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Previous DIF research found that African American and White test takers performed differently across mathematics content areas and item difficulty level. This study extends previous DIF research results from a national mathematics assessment with a combination of DIF criteria. Possible explanations for the patterns of items that show DIF are also d...
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Collaborative problem solving (CPS) competency has become increasingly important which has led to an increase in developing CPS tasks for assessment purposes. The design of CPS tasks is critical, as design decisions can influence the opportunities individuals have to display targeted CPS behaviors. In this study, we describe how item characteristic...
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En este trabajo exploramos el uso de una base de orientación (Jorba y Sanmartí, 1996) como herramienta para promover los procesos metacognitivos en resolución de problemas de patrones. Realizamos un análisis inductivo de las producciones del alumnado con el objetivo de caracterizar los procesos metacognitivos escritos derivados de la creación y apl...

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... Affective variables Affect reflects an important aspect of learning in general and of mathematics education in particular (e.g., Goldin et al., 2016). Two studies (1%) related eye movements to mathematics-specific affective variables, namely mathematical self-concept (Strohmaier et al., 2017) and mathematics anxiety (Hunt et al., 2015). ...
... In general, if data types were analyzed in relation to each other, it was often the relation between eye movements and accuracy that was analyzed. Richer triangulations were done with gestures and communication (Hannula & Williams, 2016;Shvarts, 2018aShvarts, , 2018b, interviews and stimulated recall (Klein et al., 2018;; see also , think-aloud protocols and selfreports (Cimen & Campbell, 2012;Green et al., 2007;Ögren et al., 2017;, cognitive load (Lin & Lin, 2014b), affective variables (Hunt et al., 2015;Strohmaier et al., 2017), or skin conductance and EEG (Muldner & Burleson, 2015). ...
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Eye tracking is an increasingly popular method in mathematics education. While the technology has greatly evolved in recent years, there is a debate about the specific benefits that eye tracking offers and about the kinds of insights it may allow. The aim of this review is to contribute to this discussion by providing a comprehensive overview of the use of eye tracking in mathematics education research. We reviewed 161 eye-tracking studies published between 1921 and 2018 to assess what domains and topics were addressed, how the method was used, and how eye movements were related to mathematical thinking and learning. The results show that most studies were in the domain of numbers and arithmetic, but that a large variety of other areas of mathematics education research was investigated as well. We identify a need to report more methodological details in eye-tracking studies and to be more critical about how to gather, analyze, and interpret eye-tracking data. In conclusion, eye tracking seemed particularly beneficial for studying processes rather than outcomes, for revealing mental representations, and for assessing subconscious aspects of mathematical thinking.
... In 2016, we first presented fundamental observations on eye movements on complex word problems and correlations with several outcome variables based on pilot data (Strohmaier et al., 2016b). In 2017, we analyzed the relation between global measures of eye movements and the mathematical self-concept and mathematics anxiety (Strohmaier et al., 2017). In this study as well as in 2018, we used global measures of eye movements to investigate how the contextual framing of the testing situation affects word problem solving . ...
... Our results support the assumption that these affective-motivational outcomes are relevant when addressing complex word problem solving, as they were uniquely connected to eye movements and thus, their solution process. This indicates that for example, students with higher mathematical anxiety approach complex word problem differently, irrespective of their mathematical abilities (Strohmaier, Schiepe-Tiska, Chang, et al., 2020;Strohmaier et al., 2017). Again, this calls for a comprehensive view on word problem solving that focuses not solely on the cognitive mathematical aspects of word problem solving but takes into account how affective and motivational student characteristics influence the way that complex word problems are approached and solved. ...
