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<xml><records><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>0</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Vogel, Sebastian</author><author>Blum, Werner</author><author>Achmetli, Kay</author><author>Krawitz, Janina</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Qualifizierung von Lehrkr&#228;ften zum konstruktiven Umgang mit zentralen Lernstandserhebungen &#8211; Ergebnisse aus dem Projekt VELM-8</style></title><secondary-title><style face="normal" font="default" size="100%">Journal f&#252;r Mathematik-Didaktik</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Journal f&#252;r Mathematik-Didaktik</style></full-title></periodical><pages><style face="normal" font="default" size="100%">319&#8211;348</style></pages><volume><style face="normal" font="default" size="100%">37</style></volume><number><style face="normal" font="default" size="100%">2</style></number><dates><year><style face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1869-2699</style></isbn><abstract><style face="normal" font="default" size="100%">Seit 2009 finden allj&#228;hrlich deutschlandweit in Klasse 8 Lernstandserhebungen statt (auch &#8222;Vergleichsarbeiten&#8220; oder kurz &#8222;VerA-8&#8220; genannt), unter anderem f&#252;r das Fach Mathematik. Mit diesem Instrument sollen den Lehrkr&#228;ften Orientierungen und M&#246;glichkeiten zur Diagnose der Kompetenzentwicklung ihrer Sch&#252;lerinnen und Sch&#252;ler gegeben werden, um damit eine gezielte individuelle F&#246;rderung und eine Qualit&#228;tsentwicklung im Unterricht anzusto&#223;en. Dieser Nutzen der Lernstandserhebungen ist jedoch im hohen Ma&#223; abh&#228;ngig von den Kompetenzen und Einstellungen der Lehrkr&#228;fte sowie deren Umgang mit den Lernstandserhebungen und ihren R&#252;ckmeldungen. Mit dem Projekt VELM-8 (Verbesserung der Effektivit&#228;t der Lernstandserhebungen Mathematik Klasse 8) wurde im Laufe des Schuljahres 2012/13 eine vierteilige Fortbildungsreihe entwickelt, um Lehrkr&#228;fte im Umgang mit den Lernstandserhebungen weiterzubilden. Ziel von VELM-8 war es, exemplarisch zu zeigen, wie die Lernstandserhebungen f&#252;r die Unterrichtspraxis genutzt werden k&#246;nnen. In einem Pr&#228;-/Posttest-Design wurden u.&#8201;a. die Einstellungen der Lehrkr&#228;fte bez&#252;glich der Lernstandserhebung sowie deren Nutzung durch die Lehrkr&#228;fte erfasst. Die Erhebungen fanden parallel in einer Projekt- und einer Wartekontrollgruppe statt. Im folgenden Beitrag soll zun&#228;chst die Fortbildungsreihe vorgestellt werden und anschlie&#223;end &#252;ber wesentliche Befunde der zugeh&#246;rigen Evaluation berichtet werden.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s13138-016-0092-6</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s13138-016-0092-6</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>1</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Achmetli, Kay</author><author>Blum, Werner</author><author>Vogel, Sebastian</author><author>Besser, Michael</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Report on the relative strengths and weaknesses of the United States in PISA 2012 mathematics</style></title><secondary-title><style face="normal" font="default" size="100%">OECD Education Working Papers</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">OECD Education Working Papers</style></full-title></periodical><number><style face="normal" font="default" size="100%">151</style></number><dates><year><style face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">OECD</style></publisher><isbn><style face="normal" font="default" size="100%">1993-9019</style></isbn><abstract><style face="normal" font="default" size="100%">This paper aims to investigate the performance of the students in the United States in all 84 mathematics items that were administered in the United States as part of the PISA 2012 assessment. It compares the performance of the United States with the OECD average and with the performance of five reference countries/economies that were ranked higher on the PISA scale. The analysis reveals specific relative strengths and weaknesses of the 15-year-olds in the United States, referring to items in which they performed unexpectedly well or unexpectedly badly compared to their overall distance from the OECD average or from the reference countries/economies. On that basis, certain patterns &#8211; that means certain clusters &#8211; of items with similar cognitive requirements, are identified. There are seven altogether, three for strengths and four for weaknesses of the US students. An analysis of student solutions illustrates and further clarifies these strengths and weaknesses. The results show that the relative strengths are mostly revealed in easy items, whereas the relative weaknesses are mostly reflected in particularly demanding items.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1787/bc544d1e-en</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1787/bc544d1e-en</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>2</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Realkontext ernst nehmen. H&#252;rden beim L&#246;sen von unterbestimmten Modellierungsaufgaben</style></title><secondary-title><style face="normal" font="default" size="100%">mathematik lehren</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">mathematik lehren</style></full-title></periodical><pages><style face="normal" font="default" size="100%">10&#8211;15</style></pages><number><style face="normal" font="default" size="100%">207</style></number><dates><year><style face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">Friedrich Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">0175-2235</style></isbn><abstract><style face="normal" font="default" size="100%">Oft werden zum L&#246;sen von Modellierungsaufgaben mehr Informationen ben&#246;tigt, als explizit angegeben sind. Ein Fehlen von Informationen ist nicht immer offensichtlich - und so f&#228;llt es Sch&#252;lerinnen und Sch&#252;lern schwer, die Notwendigkeit zu erkennen, Werte durch Sch&#228;tzungen, Recherche oder eigene Datenerhebung zu erg&#228;nzen. Wir zeigen, wie Lernende darin gef&#246;rdert werden k&#246;nnen, solche unterbestimmten Modellierungsaufgaben durch R&#252;ckgriff auf ihr Alltagswissen zu l&#246;sen.</style></abstract><work-type><style face="normal" font="default" size="100%">Practical</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.friedrich-verlag.de/friedrich-plus/sekundarstufe/mathematik/modellieren-problemloesen/realkontexte-ernst-nehmen-227</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>3</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Do students value modelling problems, and are they confident they can solve such problems? Value and self-efficacy for modelling, word, and intra-mathematical problems</style></title><secondary-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></full-title></periodical><pages><style face="normal" font="default" size="100%">143&#8211;157</style></pages><volume><style face="normal" font="default" size="100%">50</style></volume><dates><year><style face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1863-9704</style></isbn><abstract><style face="normal" font="default" size="100%">Posing modelling problems in class is supposed to increase students&#8217; motivation. As motivation is assumed to emerge from task value and self-efficacy expectations, the present study considered both constructs with the aims to examine (1) whether students have different values and self-efficacy expectations concerning modelling problems versus dressed up word problems and intra-mathematical problems and (2) whether mathematical content influences task value and self-efficacy concerning different types of problems. We asked 90 high- and middle-track students (ninth- and tenth-graders) how much they valued modelling problems, dressed up word problems, and intra-mathematical problems and if they were confident they could solve these types of problems. All of the problems that we used could be solved by applying mathematical procedures from two different mathematical content areas (Pythagorean theorem or linear functions). The results indicated that there were significant differences in students&#8217; task values and self-efficacy depending on the type of problem. Students reported the lowest task values and self-efficacy expectations for modelling problems compared with the other types of problems. Moreover, the differences between students&#8217; task values (but not between students&#8217; self-efficacy expectations) within the three types of problems seemed to depend on the mathematical content area. Intra-mathematical problems that could be solved by applying the Pythagorean theorem were valued higher than problems involving linear functions, whereas for modelling and dressed up word problems, it was the other way around. Implications for future research and classroom practice are discussed.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11858-017-0893-1</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s11858-017-0893-1</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>4</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Van Dooren, Wim</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Unrealistic responses to realistic problems with missing information: What are important barriers?</style></title><secondary-title><style face="normal" font="default" size="100%">Educational Psychology</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Educational Psychology</style></full-title></periodical><pages><style face="normal" font="default" size="100%">1221&#8211;1238</style></pages><volume><style face="normal" font="default" size="100%">38</style></volume><dates><year><style face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">Taylor &amp; Francies</style></publisher><isbn><style face="normal" font="default" size="100%">1469-5820</style></isbn><abstract><style face="normal" font="default" size="100%">It is a well-documented finding that students tend to neglect their real-world knowledge when solving word problems, even when realistic assumptions are needed. Although studies have successfully shown the extent to which students tend to provide unrealistic responses, the question of where this tendency comes from has yet to be answered. We focused on two major steps needed to solve realistic word problems: noticing missing information and making realistic assumptions. We conducted two studies with fifth graders (Study 1, N&#8201;=&#8201;108; Study 2, N&#8201;=&#8201;60) in which we compared students&#8217; (un-)realistic responses to problems that differed in how obvious the missing information was. Study 1 fostered only students&#8217; ability to make assumptions. Study 2 fostered this ability plus the ability to notice missing information. The results indicate that, if the missing information is not obvious, students&#8217; failure to notice it seems to be what prevents them from arriving at a realistic solution.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1080/01443410.2018.1502413</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1080/01443410.2018.1502413</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>5</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Chang, Yu-Ping</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Yang, Kai-Lin</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Comparing German and Taiwanese secondary school students&#8217; knowledge in solving mathematical modelling tasks requiring their assumptions</style></title><secondary-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></full-title></periodical><pages><style face="normal" font="default" size="100%">59&#8211;72</style></pages><volume><style face="normal" font="default" size="100%">52</style></volume><dates><year><style face="normal" font="default" size="100%">2019</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1863-9704</style></isbn><abstract><style face="normal" font="default" size="100%">Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In this study, we intentionally designed two types of assumptions in two modelling tasks, namely, one task that requires non-numerical assumptions only and another that requires both non-numerical and numerical assumptions. Moreover, conceptual knowledge and procedural knowledge are also two factors influencing students&#8217; modelling performance. However, current studies comparing modelling performance between Western and non-Western students do not consider the differences in students&#8217; knowledge. This gap in research intrigued us and prompted us to investigate whether Taiwanese students can still perform better than German students if students&#8217; mathematical knowledge in solving modelling tasks is differentiated. The results of our study showed that the Taiwanese students had significantly higher mathematical knowledge than did the German students with regard to either conceptual knowledge or procedural knowledge. However, if students of both countries were on the same level of mathematical knowledge, the German students were found to have higher modelling performance compared to the Taiwanese students in solving the same modelling tasks, whether such tasks required non-numerical assumptions only, or both non-numerical and numerical assumptions. This study provides evidence that making assumptions is a strength of German students compared to Taiwanese students. Our findings imply that Western mathematics education may be more effective in improving students&#8217; ability to solve holistic modelling problems.