Die Entwicklung und Lösung von Modellierungsaufgaben – Eine Erweiterung des Modellierungsprozesses aus einer Problem Posing-Perspektive

Abstract

In mathematics education, pre-formulated modelling problems are used to teach mathematical modelling. However, in out-of-school scenarios problems have to be identified and posed often first before they can be solved. Despite the ongoing emphasis on the activities involved in solving given modelling problems, little is known about the activities involved in developing and solving own modelling problems and the connection between these activities. To help fill this gap, we explored the modelling process from a problem posing perspective by asking the questions: (1) What activities are involved in developing modelling problems? and (2) What activities are involved in solving self-generated modelling problems? To answer these research questions, we conducted a qualitative study with seven pre-service teachers. The pre-service teachers were asked to pose problems that were based on given real-world situations and to solve their self-generated problems while thinking aloud. We analyzed pre-service teachers’ developing and subsequent solving phases with respect to the problem posing and modelling activities they were engaged in. Based on theories of problem posing and modelling, we developed an integrated process-model of posing and solving own modelling problems and validated it in the present study. The results indicate that posing own modelling problems might foster important modelling activities. The integrated process-model of developing and solving own modelling problems provides the basis for future research on modelling problems from a problem posing perspective.

Personalizing real‐world problems: Posing own problems increases self‐efficacy expectations, intrinsic value, attainment value, and utility value

“…This finding adds to previous research showing that problem‐posing interventions promoted students' self‐efficacy (Voica et al., 2020), stimulated their interest (Xia et al., 2008), enhanced utility value (Walkington & Bernacki, 2015), and promoted their attitudes and beliefs (Rosli et al., 2014). One explanation is that posing their own problems allows students to anticipate solutions (Hartmann et al., 2023), align problems with their interests, experience responsibility and personal importance, and create problems aligned with their goals.…”

“…In mathematics education, one activity for realizing active personalization is problem posing. Problem posing refers to activities of developing new problems and reformulating given problems (Hartmann et al., 2023). Prompts to stimulate problem posing activities can be classified as unstructured, semi‐structured, or structured problem posing prompts (Baumanns & Rott, 2021; Stoyanova, 1999): Structured prompts are based on a given problem and ask students to pose further questions based on the provided problem.…”