The role of reading comprehension in mathematical modelling: improving the construction of a real-world model and interest in Germany and Taiwan

Abstract

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.

Welcome to the era of vague news: a study of the demands of statistical and mathematical products in the COVID-19 pandemic media

“…The pandemic has also introduced new language demands into the public arena because of the need to communicate a wide range of mathematical and statistical ideas, as illustrated by the excerpts in Table 7 . Such and related examples illustrate that citizens must acquire and activate sophisticated text comprehension capabilities if they are to access and understand descriptive quantitative information and more advanced mathematical and statistical ideas within media items (e.g., regarding modelling; Krawitz et al, 2022 ). Furthermore, an awareness of language and literacy demands is key to comprehending news and professional jargon as well as to its (cautious) interpretation.…”

I value the problem, but I don’t think my students will: preservice teachers’ judgments of task value and self-efficacy for modelling, word, and intramathematical problems

“…Solving modelling problems might be associated with high cost because of the complexity of the cognitive demands of this type of problem, thus possibly negating the gain in task value from a problem's relation to reality, especially when students are not familiar with this type of problem. Attainment and utility value for modelling problems can be lower for students when compared with word and intramathematical problems because modelling problems are not (yet) common on exams or in school curricula (Blum & Borromeo Ferri, 2009;Krawitz et al, 2021). Thus, school students have not built an identity regarding modelling problems and do not fully recognize and appreciate the necessity of being able to solve them.…”

Analysing mathematical modelling tasks in light of citizenship education using the COVID-19 pandemic as a case study

“…Obviously, following the “bottom-up” view does not capture the whole picture, as there are many aspects of modelling competences which are not linked to the individual steps of the modelling cycle but are overarching. Relevant overarching competences identified by research, for example, are as follows: metacognition (Stillman, 2011 ; Schukajlow et al, 2021 ; Vorhölter, 2018 , 2021 ); creativity (Lu & Kaiser, 2022 ); reading competences (Krawitz et al, 2022 ). …”

“…• metacognition (Stillman, 2011;Schukajlow et al, 2021;Vorhölter, 2018Vorhölter, , 2021); • creativity (Lu & Kaiser, 2022); • reading competences (Krawitz et al, 2022).…”