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11858-019-01090-4</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s11858-019-01090-4</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>6</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Ist L&#246;sungsvielfalt lernf&#246;rderlich? Multiple L&#246;sungen beim Mathematischen Modellieren</style></title><secondary-title><style face="normal" font="default" size="100%">MNU-Journal</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">MNU-Journal</style></full-title></periodical><pages><style face="normal" font="default" size="100%">182&#8211;187</style></pages><volume><style face="normal" font="default" size="100%">73</style></volume><number><style face="normal" font="default" size="100%">3</style></number><dates><year><style face="normal" font="default" size="100%">2020</style></year></dates><publisher><style face="normal" font="default" size="100%">Verlag Klaus Seeberger</style></publisher><isbn><style face="normal" font="default" size="100%">0025-5866</style></isbn><abstract><style face="normal" font="default" size="100%">Lo&#776;sungsvielfalt gilt als ein wichtiges Merkmal einer qualitativ hochwertigen Unterrichtsgestaltung. Analysen von empirischen Studien in Mathematik zeigen, dass der Unterricht mit multiplen Lo&#776;sungen a&#776;hnliche Wirkungen auf die Leistungen erzielt wie der traditionelle Unterricht, dabei jedoch einzelne Faktoren wie Interesse, Kompetenzerleben und Freude positiv beeinflusst. Lernfo&#776;rderliche Elemente in der Gestaltung des Unterrichts mit multiplen Lo&#776;sungen werden im Beitrag pra&#776;sentiert und diskutiert.</style></abstract><work-type><style face="normal" font="default" size="100%">Practical</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.mnu.de/zeitschriften/582-mnu-heft-2020-03</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>7</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">When can making a drawing hinder problem solving? Effect of the drawing strategy on linear overgeneralizations and problem solving</style></title><secondary-title><style face="normal" font="default" size="100%">Frontiers in Psychology</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Frontiers in Psychology</style></full-title></periodical><volume><style face="normal" font="default" size="100%">11</style></volume><dates><year><style face="normal" font="default" size="100%">2020</style></year></dates><publisher><style face="normal" font="default" size="100%">Frontiers</style></publisher><isbn><style face="normal" font="default" size="100%">1664-1078</style></isbn><abstract><style face="normal" font="default" size="100%">The strategy of making a drawing has been claimed to facilitate mathematical problem solving. However, De Bock et al. (2003) surprisingly found that drawing negatively affected performance in solving non-linear geometry problems, in which the area or volume of similar figures or solids had to be determined by a given scaling factor. The authors suggested that making a drawing increased the number of overgeneralizations and negatively affected students&#8217; performance. Our study involves a partial replication and also an important validation and extension of this study by addressing two factors: low-quality drawing strategy and poor visual monitoring, both of which might explain the negative effect of drawing. First, we expected that improving the quality of the drawing strategy by prompting students to highlight important information in their drawings would diminish the negative effect of the drawing strategy. Second, we expected that fostering visual monitoring while drawing, by offering problems with small scaling factors, would diminish the negative effect of the drawing strategy. We conducted a randomized controlled trial with 180 students (ninth- to eleventh-graders) to investigate the effects of drawing and visual monitoring on solving non-linear geometry problems. Our results replicated the previous finding that drawing negatively affects performance. We confirmed that linear overgeneralizations are a prevalent reason for this finding. Elaborating on previous findings revealed that the quality of the drawing strategy but not visual monitoring was responsible for the effect of the drawing strategy on linear overgeneralizations. Furthermore, an exploratory analysis of students&#8217; awareness of linear overgeneralizations indicated that improving the quality of drawing strategy and enhancing visual monitoring did not lead to a greater awareness of the mistakes learners made because of linear overgeneralizations. We conclude that the way the drawing strategy is used determines whether it is useful or damaging, and more efforts are essential to enable students to apply it appropriately.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.3389/fpsyg.2020.00506</style></url></related-urls></urls><custom7><style face="normal" font="default" size="100%">506</style></custom7><electronic-resource-num><style face="normal" font="default" size="100%">10.3389/fpsyg.2020.00506</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>8</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hartmann, Luisa-Marie</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Create your own problem! When given descriptions of real-world situations, do students pose and solve modelling problems?</style></title><secondary-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></full-title></periodical><pages><style face="normal" font="default" size="100%">919&#8211;935</style></pages><volume><style face="normal" font="default" size="100%">53</style></volume><dates><year><style face="normal" font="default" size="100%">2021</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1863-9704</style></isbn><abstract><style face="normal" font="default" size="100%">As problem posing has been shown to foster students&#8217; problem-solving abilities, problem posing might serve as an innovative teaching approach for improving students&#8217; 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&#8217; 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.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11858-021-01224-7</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s11858-021-01224-7</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>9</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Chang, Yu-Ping</author><author>Yang, Kai-Lin</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">The role of reading comprehension in mathematical modelling: Improving the construction of a real-world model and interest in Germany and Taiwan</style></title><secondary-title><style face="normal" font="default" size="100%">Educational Studies in Mathematics</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Educational Studies in Mathematics</style></full-title></periodical><pages><style face="normal" font="default" size="100%">337&#8211;359</style></pages><number><style face="normal" font="default" size="100%">109</style></number><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1573-0816</style></isbn><abstract><style face="normal" font="default" size="100%">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&#8217; situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students&#8217; interest in modelling improved more in Germany. An in-depth quantitative analysis of students&#8217; 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.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s10649-021-10058-9</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s10649-021-10058-9</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>10</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Eine Aufgabe viele L&#246;sungen: Nat&#252;rlich differenzieren mit Modellierungsaufgaben</style></title><secondary-title><style face="normal" font="default" size="100%">mathematik lehren</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">mathematik lehren</style></full-title></periodical><pages><style face="normal" font="default" size="100%">28&#8211;32</style></pages><number><style face="normal" font="default" size="100%">233</style></number><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">Friedrich Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">0175-2235</style></isbn><abstract><style face="normal" font="default" size="100%">In welche Dose passt der L&#246;ffel? Und welche Geschenke passen zusammen in einen Karton? Modellierungsaufgaben erm&#246;glichen differenzierte Zug&#228;nge und Ergebnisse. Alle arbeiten auf individuellen Wegen an derselben Aufgabe.</style></abstract><work-type><style face="normal" font="default" size="100%">Practical</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.friedrich-verlag.de/friedrich-plus/sekundarstufe/mathematik/modellieren-problemloesen/eine-aufgabe-viele-losungen-12542</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>11</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Hartmann, Luisa-Marie</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Posing and Solving Modelling Problems&#8212;Extending the Modelling Process from a Problem Posing Perspective</style></title><secondary-title><style face="normal" font="default" size="100%">Journal f&#252;r Mathematik-Didaktik</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Journal f&#252;r Mathematik-Didaktik</style></full-title></periodical><pages><style face="normal" font="default" size="100%">533&#8211;561</style></pages><volume><style face="normal" font="default" size="100%">44</style></volume><number><style face="normal" font="default" size="100%">2</style></number><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1869-2699</style></isbn><abstract><style face="normal" font="default" size="100%">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&#8217; 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.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s13138-023-00223-3</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s13138-023-00223-3</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>12</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author><author>Kanefke, Jonas</author><author>Blum, Werner</author><author>Rakoczy, Katrin</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Open modelling problems: cognitive barriers and instructional prompts</style></title><secondary-title><style face="normal" font="default" size="100%">Educational Studies in Mathematics</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Educational Studies in Mathematics</style></full-title></periodical><pages><style face="normal" font="default" size="100%">417&#8211;438</style></pages><volume><style face="normal" font="default" size="100%">114</style></volume><number><style face="normal" font="default" size="100%">3</style></number><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1573-0816</style></isbn><abstract><style face="normal" font="default" size="100%">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&#8217; 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&#8201;=&#8201;263) and a qualitative study (N&#8201;=&#8201;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&#8217; 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&#8217; solution processes in the classroom.