.
... The findings presented in this subsection support the idea that performance is a factor to be considered in task-specific interest research (Carmichael et al., 2009). Indeed, task-specific interest was found to be positively related to performance in solving problems (Nuutila et al., 2020;Schukajlow et al., 2022). ...
... The results have shown that, both for secondary students and for prospective teachers, there are significant relationships between task-specific interest and performance, which is consistent with previous studies and is in line with our initial hypothesis (Carmichael et al., 2009;Nuutila et al., 2020;Schukajlow et al., 2022). ...
... In our work we have found that there are significant relationships between interest and performance, in line with other studies (Carmichael et al., 2009;Köller et al., 2001;Nuutila et al., 2020;Schukajlow et al., 2022;Renninger, 1998). However, we must point out as a limitation that our study finds correlations, so we do not know to what extent performance influences interest, or interest influences performance. ...
Several studies confirm the importance of the role of students’ interest in learning mathematics. This article describes the process of conceptual replication of Rellensmann and Schukajlow’s (2017) research on how the connection to the reality of a mathematical problem affects the interest in solving it. Our study distinguishes between intramathematical problems, word problems and modelling problems. It was implemented with 80 Spanish ninth-grade students and 80 pre-service teachers. The results show that Spanish students are more interested in intramathematical problems and less interested in modelling problems, while pre-service teachers are more interested in problems connected to reality, especially word problems. We also provide data regarding the performance of students and prospective teachers, which is higher in word problems. In addition, we find that there are significant relationships between performance and task-specific interest. These results complement the original study, as they allow us to contrast whether there are differences with German students and to explain the German pre-service teachers’ judgements of students’ interest in problems with and without a connection to reality.
The impact sheet to this article can be accessed at 10.6084/m9.figshare.25507636 .
... This might be particularly beneficial for students with a low level of mathematical competence because they might focus more on non-mathematical aspects and might appreciate the chance to deal with these aspects more in mathematics class. The findings from the study conducted by Schukajlow et al. (2022) support these considerations. The study revealed that low-achieving students reported greater interest in solving open modelling problems when compared to closed problems, whereas high-achieving students reported similar interest in both open and closed modelling problems with a slight preference for closed problems. ...
Problem posing-generating one's own problems-is considered a powerful teaching approach for fostering students' motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students' interest is largely missing. In this contribution, we present a study with 105 ninth-and tenth-graders to address the question of whether the task variables modelling potential, assessed by openness and authenticity, or complexity of self-generated problems have an impact on students' interest in solving them. Further, we investigated whether the effect of task variables of self-generated problems on stu-dents' interest differed among students with different levels of mathematical competence. High modelling potential had a positive effect on interest in solving the problem for students with low mathematical competence, whereas it had a negative effect for those with high mathematical competence. However, complexity of self-generated problems did not affect students' interest in solving problems.
One characteristic feature of modelling problems is their openness. In current research, there is a lack of theoretical and empirical information on how to deal with the openness of modelling problems in the classroom. In this chapter, we summarise research on open problems and present a process model for dealing with modelling problems with a specific focus on openness. We use prior research and the theoretical process model to create a teaching method that is designed to help ninth-graders solve open modelling problems. The essential characteristics of this teaching method is that it is closely linked to the presented process model, it scaffolds students’ learning with the use of situational objects and guiding questions, and it is embedded in a learner-centred learning environment.
Open mathematical modelling problems that can be solved with multiple methods and have multiple possible results are an important part of school curricula in mathematics and science. Solving open modelling problems in school should prepare students to apply their mathematical knowledge in their current and future lives. One characteristic of these problems is that information that is essential for solving the problems is missing. In the present study, we aimed to analyze students’ cognitive barriers while they solved open modelling problems, and we evaluated the effects of instructional prompts on their success in solving such problems. A quantitative experimental study (N = 263) and a qualitative study (N = 4) with secondary school students indicated that identifying unknown quantities and making numerical assumptions about these quantities are important cognitive barriers to solving open modelling problems. Task-specific instructional prompts helped students overcome these barriers and improved their solution rates. Students who were given instructional prompts included numerical assumptions in their solutions more often than students who were not given such prompts. These findings contribute to theories about solving open modelling problems by uncovering cognitive barriers and describing students’ cognitive processes as they solve these problems. In addition, the findings contribute to improving teaching practice by indicating the potential and limitations of task-specific instructional prompts that can be used to support students’ solution processes in the classroom.
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