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Word problems are a vital part of mathematics education. In the last decades, the goals of mathematics education have shifted towards real-world applications, modelling, and a functional use of mathematics. Complex word problems are a feasible tool for the learning and assessment of these mathematical competencies. They typically include both functional and redundant contextual information, substantial amounts of text, a complex syntax, and multiple representations. Thus, complex word problems provide specific challenges to both students and researchers. In particular, linguistic factors play a pivotal role in complex word problem solving, and mathematical thinking and reading are tightly interwoven in the solution process. In the research project presented here, the method of eye tracking was used to address a number of these challenges. Knowledge about the process of word problem solving was integrated with previous research on eye movements, taking into account both mathematical thinking and processes of reading as a foundation for a meaningful interpretation of global measures of eye movements during complex word problem solving. This integration had not been utilized in this context before. Based on these considerations, it was investigated how eye movements were associated with solution strategies and how they were related to per-formance as well as motivational-affective variables. Moreover, the approach provided the possibility to directly compare complex word problem solving in two fundamentally different languages, namely Chinese and German. This dissertation summarizes two publications that report a total of three studies. The studies all analyzed eye movements during complex word problem solving. The first (N = 17) and second study (N = 42) are reported in Paper A and included the development and evaluation of appropriate global measures of eye movements. Further, they investigated their associa-tion with task difficulty and students’ performance. The third study (N = 139) reported in Paper B compared word problem solving in Chinese and German and associated emerging reading patterns with achievement, mathematical self-concept, mathematics anxiety and flow experience. Furthermore, studies that were associated with the research project but were not part of this dissertation are briefly discussed. The results indicated that patterns of eye movements were associated with the solution pro-cess of complex word problems and with cognitive and motivational-affective outcomes. Moreover, this association is very similar throughout Chinese and German. Therefore, the approach presented here provides specific possibilities to analyze and interpret complex word problems and offers unique insights into the close interplay between reading and mathematics.
... For example, mathematical self-concept and mathematical anxiety have been shown to be related to eye movements during word problem solving and to performance (Strohmaier et al. 2017). Even though the causality between these variables and reading patterns is still unclear, it indicates that cognitive aspects might not be the only factor influencing how word problems are solved. ...
... Even though the causality between these variables and reading patterns is still unclear, it indicates that cognitive aspects might not be the only factor influencing how word problems are solved. Strohmaier et al. (2017) found that students reporting a higher mathematical selfconcept showed a longer mean fixation duration and less fixations, saccades and regressions, even when statistically controlling for performance. Similar effects were assumed for mathematical anxiety. ...
... Participants with reading pattern B (associated with a problem model strategy) reported less mathematics anxiety and a higher self-concept compared to both other patterns. This supports our assumption that the strategic approach in word problem solving is not merely related to cognitive, but also motivational-affective variables (Strohmaier et al. 2017). By including these measures, we can characterize students in reading pattern B as participants who seem to work confidently with word problems, who scan them for useful information, and who are in a highly motivated state. ...
Article
Language plays an important role in word problem solving. Accordingly, the language in which a word problem is presented could affect its solution process. In particular, East-Asian, non-alphabetic languages are assumed to provide specific benefits for mathematics compared to Indo-European, alphabetic languages. By analyzing students’ eye movements in a cross-linguistic comparative study, we analyzed word problem solving processes in Chinese and German. 72 German and 67 Taiwanese undergraduate students solved PISA word problems in their own language. Results showed differences in eye movements of students, between the two languages. Moreover, independent cluster analyses revealed three clusters of reading patterns based on eye movements in both languages. Corresponding reading patterns emerged in both languages that were similarly and significantly associated with performance and motivational-affective variables. They explained more variance among students in these variables than the languages alone. Our analyses show that eye movements of students during reading differ between the two languages, but very similar reading patterns exist in both languages. This result supports the assumption that the language alone is not a sufficient explanation for differences in students’ mathematical achievement, but that reading patterns are more strongly related to performance.
... More difficult WP are read slower, fixations last longer, readers show more saccades and re-read text passages more often (Strohmaier et al., 2017a). These parameters are also related to mathematical self-concept (Strohmaier, Schiepe-Tiska, Müller, & Reiss, 2017b). Accordingly, we expected that a mathematical context would lead to an increase in fixation times, number of saccades, and ratio of regressions per saccade and a decrease in reading speed (Hypothesis 2). ...
Conference Paper
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Both the content and the context of a mathematical word problem (WP) influence its solution process. We focus on the external context beyond the problem text, e.g. the classroom and the cover sheet of the WP. The few studies analysing influences of the external context commonly focus on the mathematical solution. In contrast, we report two experiments analysing processes beyond solutions. First, we found that a mathematical external context increases physiological arousal indicated by electrodermal activity, but not self-reported state anxiety. In contrast, eye movements during WP reading did not differ between a mathematical and a problem-solving external context. This indicates that the external context can initiate a variety of processes and emphasizes its relevance for mathematical WP.