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s10649-023-10265-6</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s10649-023-10265-6</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>13</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Hartmann, Luisa-Marie</author><author>Schukajlow, Stanislaw</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students&#8217; interest in solving self-generated modelling problems</style></title><secondary-title><style face="normal" font="default" size="100%">The Journal of Mathematical Behavior</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">The Journal of Mathematical Behavior</style></full-title></periodical><volume><style face="normal" font="default" size="100%">73</style></volume><dates><year><style face="normal" font="default" size="100%">2024</style></year></dates><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><isbn><style face="normal" font="default" size="100%">0732-3123</style></isbn><abstract><style face="normal" font="default" size="100%">Problem posing&#8212;generating one&#8217;s own problems&#8212;is considered a powerful teaching approach for fostering students&#8217; motivation such as their interest. However, research investigating the effects of task variables of self-generated problems on students&#8217; 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&#8217; interest in solving them. Further, we investigated whether the effect of task variables of self-generated problems on students&#8217; 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&#8217; interest in solving problems.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1016/j.jmathb.2024.101129</style></url></related-urls></urls><custom7><style face="normal" font="default" size="100%">101129</style></custom7><electronic-resource-num><style face="normal" font="default" size="100%">10.1016/j.jmathb.2024.101129</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>14</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Yang, Kai-Lin</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Yang, Chai-Ching</author><author>Chang, Yu-Ping</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">German and Taiwanese secondary students&#8217; mathematical modelling task value profiles and their relation to mathematical knowledge and modelling performance</style></title><secondary-title><style face="normal" font="default" size="100%">European Journal of Psychology of Education</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">European Journal of Psychology of Education</style></full-title></periodical><pages><style face="normal" font="default" size="100%">2969&#8211;2989</style></pages><volume><style face="normal" font="default" size="100%">39</style></volume><number><style face="normal" font="default" size="100%">3</style></number><dates><year><style face="normal" font="default" size="100%">2024</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Science+Business Media</style></publisher><isbn><style face="normal" font="default" size="100%">1878-5174</style></isbn><abstract><style face="normal" font="default" size="100%">Based on expectancy-value theory, this study adopted a person-centred approach to explore the heterogeneous profiles of secondary German and Taiwanese students&#8217; mathematical modelling task values, and examined the differences in their mathematical modelling performance, controlling for the variable of intra-mathematical knowledge among the heterogeneous profiles. Authors conducted a survey study of 452 ninth graders (201 German students and 251 Taiwanese students). The results showed that German and Taiwanese students respectively displayed three profiles of mathematical modelling task values: a) moderate utility and moderate interest/attainment, b) high utility but low interest/attainment, and c) low utility but high interest/attainment. Furthermore, different profiles of mathematical modelling task values showed significant differences in mathematical modelling performance for Taiwanese students but not for German students, even after removing the variable of intra-mathematical knowledge. This study advances the understanding of students&#8217; mathematical modelling task values and its relation with their mathematical modelling performance by the expectancy-value model of achievement motivation and person-centred analyses, and sheds light on the learning and teaching of mathematical modelling.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s10212-024-00866-x</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s10212-024-00866-x</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>15</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Hartmann, Luisa-Marie</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Does problem posing affect self-efficacy, task value, and performance in mathematical modelling?</style></title><secondary-title><style face="normal" font="default" size="100%">Educational Studies in Mathematics</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">Educational Studies in Mathematics</style></full-title></periodical><pages><style face="normal" font="default" size="100%">445&#8211;466</style></pages><volume><style face="normal" font="default" size="100%">119</style></volume><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1573-0816</style></isbn><abstract><style face="normal" font="default" size="100%">Problem posing is a promising teaching method for enhancing motivation and performance in mathematics and more specifically in mathematical modelling. Hence, the goals of our study were twofold: (1) to examine the effects of problem posing on modelling performance, self-efficacy, and task values in solving modelling problems, and (2) to analyze whether problem posing affects modelling performance via self-efficacy and task values. In a randomized control trial involving ninth- and tenth-grade students (N&#8201;=&#8201;210), participants were assigned to either a problem-posing and problem-solving group or to one of two problem-solving groups. Students in the problem-posing and problem-solving group received a booklet with descriptions of real-world situations and were prompted to pose and subsequently solve their own problems. Students in the two problem-solving groups received the same real-world situations with given problems and were asked to solve the problems. Before solving the problems, students in all groups reported their self-efficacy and task values. Prompting students to pose their own problems positively enhanced students&#8217; self-efficacy and partially improved their task values in solving modelling problems. Further, problem posing indirectly affected modelling performance via self-efficacy but not task values. However, problem posing had no total effect on modelling performance. The findings for self-efficacy and task values are in line with expectancy-value theories, adding new insights to the field by highlighting the importance of motivational constructs in problem-posing approaches and instructions aimed at fostering mathematical modelling.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s10649-025-10385-1</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s10649-025-10385-1</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>16</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Wiehe, Katharina</author><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author><author>Rakoczy, Katrin</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Openness in mathematical modelling: do experiences of competence and autonomy mediate the effects of an intervention on modelling problems on task values and cost?</style></title><secondary-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></full-title></periodical><pages><style face="normal" font="default" size="100%">519&#8211;534</style></pages><volume><style face="normal" font="default" size="100%">57</style></volume><number><style face="normal" font="default" size="100%">2</style></number><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1863-9704</style></isbn><abstract><style face="normal" font="default" size="100%">Motivation is crucial for learning and achievement. An effective way to increase students&#8217; motivational outcomes, such as task values and cost, can be to incorporate modelling problems in mathematics lessons. Due to their openness, working on modelling problems can lead to experiences of competence and autonomy. In this study, we aimed to analyze (1) whether an intervention on modelling problems with open initial state affects students&#8217; task values and cost, (2) whether this intervention affects students&#8217; experiences of competence and autonomy, (3) whether experiences of competence and autonomy affect task values and cost, and (4) whether this intervention has an indirect effect on students&#8217; task values and cost via their experiences of competence and autonomy. To achieve this aim, we conducted an experimental study with 295 ninth graders using a pre-posttest design. We found positive effects of the intervention on students&#8217; motivational outcomes. Furthermore, experiences of competence and autonomy mediated these effects. By demonstrating effects of the intervention on modelling problems with open initial state on task values and cost, our study contributes to the theory of modelling. Furthermore, the results of our study contribute to motivational theories by uncovering the crucial role of the experiences of competence and autonomy as an intervening variable that explains how the intervention on modelling problems with open initial state affects intrinsic and attainment values.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11858-025-01670-7</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s11858-025-01670-7</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>17</rec-number><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Yang, Xinrong</author><author>Geiger, Vince</author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A Systematic Review of International Perspectives on Mathematical Modelling: Modelling Goals and Task Characteristics</style></title><secondary-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></secondary-title></titles><periodical><full-title><style face="normal" font="default" size="100%">ZDM Mathematics Education</style></full-title></periodical><pages><style face="normal" font="default" size="100%">193&#8211;212</style></pages><volume><style face="normal" font="default" size="100%">57</style></volume><number><style face="normal" font="default" size="100%">3</style></number><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Nature</style></publisher><isbn><style face="normal" font="default" size="100%">1863-9704</style></isbn><abstract><style face="normal" font="default" size="100%">Mathematical modelling is a dynamic research field. This article presents a systematic literature review of recent developments in mathematical modelling from an international perspective. In identifying relevant modelling perspectives, we draw on the goals of modelling and the characteristics of modelling tasks as our theoretical foundation and analyzed recent modelling research in terms of (1) the attributes of studies, including geographical distribution, participants, methodological approaches, and conceptual frameworks; (2) the goals of modelling, characteristics of tasks, and perspectives on modelling; and (3) the relationships between modelling perspectives and study attributes. Focusing on studies concerning students from early childhood to secondary school, we identified 4045 initial publications, from which we selected and analyzed 108 peer-reviewed journal articles and ICTMA book chapters published between January 2020 and April 2024. The analysis revealed significant interest in mathematical modelling across a range of perspectives and, in particular, an emphasis on formative goals related to the development of modelling competence. Authenticity and cognitive richness also emerged as key characteristics of modelling tasks. Additionally, we noted that the educational modelling perspective defined by a combination of formative goals and cognitively rich tasks emerged as a prominent focal point within recent modelling research. A key finding of the review was that further research is needed on under-explored nuances of each modelling perspective, such as upper-secondary students within the educational perspective. Our findings also highlighted the need for theory development to connect the various conceptual frameworks in modelling.