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... 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.
... 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. ...
Book
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.
... 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.
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In this paper, the state of research on the assessment of competencies in higher education is reviewed. Fundamental conceptual and methodological issues are clarified by showing that current controversies are built on misleading dichotomies. By systematically sketching conceptual controversies, competing competence definitions are unpacked (analytic/trait vs. holistic/real-world performance) and commonplaces are identified. Disagreements are also highlighted. Similarly, competing statistical approaches to assessing competencies, namely itemresponse theory (latent trait) versus generalizability theory (sampling error variance), are unpacked. The resulting framework moves beyond dichotomies and shows how the different approaches complement each other. Competence is viewed along a continuum from traits that underlie perception, interpretation, and decision-making skills, which in turn give rise to observed behavior in real-world situations. Statistical approaches are also viewed along a continuum from linear to nonlinear models that serve different purposes. Item response theory (IRT) models may be used for scaling item responses and modeling structural relations, and generalizability theory (GT) models pinpoint sources of measurement error variance, thereby enabling the design of reliable measurements. The proposed framework suggests multiple new research studies and may serve as a "grand" structural model.
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Recent efforts to identify non-cognitive predictors of academic achievement and school success have largely focused on self-constructs such as self-efficacy, self-concept and anxiety that are measured with respect to a specific domain (e.g. mathematics). We extend the measurement of the non-cognitive realm in education to incorporate both social and psychological adjustment variables and ratings of confidence in addition to these self-constructs. Our findings show that confidence explains most of the variance in achievement captured by the other self-constructs combined, and that psychological adjustment variables add little to the equation. Furthermore, in contrast to other cognitive and non-cognitive variables, confidence accounts for 46.3% of total variance in achievement, while measures of previous cognitive performance in combination with other non-cognitive variables account for 40.5% of the total variance. We discuss the ways in which confidence is important in education.
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This is a review of five studies that reported new empirical data relevant for the predictability gradient hypothesis. This hypothesis is focused on within-person psychological variables typically collected in background questionnaires that examine the role of non-cognitive influences on students’ academic achievement. Broad measures of maladjustment and motivation/goal orientation have the lowest correlations with achievement. Measures of confidence, on the other hand, have the highest predictive validity. The other self-beliefs measures are in the middle, although they can also be ordered from lower (self-concept) through medium (academic anxiety) to high (self-efficacy) levels of predictability.
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A meta-analysis of 69 data sets (N = 125,308) was carried out on studies that simultaneously evaluate the effects of math and verbal achievements on math and verbal self-concepts. As predicted by the internal/external frame of reference (I/E) model, math and verbal achievements were highly correlated overall (.67), but the correlation between math and verbal self-concepts (.10) was close to zero. Correlations between math and verbal achievement and correlations between achievements and self-concepts within the domains were more positive when grades instead of standardized test results were used as achievement indicators. A path analysis revealed support for the I/E model, with positive paths from achievement to the corresponding self-concepts (.61 for math, .49 for verbal) and negative paths from achievement in one subject to self-concept in the other subject (−.21 from math achievement on verbal self-concept, −.27 from verbal achievement to math self-concept). Furthermore, results showed that the I/E model is valid for different age groups, gender groups, and countries. The I/E model did not fit the data when self-efficacy measures were used instead of self-concept measures. These results demonstrate the broad scope of the I/E model as an adequate description of students’ self-evaluation processes as they are influenced by internal and external frames of reference.
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Ergebnisse aus PISA 2003 zeigen fur Deutschland eine Diskrepanz zwischen der im internationalen Vergleich hohen Problemlosekompetenz und der durchschnittlichen Mathematikkompetenz. Nach der Potenzialnutzungshypothese kann dies teilweise auf eine mangelnde Nutzung vorhandener Fachkompetenzen wahrend der Testbearbeitung zuruckgefuhrt werden. Der vorliegende Beitrag geht dieser Hypothese im Rahmen von zwei experimentellen Studien nach. Hierbei wurden Effekte der kontextuellen Einkleidung von Mathematikaufgaben (Studie 1, n = 256) und Problemloseaufgaben (Studie 2, n = 259) auf Schulerleistungen untersucht sowie Moderationseffekte durch das mathematische Selbstkonzept und die Mathematikangst uberpruft. In beiden Studien zeigten sich negative Effekte der mathematischen Kontexteinkleidung, insbesondere bei Lernenden mit geringem mathematischem Selbstkonzept sowie bei Lernenden mit hoher Mathematikangst. Implikationen der Ergebnisse fur die Erfassung sowie die Forderung domanenubergreifender und domanenspezifisc...
Book
Accession Number: 2012-07127-000. Partial author list: First Author & Affiliation: Hattie, John; Melbourne Education Research Institute, University of Melbourne, Melbourne, Australia. Release Date: 20120611. Publication Type: Book (0200). Format Covered: Print. ISBN: 978-0-415-69014-0, Hardcover; 978-0-415-69015-7, Paperback; 978-0-203-18152-2, Electronic. Language: English. Major Descriptor: Academic Achievement; Learning; School Based Intervention; Teachers; Teaching Methods. Minor Descriptor: Classroom Management; Meta Analysis; Preservice Teachers; Student Teachers. Classification: Curriculum & Programs & Teaching Methods (3530). Population: Human (10). Age Group: Childhood (birth-12 yrs) (100); Adolescence (13-17 yrs) (200); Adulthood (18 yrs & older) (300). Intended Audience: Psychology: Professional & Research (PS). References Available: Y. Page Count: 269.
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A comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians is explored. Participants' eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short purported proofs; (b) compared with mathematicians, undergraduate students spend proportionately more time focusing on “surface features” of arguments, suggesting that they attend less to logical structure; and (c) compared with undergraduates, mathematicians are more inclined to shift their attention back and forth between consecutive lines of purported proofs, suggesting that they devote more effort to inferring implicit warrants.