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s11858-025-01683-2</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/s11858-025-01683-2</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>18</rec-number><ref-type name="Book">6</ref-type><contributors><authors><author>Krawitz, Janina</author></authors><secondary-authors><author>Greefrath, Gilbert</author><author>Inprasitha, Maitree</author><author>Chang, Yu-Ping</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Vorwissen als n&#246;tige Voraussetzung und potentieller St&#246;rfaktor beim mathematischen Modellieren</style></title><secondary-title><style face="normal" font="default" size="100%">Studien zur theoretischen und empirischen Forschung in der Mathematikdidaktik</style></secondary-title></titles><dates><year><style face="normal" font="default" size="100%">2020</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Spektrum</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-658-29715-2</style></isbn><abstract><style face="normal" font="default" size="100%">Um erfolgreich modellieren zu k&#246;nnen, muss Vorwissen &#252;ber mathematische und realit&#228;tsbezogene Sachverhalte verkn&#252;pft und sinnbringend zum L&#246;sen eines Problems eingesetzt werden. Janina Krawitz untersucht mit inhaltsanalytischen Methoden, wie sich die Aktivierung verschiedenen Vorwissens auf die L&#246;sungsprozesse von mathematischen Modellierungsaufgaben auswirkt. Die Ergebnisse zeigen, wie eine inad&#228;quate Aktivierung von Vorwissen die Bearbeitung von Modellierungsaufgaben behindert. Die Autorin leitet Ursachen f&#252;r die Schwierigkeiten der Lernenden ab und diskutiert Faktoren f&#252;r eine flexible Vorwissensaktivierung.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/978-3-658-29715-2</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/978-3-658-29715-2</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>19</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Wiehe, Katharina</author></authors><secondary-authors><author>Evans, Tanya</author><author>Marmur, Ofer</author><author>Hunter, Jodie</author><author>Leach, Generosa</author><author>Jhagroo, Jyoti</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Impact of prompts on expectancies for success, task values, and costs in problem posing</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education, PME 47, Auckland, New Zealand, July 17&#8211;21, 2024</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">162&#8211;168</style></pages><dates><year><style face="normal" font="default" size="100%">2024</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-1-0670278-3</style></isbn><abstract><style face="normal" font="default" size="100%">Recent research has shown that problem-posing prompts affect students&#8217; achievement-related outcomes in problem-posing tasks. This study extends such findings by investigating the effects of problem-posing prompts on students&#8217; motivational outcomes. Ninth-and tenth-graders (N = 78) were prompted to pose easy and difficult problems. Subsequently, each student reported their expectancy for success, task values, and perceived cost in relation to posing easy versus difficult problems. The results revealed that posing easy compared with difficult problems positively affected expectancy for success, utility value, attainment value, and perceived cost but not intrinsic value. An implication of this study is that including the prompt to pose easy problems in problem-posing tasks is important for students&#8217; motivation.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.researchgate.net/publication/381988106_Impact_of_prompts_on_expectancies_for_success_task_values_and_costs_in_problem_posing</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>20</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author><author>Wiehe, Katharina</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>Evans, Tanya</author><author>Marmur, Ofer</author><author>Hunter, Jodie</author><author>Leach, Generosa</author><author>Jhagroo, Jyoti</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Effects of teaching students to solve open modelling problems on utility, intrinsic, and attainment values</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education, PME 47, Auckland, New Zealand, July 17&#8211;21, 2024</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">81&#8211;88</style></pages><dates><year><style face="normal" font="default" size="100%">2024</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-1-0670278-4</style></isbn><abstract><style face="normal" font="default" size="100%">Task values are important for learning. However, prior research has indicated a lack of studies that have addressed students&#8217; task values in mathematics. In the following study (N = 293), we analyzed (1) the relationships between intrinsic, attainment, and utility values and (2) how teaching students to solve open modelling problems affects these values. Students in the experimental group were taught how to solve open modelling problems, whereas those in the control group were taught how to solve real-world problems with no missing information. Students reported their values before and after the intervention. The results revealed positive relationships between values plus a trend toward a positive effect of the intervention on utility value. We conclude that content-related interventions in modelling can improve motivational outcomes.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.researchgate.net/publication/381937766_EFFECTS_OF_TEACHING_STUDENTS_TO_SOLVE_OPEN_MODELLING_PROBLEMS_ON_UTILITY_INTRINSIC_AND_ATTAINMENT_VALUES</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>21</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Van Dooren, Wim</author></authors><secondary-authors><author>Cs&#237;kos, Csaba</author><author>Rausch, Attila</author><author>Szit&#225;nyi, Judit</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Effects of short-term practicing on realistic responces to missing data problems</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 40th Conference of the International Group for the Psychology of Mathematics Education, PME 40, Szeged, Hungary, August 3&#8211;7, 2016</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">131&#8211;138</style></pages><dates><year><style face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-1-365-46338-9</style></isbn><abstract><style face="normal" font="default" size="100%">In an experimental study with fifth-graders (N=108), we carried out a short-term intervention aimed at improving students&#8217; realistic responses to missing data problems. A control group received nonspecific instructions about solving problems with missing data. An experimental group additionally solved a sample problem and discussed possible solutions. At posttest, students from both groups solved missing data problems. In line with our expectations, the experimental group gave more realistic responses to problems with missing data in which the problem statement did not contain any numbers. However, problems that contained data that, at first glance, appeared sufficient to conduct the required calculations were still answered unrealistically by both groups.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/Krawitz_etal_2016_PME40.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>22</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Hartmann, Luisa-Marie</author></authors><secondary-authors><author>Ikeda, Toshikazu</author><author>Saeki, Akihiko</author><author>Geiger, Vince</author><author>Kaiser, Gabriele</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Taking up Ownership&#8212;What Can Be Learned from Varying Modelling Problems?</style></title><secondary-title><style face="normal" font="default" size="100%">International Horizons in Mathematics Modelling Education</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">333&#8211;343</style></pages><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Cham</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-031-53533-8</style></isbn><abstract><style face="normal" font="default" size="100%">Modelling and problem posing can be seen as activities that mutually support each other. The aim of this study was to investigate the problem posing processes that take place when a modelling problem is reformulated and how these processes target modelling competencies. Sixteen ninth- and tenth-graders were asked to reformulate a modelling problem, and their solution processes were analysed. The findings showed that students extensively engaged in problem variation. They set up and varied situational and numerical assumptions and discussed how these assumptions influenced the authenticity and difficulty of the problem. The findings contribute to a better understanding of the processes involved in reformulating modelling problems and provide a basis for developing teaching approaches that target specific modelling competencies, such as making assumptions through problem variation.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/978-3-031-53533-8_24</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/978-3-031-53533-8_24</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>23</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author><author>Wiehe, Katharina</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>Ikeda, Toshikazu</author><author>Saeki, Akihiko</author><author>Geiger, Vince</author><author>Kaiser, Gabriele</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Students&#8217; Preferences and Beliefs About the Openness of Modelling Problems&#8212;Does Teaching Students How to Solve Open Problems Matter?</style></title><secondary-title><style face="normal" font="default" size="100%">International Horizons in Mathematics Modelling Education</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">369&#8211;379</style></pages><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Cham</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-031-53533-8</style></isbn><abstract><style face="normal" font="default" size="100%">This paper analyses students&#8217; preferences for solving open modelling problems and the belief that a mathematical problem includes all the information needed to find a solution. The research questions were: What are students&#8217; preferences, and what do they believe about openness? How are students&#8217; preferences and beliefs about openness related to achievement in mathematics? Does teaching students how to solve open modelling problems affect their preferences and beliefs about openness? Ninth graders (N&#8201;=&#8201;293) were asked about their preferences, beliefs, and grades and were taught how to solve open modelling problems or closed problems. One important finding was that students with lower grades believed more strongly that mathematical problems are not open. Teaching students how to solve open problems improved this belief and their preferences for solving open modelling problems.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/978-3-031-53533-8_27</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/978-3-031-53533-8_27</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>24</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Hochmuth, Reinhard</author><author>Biehler, Rolf</author><author>Blum, Werner</author><author>Achmetli, Kay</author><author>Rode, Jana</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Bender, Peter</author><author>Haase, J&#252;rgen</author></authors><secondary-authors><author>Biehler, Rolf</author><author>Eichler, Andreas</author><author>Hochmuth, Reinhard</author><author>Rach, Stefanie</author><author>Schaper, Niclas</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Fachwissen zur Arithmetik bei Grundschullehramtsstudierenden &#8211; Entwicklung im ersten Semester und Ver&#228;nderungen durch eine Lehrinnovation</style></title><secondary-title><style face="normal" font="default" size="100%">Lehrinnovationen in der Hochschulmathematik: praxisrelevant &#8211; didaktisch fundiert &#8211; forschungsbasiert</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">611&#8211;644</style></pages><dates><year><style face="normal" font="default" size="100%">2021</style></year></dates><publisher><style face="normal" font="default" size="100%">Springer Spektrum</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-662-62854-6</style></isbn><abstract><style face="normal" font="default" size="100%">In diesem Beitrag berichten wir &#252;ber eine methodisch-inhaltliche Lehrinnovation in der Fachvorlesung &#8222;Arithmetik f&#252;r die Grundschule&#8220; an der Universit&#228;t Kassel und deren Untersuchung im Rahmen des KLIMAGS-Projekts. Die Untersuchung evaluierte Wirkungen der Innovation in einem Vortest-Nachtest-Design mit Experimental- und Kontrollgruppe (n&#8201;=&#8201;131). Die hier haupts&#228;chlich fokussierte Innovation ist die Verwendung mehrerer Darstellungen von Zahlen und Operationen, deren Wechsel sowie deren metakognitive und auf didaktischen Kenntnissen beruhende Explizierung in dem Inhaltsbereich &#8222;Stellenwertsysteme und Teilbarkeitsregeln&#8220;. Dabei werden &#252;ber die verschiedenen Darstellungsebenen schul- und hochschulmathematische Argumentations- und Arbeitsweisen miteinander verkn&#252;pft. Zur Evaluation wurden sowohl quantitative Verfahren verwendet als auch inhaltliche Detailanalysen zu ausgew&#228;hlten Testitems durchgef&#252;hrt. Die Befunde geben Hinweise darauf, dass die Lehrinnovation im Vergleich zu einer Fachvorlesung ohne diese Elemente zu signifikant h&#246;heren Leistungsentwicklungen in dem fokussierten Inhaltsbereich f&#252;hrt, ohne dass die Leistungen in anderen Bereichen nachlassen.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/978-3-662-62854-6_24</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.1007/978-3-662-62854-6_24</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>25</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Achmetli, Kay</author><author>Kolter, Jana</author><author>Blum, Werner</author><author>Bender, Peter</author><author>Biehler, Rolf</author><author>Haase, J&#252;rgen</author><author>Hochmuth, Reinhard</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Roth, J&#252;rgen</author><author>Ames, Judith</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Verbesserte Lehre f&#252;r Grundschullehramtsstudierende &#8211; Ergebnisse aus dem KLIMAGS-Projekt</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2014: Vortr&#228;ge auf der 48. Tagung f&#252;r Didaktik der Mathematik vom 10.03.2014 bis 14.03.2014 in Koblenz</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">659&#8211;662</style></pages><dates><year><style face="normal" font="default" size="100%">2014</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-942197-27-4</style></isbn><abstract><style face="normal" font="default" size="100%">In diesem Beitrag berichten wir von einem Versuch an der Universit&#228;t Kassel im Rahmen des KLIMAGS-Projekt (Kompetenzorientierte LehrInnovation im MAthematikstudium f&#252;r die GrundSchule, im Kompetenzzentrum Hochschuldidaktik Mathematik, www.khdm.de) mit dem Ziel, die universit&#228;re Lehre das Fachs Mathematik im Grundschulstudium zu verbessern.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-1082</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-1082</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>26</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Vogel, Sebastian</author><author>Achmetli, Kay</author><author>Krawitz, Janina</author><author>Blum, Werner</author></authors><secondary-authors><author>Roth, J&#252;rgen</author><author>Ames, Judith</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Wie k&#246;nnen die Lernstandserhebungen in Klasse 8 effektiv genutzt werden? &#8211; Evaluation des Projekts VELM-8</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2014: Vortr&#228;ge auf der 48. Tagung f&#252;r Didaktik der Mathematik vom 10.03.2014 bis 14.03.2014 in Koblenz</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1251&#8211;1254</style></pages><dates><year><style face="normal" font="default" size="100%">2014</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-942197-27-4</style></isbn><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-1045</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-1045</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>27</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Vogel, Sebastian</author><author>Achmetli, Kay</author><author>Krawitz, Janina</author><author>Blum, Werner</author></authors><secondary-authors><author>Greefrath, Gilbert</author><author>K&#228;pnick, Friedhelm</author><author>Stein, Martin</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">VELM-8 &#8211; Ein Projekt zur Verbesserung der Effektivit&#228;t der Lernstandserhebungen Mathematik Klasse 8</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2013: Vortr&#228;ge auf der 47. Tagung f&#252;r Didaktik der Mathematik vom 04.03.2013 bis 08.03.2013 in M&#252;nster</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1042&#8211;1045</style></pages><dates><year><style face="normal" font="default" size="100%">2013</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-942197-33-5</style></isbn><abstract><style face="normal" font="default" size="100%">Im vorliegenden Beitrag soll die Ausgangslage fu&#776;r das aktuelle Projekt VELM-8 (&#8222;Verbesserung der Effektivita&#776;t der Lernstandserhebungen Mathematik Klasse 8&#8220;) beschrieben und soll dieses Projekt vorgestellt werden.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-14066</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-14066</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>28</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Vogel, Sebastian</author><author>Blum, Werner</author><author>Achmetli, Kay</author><author>Krawitz, Janina</author></authors><secondary-authors><author>Bausch, Isabell</author><author>Pinkernell, Guido</author><author>Schmitt , Oliver</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Zum Potential von Lernstandserhebungen f&#252;r die Unterrichtsentwicklung - Das Projekt VELM-8</style></title><secondary-title><style face="normal" font="default" size="100%">Unterrichtsentwicklung und Kompetenzorientierung</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">105&#8211;118</style></pages><dates><year><style face="normal" font="default" size="100%">2013</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-942197-48-9</style></isbn><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://miami.uni-muenster.de/Record/5041085d-78e8-4058-ab08-556f4f8718a3/TOC</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>29</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Caluori, Franco</author><author>Linneweber-Lammerskitten, Helmut</author><author>Streit, Christine</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Wenn der Realit&#228;tsbezug zum Problem wird: &#8222;problematische&#8220; Aufgaben und multiple L&#246;sungen in der Primarstufe</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2015: Vortr&#228;ge auf der 49. Tagung f&#252;r Didaktik der Mathematik vom 09.02.2015 bis 13.02.2015 in Basel</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">504&#8211;507</style></pages><dates><year><style face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-942197-92-2</style></isbn><abstract><style face="normal" font="default" size="100%">Die F&#228;higkeit, realit&#228;tsbezogene Aufgaben zu l&#246;sen, ist eine wichtige Kompetenz, die national und international gro&#223;e Beachtung gefunden hat und im Unterricht weltweit vermittelt werden soll. Empirische Studien zeigen jedoch, dass Sch&#252;lerinnen und Sch&#252;ler bei Modellierungsaufgaben h&#228;ufig direkte Rechenoperationen mit den gegebenen Zahlen durchf&#252;hren, ohne den in der Aufgabenstellung gegebenen Realkontext angemessen zu ber&#252;cksichtigen (Verschaffel et al., 2000). In der vorliegenden Untersuchung wurde der Einfluss der Aufforderung, eine zweite L&#246;sung zu offenen Modellierungsaufgaben zu erstellen, auf diese ausgepr&#228;gte Neigung von Dritt- und Viertkl&#228;ssler (N=75) analysiert. Exemplarisch wird das L&#246;sungsverhalten von Lernenden beim Bearbeiten einer spezifischen Modellierungsaufgabe, die in der Forschung als eine der so genannten Problematic Problems bekannt ist, betrachtet.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-16692</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-16692</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>30</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>B&#246;ckmann, Matthias</author><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author></authors><secondary-authors><author>Institut f&#252;r Mathematik und Informatik Hochschule Heidelberg</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Realit&#228;t oder Mathematik? Wie bewerten zuk&#252;nftige Lehrer Sch&#252;lerl&#246;sungen zu realit&#228;tsbezogenen Aufgaben?</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2016: Vortr&#228;ge auf der 50. Tagung f&#252;r Didaktik der Mathematik vom 07.03.2016 bis 11.03.2016 in Heidelberg</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">165&#8211;168</style></pages><dates><year><style face="normal" font="default" size="100%">2016</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-014-6</style></isbn><abstract><style face="normal" font="default" size="100%">Ein wichtiges Ziel des Mathematikunterrichts ist Schu&#776;lerInnen zu befa&#776;higen, realita&#776;tsbezogene Probleme im Alltag zu lo&#776;sen. Dieses Ziel la&#776;sst sich durch den Einsatz von realita&#776;tsbezogenen Aufgaben im Unterricht und ada&#776;quaten Unterrichtsmethoden umsetzen. Allerdings kommen Realita&#776;tsbezu&#776;ge in der Schule ha&#776;ufig zu kurz und Schu&#776;lerInnen sind daher nicht in der Lage, realistische Lo&#776;sungen zu erstellen. In diesem Beitrag soll untersucht werden, in wie weit ku&#776;nftige Lehrerinnen und Lehrer Realita&#776;tsbezu&#776;ge beim Erstellen eigener Lo&#776;sungen beachten und wie sie mathematische und realita&#776;tsbezogene Fehler bewerten. Dafu&#776;r wurden in der vorliegenden Studie so genannte &#8222;Problematic Problems&#8220; (P-Problems) eingesetzt.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-17325</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-17325</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>31</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Chang, Yu-Ping</author><author>Yang, Kai-Lin</author></authors><secondary-authors><author>Kortenkamp, Ulrich</author><author>Kuzle, Ana</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Leseverst&#228;ndnisfragen und ihre Auswirkungen auf Freude und Leistungen beim mathematischen Modellieren: Was nutzt ein tieferes Situationsverst&#228;ndnis?</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2017: Vortr&#228;ge auf der 51. Tagung f&#252;r Didaktik der Mathematik vom 27.02.2017 bis 03.03.2017 in Potsdam</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">573&#8211;576</style></pages><dates><year><style face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-071-9</style></isbn><abstract><style face="normal" font="default" size="100%">Leseverst&#228;ndnis gilt als wichtige Voraussetzung f&#252;r das erfolgreiche L&#246;sen von Modellierungsaufgaben. Im Beitrag wird berichtet, inwiefern die Modellierungsleistung von Neuntkl&#228;sslern und ihre Freude an der Aufgabenbearbeitung (N=165) durch das Stellen von Leseverst&#228;ndnisfragen und die damit einhergehende tiefere Besch&#228;ftigung mit dem Aufgabentext positiv beeinflusst werden kann.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-18492</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-18492</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>32</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>B&#246;ckmann, Matthias</author><author>Schmelzer, Madlin</author></authors><secondary-authors><author>B&#246;nnighausen, Marion</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Textverstehen und mathematisches Modellieren. Konzeption und Evaluation des Praxisprojekts Mathematik</style></title><secondary-title><style face="normal" font="default" size="100%">Praxisprojekte in Kooperationsschulen: Fachdidaktische Modellierung von Lehrkonzepten zur F&#246;rderung strategiebasierten Textverstehens in den F&#228;chern Deutsch, Geographie, Geschichte und Mathematik</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">223&#8211;249</style></pages><dates><year><style face="normal" font="default" size="100%">2019</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-079-5</style></isbn><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>33</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Chang, Yu-Ping</author><author>Yang, Kai-Lin</author></authors><secondary-authors><author>Fachgruppe Didaktik der Mathematik der Universit&#228;t Paderborn</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Helfen Leseverst&#228;ndnisfragen, Modellierungsaufgaben zu l&#246;sen? Deutsche und taiwanesische Sch&#252;ler im Vergleich</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2018: Vortr&#228;ge auf der 52. Tagung f&#252;r Didaktik der Mathematik vom 05.03.2018 bis 09.03.2018 in Paderborn</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1083&#8211;1086</style></pages><dates><year><style face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-089-4</style></isbn><abstract><style face="normal" font="default" size="100%">Im Beitrag werden die Befunde einer experimentellen Studie zum Leseversta&#776;ndnis beim mathematischen Modellieren vorgestellt. Die zentrale Frage der Studie war, welche Effekte das Stellen von Leseversta&#776;ndnisfragen und die damit einhergehende intensivere Auseinandersetzung mit dem Aufga- bentext, auf das Situationsversta&#776;ndnis und die Modellierungsleistung von deutschen und taiwanesischen Neuntkla&#776;sslern hat. Des Weiteren werden Zusammenha&#776;nge zwischen Leseversta&#776;ndnis und Modellierungsleistung sowie Unterschiede der deutschen und taiwanesischen Lernenden analysiert.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-19482</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-19482</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>34</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Siller, Hans-Stefan</author><author>Weigel, Wolfgang</author><author>W&#246;rler, Jan Franz</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Negative Effekte des Zeichnens auf das Probleml&#246;sen: Eine Frage der Qualit&#228;t?</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2020: Vortr&#228;ge auf der 54. Tagung f&#252;r Didaktik der Mathematik vom 09.03.2018 bis 13.03.2018 in W&#252;rzburg</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">557&#8211;560</style></pages><dates><year><style face="normal" font="default" size="100%">2020</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-139-6</style></isbn><abstract><style face="normal" font="default" size="100%">Eine Skizze zu zeichnen gilt als hilfreiche Strategie fu&#776;r das mathematische Problemlo&#776;sen. Allerdings wurde ein negativer Effekt des Skizzenzeichnens auf die Leistung beim Lo&#776;sen nichtlinearer Geometrieaufgaben gefunden. Der Beitrag berichtet von einer experimentellen Studie, die zum Ziel hat, diesen u&#776;berraschenden, negativen Effekt zu replizieren und zu erkla&#776;ren. Als mo&#776;gliche Ursachen werden lineare U&#776;bergeneralisierungen der Neunt- bis Elftkla&#776;ssler und die Qualita&#776;t der Strategienutzung analysiert.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-21382</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-21382</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>35</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Hartmann, Luisa-Marie</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Hein, Kerstin</author><author>Heil, Cathleen</author><author>Ruwisch, Silke</author><author>Prediger, Susanne</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Ist selbstentwickelt besser? Einfluss von Problem Posing auf Interesse und Leistungen beim Modellieren</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2021: Vortr&#228;ge vom GDM-Monat 2021 der Gesellschaft f&#252;r Didaktik der Mathematik vom 01.03.2021 bis 25.03.2021</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">257&#8211;260</style></pages><dates><year><style face="normal" font="default" size="100%">2021</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-183-9</style></isbn><abstract><style face="normal" font="default" size="100%">Problem Posing gilt als innovative Methode, um kognitive wie auch affektiv-motivationale Aspekte des Lernens von Mathematik zu f&#246;rdern. Der Beitrag fokussiert modellierungsbezogenes Problem Posing, das Entwickeln eigener Fragestellungen zu realen Situationen. Vorgestellt werden die Ergebnisse einer experimentellen Studie mit 196 Neunt- und Zehntkl&#228;sslern. In der Studie wurde untersucht, ob das Entwickeln und L&#246;sen eigener Fragestellungen zu realen Situationen einen positiven Effekt auf das Interesse und die Leistung der Lernenden bei der Aufgabenbearbeitung haben. Im Beitrag werden Implikationen f&#252;r Theorien des Problem Posings und des Interesses sowie praktische Implikationen f&#252;r das Lernen durch Problem Posing diskutiert.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-22298</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-22298</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>36</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Baumanns, Lukas</author><author>Fritzlar, Torsten</author></authors><secondary-authors><author>IDMI - Primar Goethe-Universit&#228;t Frankfurt</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Minisymposium 08: Problem Posing und Probleml&#246;sen</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2022: Vortr&#228;ge auf der 56. Tagung f&#252;r Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">217&#8211;218</style></pages><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-207-2</style></isbn><abstract><style face="normal" font="default" size="100%">Probleml&#246;sen ist seit vielen Jahrzehnten ein zentrales Forschungsgebiet mit gro&#223;er Bedeutung f&#252;r das Lehren und Lernen von Mathematik. Innerhalb dieser langen Forschungstradition ergeben sich stets neue Perspektiven auf das Probleml&#246;sen, die den Diskurs weiterf&#252;hren. Problem Posing &#8211; das Aufwerfen eigener Probleme &#8211; ist ein wesentlich j&#252;ngeres Thema in der Mathematikdidaktik. Problem Posing besitzt gro&#223;es Potential f&#252;r die F&#246;rderung des Probleml&#246;sens, stellt aber auch f&#252;r sich genommen ein wichtiges Lernziel dar. Im Gegensatz zum Probleml&#246;sen steht die Forschung zum Problem Posing noch am Anfang. Auch wenn bereits erste Vorschl&#228;ge f&#252;r eine systematische, theoriebasierte Strukturierung des Feldes gemacht wurden, fehlt es bislang an etablierten, empirisch abgesicherten Modellen. Im Minisymposium wurden aktuelle Forschungsprojekte und -ergebnisse zum Probleml&#246;sen und zum Problem Posing vorgestellt und gemeinsam diskutiert. Im Folgenden werden die Beitr&#228;ge des Minisymposiums zusammengefasst.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-23435</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-23435</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>37</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Hartmann, Luisa-Marie</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>IDMI - Primar Goethe-Universit&#228;t Frankfurt</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Modellieren beim Problem Posing &#8211; Modellierungsaktivit&#228;ten beim Problem Posing zu realweltlichen Situationen</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2022: Vortr&#228;ge auf der 56. Tagung f&#252;r Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">223&#8211;226</style></pages><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-207-2</style></isbn><abstract><style face="normal" font="default" size="100%">Das L&#246;sen von mathematischen Problemen ist eine zentrale Grundlage f&#252;r das Betreiben von Mathematik. Au&#223;erhalb des Schulunterrichts liegen diese Probleme jedoch nur selten vorgefertigt vor und m&#252;ssen zun&#228;chst entwickelt werden. Die Entwicklung eigener Probleme (Problem Posing) hat in den letzten Jahren in der mathematikdidaktischen Forschung stark an Bedeutung gewonnen. Insbesondere gilt das Problem Posing als ein gewinnbringender Ansatz zur F&#246;rderung des Probleml&#246;sens, da die Entwicklung eigener Probleme wichtige Probleml&#246;seprozesse anspricht (Cai &amp; Leikin, 2020). Das Modellieren kann als Probleml&#246;sen realweltlicher Probleme charakterisiert werden. Demnach ist es m&#246;glich, dass Problem Posing zu gegebenen realweltlichen Situationen (modellierungsbezogenes Problem Posing) auch zur F&#246;rderung des mathematischen Modellierens gewinnbringend eingesetzt werden kann. Bisher existiert nur wenig Forschung zum Problem Posing aus Modellierungsperspektive. Um das Potential des Problem Posings f&#252;r das Modellieren zu untersuchen, soll die Verbindung zwischen den Problem Posing und Modellierungsprozessen aus einer kognitiven Perspektive analysiert werden.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-23436</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-23436</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>38</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Volbers, Gudula</author><author>Schukajlow, Stanislaw</author><author>Greefrath, Gilbert</author><author>Krawitz, Janina</author></authors><secondary-authors><author>IDMI - Primar Goethe-Universit&#228;t Frankfurt</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Zeichnen einer Skizze - (K)eine geeignete heuristische Strategie zur L&#246;sung nicht-linearer Probleme?</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2022: Vortr&#228;ge auf der 56. Tagung f&#252;r Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">231&#8211;234</style></pages><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-207-2</style></isbn><abstract><style face="normal" font="default" size="100%">W&#228;hrend das Anfertigen einer Skizze im Allgemeinen als leistungsstarke Strategie zur L&#246;sung mathematischer Probleme gilt, stellten De Bock et al. (2003) &#252;berraschenderweise fest, dass sich das Zeichnen einer Skizze negativ auf die Leistung von Lernenden beim L&#246;sen von Aufgaben zu nicht linearen Geometrieproblemen auswirkt. Als wichtigen Grund f&#252;r diesen negativen Effekt erkannten die Autoren, dass das Anfertigen einer Skizze die Tendenz zur sogenannten Linearen &#220;bergeneralisierung verst&#228;rkte. Eine an die Ergebnisse der Analyse von De Bock et al. (2003) ankn&#252;pfende Studie von Krawitz &amp; Schukajlow (2020) deutete an, dass das Zeichnen einer Skizze neben Linearen &#220;bergeneralisierungen auch andere Fehler triggern muss. Ziel dieser Untersuchung ist es, weitere Faktoren f&#252;r den negativen Effekt der Skizzenerstellung auf die Leistung zu finden. Diese sollen perspektivisch Ans&#228;tze f&#252;r Interventionen geben, die eine produktive Nutzung selbst erstellter Skizzen bei der Bearbeitung von nicht-linearen Geometrieproblemen erm&#246;glichen. Daf&#252;r werden in einem ersten Schritt die Daten der Studie von Krawitz &amp; Schukajlow (2020) reanalysiert.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-23438</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-23438</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>39</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author><author>Kanefke, Jonas</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>IDMI - Primar Goethe-Universit&#228;t Frankfurt</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Effekte einer Instruktion zu offenen Aufgaben: &#8222;Wenn ich w&#252;sste, was hier fehlt, dann k&#246;nnte ich sie l&#246;sen&#8220;</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2022: Vortr&#228;ge auf der 56. Tagung f&#252;r Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">337&#8211;340</style></pages><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-207-2</style></isbn><abstract><style face="normal" font="default" size="100%">Die Bearbeitung von Modellierungsaufgaben erfordert anspruchsvolle &#220;bersetzungsprozesse zwischen Realit&#228;t und Mathematik und der Erwerb der Modellierungskompetenz ist ein wichtiges Ziel des Mathematikunterrichts. Die Erforschung der Frage, wie alltags- und berufsrelevante Inhalte erfolgreich im Unterricht vermittelt werden k&#246;nnen, wird als eine zentrale Aufgabe der Lehr-Lernforschung angesehen. Eine wichtige Eigenschaft alltags- und berufsrelevanter Inhalte ist ihre Offenheit. Im Projekt OModA (Offene Modellierungsaufgaben in einem selbst&#228;ndigkeitsorientierten Mathematikunterricht), welches von der Deutschen Forschungsgemeinschaft gef&#246;rdert wird (GZ: RA 1940/2-1 und SCHU 2629/5-1), wird untersucht, welche Effekte eine auf die Anforderungen der offenen Modellierungsaufgaben zugeschnittene Instruktion auf kognitive und motivationale Faktoren hat (Instruktionsstudie) und wie sich der Unterricht mit offenen Modellierungsaufgaben auf kognitive und motivationale Faktoren auswirkt (Unterrichtsstudie). In diesem Beitrag berichten wir erste Ergebnisse der Instruktionsstudie hinsichtlich Wirkungen auf kognitive Faktoren.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-23493</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-23493</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>40</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Wiehe, Katharina</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>IDMI - Primar Goethe-Universit&#228;t Frankfurt</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">L&#246;sen offener Aufgaben f&#246;rdern - Konzeption einer Unterrichtsstudie im Projekt OModA</style></title><secondary-title><style face="normal" font="default" size="100%">Beitr&#228;ge zum Mathematikunterricht 2022: Vortr&#228;ge auf der 56. Tagung f&#252;r Didaktik der Mathematik vom 29.08.2022 bis 02.09.2022 in Frankfurt am Main</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1371&#8211;1376</style></pages><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">WTM-Verlag</style></publisher><isbn><style face="normal" font="default" size="100%">978-3-95987-207-2</style></isbn><abstract><style face="normal" font="default" size="100%">Offene Problemstellungen nehmen im Mathematikunterricht eine wichtige Rolle ein. Auch im Alltag und in den Wissenschaften (wie den Naturwissenschaften oder der Mathematik) sind h&#228;ufig nicht alle Informationen vorhanden, die f&#252;r die L&#246;sung eines Problems n&#246;tig w&#228;ren (Wu, 1994). Ein bestimmter Typ offener Aufgaben sind offene Modellierungsaufgaben, die sich durch ihren Realit&#228;tsbezug auszeichnen und anspruchsvolle &#220;bersetzungsprozesse zwischen der Realit&#228;t und der Mathematik im Sinne des Modellierungskreislaufes erfordern. Die Offenheit wurde in bisherigen Studien zum Modellieren selten untersucht und es fehlt bislang an empirisch untersuchten F&#246;rderungsans&#228;tzen, die sich gezielt auf die Offenheit als schwierigkeitsgenerierendes Merkmal beziehen. An dieser Stelle setzt das OModA-Projekt (Offene Modellierungsaufgaben in einem selbst&#228;ndigkeitsorientierten Mathematikunterricht) an. Eine zentrale Fragestellung des Projekts ist, welche Effekte Unterricht mit offenen Modellierungsaufgaben im Vergleich zu geschlossenen Modellierungsaufgaben auf Motivation und Leistung beim Modellieren hat. Durchgef&#252;hrt wird eine Unterrichtsstudie mit experimentellem Design, in der die Wirkungen einer vierst&#252;ndigen Lernumgebung zu offenen bzw. geschlossenen Aufgaben verglichen wird. Ziele dieses Beitrages sind, die Konzeption der Lernumgebungen vorzustellen und erste Ergebnisse aus der Pilotierungsstudie zu berichten.</style></abstract><urls><related-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.17877/DE290R-23448</style></url></related-urls></urls><electronic-resource-num><style face="normal" font="default" size="100%">10.17877/DE290R-23448</style></electronic-resource-num></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>41</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Inprasitha, Maitree</author><author>Changsri, Narumon</author><author>Boonsena, Nisakorn</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">A negative effect of the drawing strategy on problem solving: a question of quality?</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 44th Conference of the International Group for the Psychology of Mathematics Education, PME 44 Virtual, Khon Kaen, Thailand, July 19&#8211;22, 2021</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">154&#8211;162</style></pages><dates><year><style face="normal" font="default" size="100%">2021</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-616-93830-2-4</style></isbn><abstract><style face="normal" font="default" size="100%">Make a drawing is known to be a powerful strategy for solving mathematical problems. But surprisingly, the drawing strategy was found to negatively affect the ability to solve non-linear geometry problems. Our study replicates and extends this finding by addressing the quality of the drawing strategy, which might explain the negative effect. In a randomized controlled trial with 180 students (ninth- to eleventh-graders), we enhanced drawing quality by prompting the students to highlight important elements in their drawings. Our results replicated the negative effect of the drawing strategy on performance and confirmed the quality of the drawing strategy as an important factor that affected the number of linear overgeneralizations. The roles of drawing quality and other factors that might influence the ability to solve such problems are discussed.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/KrawitzSchukajlow_2020_PME.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>42</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Hartmann, Luisa-Marie</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Fern&#225;ndez, Ceneida</author><author>Llinares, Salvador</author><author>Guti&#233;rrez, &#193;ngel</author><author>Planas, N&#250;ria</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">The Process of Modelling-related Problem Posing - A Case Study with Preservice Teachers</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, PME 45, Alicante, Spain, July 18&#8211;23, 2022</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">355&#8211;362</style></pages><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-84-1302-176-8</style></isbn><abstract><style face="normal" font="default" size="100%">In real life, problems emerge from situations and often need to be posed before they can be solved. Despite the ongoing emphasis on the processes involved in solving modelling problems, little is known about the process of problem posing. To help fill this gap, the current study examined (1) what activities are involved in modelling-related problem posing and (2) the sequence in which they occur. For this purpose, we invited seven preservice teachers to pose a problem based on given real-world situations and analyzed their problem-posing activities. We identified the five most frequent activities that occurred in the sequence: understanding&#8211;exploring&#8211; generating&#8211;problem solving&#8211;evaluating. These results contribute to the uncovering of important activities and contribute to theories of modelling and problem posing.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/Hartmann_etal_2022_PME45.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>43</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Kanefke, Jonas</author><author>Schukajlow, Stanislaw</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>Fern&#225;ndez, Ceneida</author><author>Llinares, Salvador</author><author>Guti&#233;rrez, &#193;ngel</author><author>Planas, N&#250;ria</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Making realistic assumptions in mathematical modelling</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, PME 45, Alicante, Spain, July 18&#8211;23, 2022</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">59&#8211;66</style></pages><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-84-1302-177-5</style></isbn><abstract><style face="normal" font="default" size="100%">Making realistic assumptions is an important part of solving open modelling problems and also a potential source of errors. But little is known about the difficulties that result from the openness of modelling problems and how they can be addressed in interventions. Here, we focus on two central solution steps that are necessary for making assumptions: noticing the openness and estimating the missing quantities. In a qualitative study with four ninth graders, we asked students to solve a modelling problem after informing them about the openness of the problem. We identified barriers that expand the two-step model (e.g., trouble integrating assumptions into the model). In addition, informing students about the openness of the problem improved their solution to the problem at hand but did not help them solve subsequent problems.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/Krawitz_etal_2022_PME45.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>44</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Schukajlow, Stanislaw</author><author>Krawitz, Janina</author><author>Kanefke, Jonas</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>Fern&#225;ndez, Ceneida</author><author>Llinares, Salvador</author><author>Guti&#233;rrez, &#193;ngel</author><author>Planas, N&#250;ria</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Interest and performance in solving open modelling problems and closed real-world problems</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 45th Conference of the International Group for the Psychology of Mathematics Education, PME 45, Alicante, Spain, July 18&#8211;23, 2022</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">403&#8211;410</style></pages><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-84-1302-177-5</style></isbn><abstract><style face="normal" font="default" size="100%">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.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/Schukajlow_etal_2022_PME45.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>45</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Bergqvist, Ewa</author><author>&#214;sterholm, Magnus</author><author>Granberg, Carina</author><author>Sumpter, Lovisa</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Activation and monitoring of prior mathematical knowledge in modelling processes</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, PME 42, Ume&#229;, Sweden, July 3&#8211;8, 2018</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">243&#8211;250</style></pages><dates><year><style face="normal" font="default" size="100%">2018</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-91-7601-904-7</style></isbn><abstract><style face="normal" font="default" size="100%">In a qualitative study with eighth to tenth graders (N=18), we investigated whether the activation of prior mathematical knowledge would promote or interfere with solution processes as students solved modelling problems. In addition, we analyzed the role of metacognitive monitoring of knowledge activation. Participants with different prior mathematical knowledge solved modelling problems in which multiple solution approaches were possible. We found that the activation of inappropriate prior mathematical knowledge negatively impacted modelling. Negative effects of prior knowledge also occurred if a second solution for a problem was required because learners stuck to the prior knowledge of their first approach. Monitoring of knowledge activation was rarely found, even when it would have been helpful.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/Krawitz_Schukajlow_2018_PME42.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>46</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Wiehe, Katharina</author><author>Rakoczy, Katrin</author></authors><secondary-authors><author>Drijvers, Paul</author><author>Csapodi, Csaba</author><author>Palm&#233;r, Hanna</author><author>Gosztonyi, Katalin</author><author>K&#243;nya, Eszter</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Experiences of competence and autonomy during a teaching intervention on mathematical modelling</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 13th Congress of the European Society for Research in Mathematics Education, CERME 13, Budapest, Hungary, July 10&#8211;14, 2023</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1458&#8211;1465</style></pages><dates><year><style face="normal" font="default" size="100%">2023</style></year></dates><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><isbn><style face="normal" font="default" size="100%">978-963-7031-04-5</style></isbn><abstract><style face="normal" font="default" size="100%">Experiences of competence and autonomy are essential for intrinsic motivation, social development, and well-being. However, little is known about how these constructs are related to previous achievement in mathematics. In the present study, we investigated whether ninth-graders (N = 83) with different levels of achievement differ in their experiences of competence and autonomy and whether their experiences change during a teaching intervention focused on modelling. We found that high- and low-achieving learners did not differ in competence or autonomy. However, competence and autonomy developed differently across the time period of the teaching intervention. The experience of competence increased for high achievers, and autonomy decreased for low achievers. The results contribute to a better understanding of how intra- and interindividual differences are related to competence and autonomy and provide insights for effective interventions.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://hal.science/CERME13/hal-04418267v1</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>47</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author><author>Chang, Yu-Ping</author><author>Yang, Kai-Lin</author></authors><secondary-authors><author>Berinderjeet, Kaur</author><author>Weng-Kin, Ho</author><author>Tin-Lam, Toh</author><author>Ban-Heng, Choy</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Reading comprehension, enjoyment, and performance: how important is a deeper situation model?</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 41st Conference of the International Group for the Psychology of Mathematics Education, PME 41, Singapore, July 17&#8211;22, 2017</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">97&#8211;104</style></pages><dates><year><style face="normal" font="default" size="100%">2017</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">978-981-11-3742-6</style></isbn><abstract><style face="normal" font="default" size="100%">In an experimental study with ninth graders (N=165), we investigated whether presenting reading comprehension prompts would have a positive impact on students&#8217; enjoyment and performance in modelling. Contrary to our expectations, the enjoyment and modelling performance of students who received reading comprehension prompts were similar to those of the students in the control group. Further, we found that students&#8217; success in answering the reading comprehension questions was positively related to their enjoyment and modelling performance. However, after we controlled for intra-mathematical performance, the relation between reading comprehension and modelling disappeared, whereas the relation between reading comprehension and enjoyment remained significant. Implications for future research are discussed.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://ivv5hpp.uni-muenster.de/u/sschu_12/pdf/Publikationen/Krawitz_et_al_2017_PME41.pdf</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>48</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Hartmann, Luisa-Marie</author><author>Krawitz, Janina</author><author>Schukajlow, Stanislaw</author></authors><secondary-authors><author>Hodgen, Jeremy</author><author>Geraniou, Eirini</author><author>Bolondi, Giorgio</author><author>Ferretti, Federica</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Modelling while problem posing - A case study of preservice teachers</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 12th Congress of the European Society for Research in Mathematics Education, CERME 12, Bozen-Bolzano, Italy, February 2&#8211;6, 2022</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1075&#8211;1082</style></pages><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><isbn><style face="normal" font="default" size="100%">979-1-221-02537-8</style></isbn><abstract><style face="normal" font="default" size="100%">Because problem posing might enhance activities that are necessary for solving real-world problems, it has the potential to foster modelling. However, systematic research on the connection between problem posing and modelling is largely missing. Therefore, in the present study, we investigated (1) the modelling activities that take place when posing problems that are based on given real-world situations and (2) the extent to which modelling activities occur with different problem-posing activities. To address these questions, we asked seven preservice teachers to first pose a problem based on a given real-world situation and then to solve their self-generated problem. A qualitative content analysis revealed that modelling activities that are close to the real-world situation (e.g., understanding, simplifying, and structuring the given pieces of information) are involved in problem posing. This result indicates that problem posing has the potential to foster mathematical modelling.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://hal.science/CERME12/hal-03759022/</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>49</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Krawitz, Janina</author><author>Hartmann, Luisa-Marie</author></authors><secondary-authors><author>Hodgen, Jeremy</author><author>Geraniou, Eirini</author><author>Bolondi, Giorgio</author><author>Ferretti, Federica</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Preservice teachers&#8217; interest and self-efficacy beliefs while posing problems</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 12th Congress of the European Society for Research in Mathematics Education, CERME 12, Bozen-Bolzano, Italy, February 2&#8211;6, 2022</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">1392&#8211;1399</style></pages><dates><year><style face="normal" font="default" size="100%">2022</style></year></dates><publisher><style face="normal" font="default" size="100%">ERME</style></publisher><isbn><style face="normal" font="default" size="100%">979-1-221-02537-8</style></isbn><abstract><style face="normal" font="default" size="100%">Problem posing is considered to have great potential to foster students&#8217; motivation because it provides the opportunity to create problems on the basis of individual interests and abilities. However, whether learners indeed use this opportunity is an open question. The aim of the present study was to investigate the role of interest and self-efficacy expectations in problem posing. In interviews, we asked preservice teachers (N = 7) why they decided to pose a certain problem, and we focused on their interest and self-efficacy expectations when we analyzed the data. The most important factor was preservice teachers&#8217; interest in the answer to the posed problem. Self-efficacy expectations have been also revealed as important for their decision to pose a certain problem. Preservice teachers wanted to be able to solve the problem or to master problem posing by posing multiple problems or a problem with adequate difficulty.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://hal.science/hal-03745611/</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>50</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Leikin, Roza</author><author>Pitta-Pantazi, Demetra</author><author>Cai, Jinfa</author><author>Hui-Yu, Hsu</author><author>Felmer, Patricio</author><author>G&#246;deke, Pia</author><author>Karp, Alexander</author><author>Koichu, Boris</author><author>Krawitz, Janina</author><author>Robison, Victoria</author><author>Schukajlow, Stanislaw</author><author>Zazkis, Rina</author></authors><secondary-authors><author>Cornejo, Claudia</author><author>Felmer, Patricio</author><author>G&#243;mez, David Maximiliano</author><author>Dartnell, Pablo</author><author>Araya, Paulina</author><author>Peri, Armando</author><author>Randolph, Valeria</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Curiosity in mathematics: Theoretical, methodological and practical lenses</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: General Contributions, PME 48, Santiago, Chile, July 28&#8211;August 02, 2025</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">151&#8211;171</style></pages><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">PME48General</style></isbn><abstract><style face="normal" font="default" size="100%">Despite its fundamental importance, mathematical curiosity has received limited attention in mathematics education research. Knuth (2002) defines it as both the desire to learn mathematics and the drive to explore mathematical concepts, particularly through problem-solving and problem-posing activities. The broader psychological understanding of curiosity emphasizes its role as an intrinsic motivator for acquiring new information, linking it to cognitive engagement, including intellectual, epistemic, and information-seeking pursuits (Gruber et al., 2019). This suggests that mathematical curiosity is associated with knowledge gaps that students are motivated to overcome. However, this definition alone does not provide mathematics educators neither with a complete understanding of the nature and structure of mathematical curiosity, nor how it develops and can be fostered. While research interest in mathematical curiosity is emerging (Leikin, 2023), overall research on curiosity in mathematics education remains limited. This research forum aims to draw the PME community&#8217;s attention to this important topic.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.researchgate.net/publication/395028169_CURIOSITY_IN_MATHEMATICS_THEORETICAL_METHODOLOGICAL_AND_PRACTICAL_LENSES</style></url></related-urls></urls></record><record><source-app name="EndNote" version="20.6">EndNote</source-app><rec-number>51</rec-number><ref-type name="Conference Paper">47</ref-type><contributors><authors><author>Schmidt, Laura</author><author>Krawitz, Janina</author><author>Schnepel, Susanne</author></authors><secondary-authors><author>Cornejo, Claudia</author><author>Felmer, Patricio</author><author>G&#243;mez, David Maximiliano</author><author>Dartnell, Pablo</author><author>Araya, Paulina</author><author>Peri, Armando</author><author>Randolph, Valeria</author></secondary-authors></contributors><titles><title><style face="normal" font="default" size="100%">Real-world connections in mathematics education for students with intellectual disabilities: A systematic literature review</style></title><secondary-title><style face="normal" font="default" size="100%">Proceedings of the 48th Conference of the International Group for the Psychology of Mathematics Education: Research Reports, PME 48, Santiago, Chile, July 28&#8211;August 02, 2025</style></secondary-title></titles><pages><style face="normal" font="default" size="100%">259&#8211;266</style></pages><dates><year><style face="normal" font="default" size="100%">2025</style></year></dates><publisher><style face="normal" font="default" size="100%">PME</style></publisher><isbn><style face="normal" font="default" size="100%">PME48Reports</style></isbn><abstract><style face="normal" font="default" size="100%">In this systematic literature review, we examined the most recent research (2020-2024) on real-world connections in mathematics education for students with special educational needs, particularly those with intellectual disabilities. Our analysis of 44 empirical studies revealed that this research primarily used experimental single-case designs, with most research conducted in the US. The majority of the studies employed standard word problems, while realistic word problems were rarely found, and only one study utilized authentic and open problems. The findings call for more consistent terminology in describing special educational needs and for the use of more authentic tasks to better help learners with special educational needs develop practical mathematical skills.</style></abstract><work-type><style face="normal" font="default" size="100%">Peer-Reviewed</style></work-type><urls><related-urls><url><style face="normal" font="default" size="100%">https://www.researchgate.net/publication/394399395_Real-world_connections_in_mathematics_education_for_students_with_intellectual_disabilities_A_systematic_literature_review</style></url></related-urls></urls></record></records></xml>