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German and Taiwanese secondary students’ mathematical modelling task value profiles and their relation to mathematical knowledge and modelling performance
Abstract
Based on expectancy-value theory, this study adopted a person-centred approach to explore the heterogeneous profiles of secondary German and Taiwanese students’ 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’ 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.
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Expectancy-value models assume that task values play an important role in engaging successfully with the learning content. However, teacher education students in mathematics only value tasks that deal with university mathematics to a low degree. Offering students profession-related tasks that uncover the connection between university mathematics and school mathematics might help increase students’ value beliefs and effort and decrease costs. Based on Eccles and Wigfield’s (2020) situated expectancy-value theory and using a sample of 133 teacher education students, we investigate whether offering profession-related tasks affects task values, costs, and effort for students with different levels of interest in school mathematics. In a within-subject design, students rated their task values, costs, and effort to solve seven mathematical tasks from number theory, which were either a profession-related task or a regular task with equal demands regarding the intended mathematical activities. Students reported higher utility value for their professional life, higher intrinsic value, and lower costs regarding profession-related tasks. No main effects were found for students’ effort. However, students with a higher interest in school mathematics reported higher effort concerning profession-related tasks than regular tasks. On the theoretical level, our findings contribute to the discussion of the interplay between personal (i.e. interest) and task-specific factors (i.e. relation to future profession) for task values, costs, and effort in university mathematics. One important practical implication of our study is the recommendation to include profession-related tasks in university mathematics courses for teacher education students.
Emotions and motivation are important for learning and achievement in mathematics. In this paper, we present an overview of research on students’ emotions and motivation in mathematics. First, we briefly review how early research has developed into the current state-of-the-art and outline the following key characteristics of emotions and motivation: objects, valence, temporal stability (vs. variability), and situational specificity (vs. generality). Second, we summarize major theories in the field (the control-value theory of achievement emotions, expectancy-value theory of achievement-related motivation, self-determination theory of human motivation, and social-cognitive theory of self-efficacy). Third, we present an overview of instructional characteristics that have been shown to foster emotions and motivation. Fourth, we provide an overview of the contributions to the special issue on “Emotions and Motivation in Mathematics Education and Educational Psychology.” Finally, we suggest directions for future research in the field with respect to advancing theory, improving measurement, and considering diversity and inclusion.
Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling competencies. The study described in this paper was a systematic literature review of the literature on modelling competencies published over the past two decades. Based on a full-text analysis of 75 peer-reviewed studies indexed in renowned databases and published in English, the study revealed the dominance of an analytical, bottom-up approach for conceptualizing modelling competencies and distinguishing a variety of sub-competencies. Furthermore, the analysis showed the great richness of methods for measuring modelling competencies, although a focus on (non-standardized) tests prevailed. Concerning design and offering for fostering modelling competencies, the majority of the papers reported training strategies for modelling courses. Overall, the current literature review pointed out the necessity for further theoretical work on conceptualizing mathematical modelling competencies while highlighting the richness of developed empirical approaches and their implementation at various educational levels.
Relevance interventions have shown a great potential to foster motivation and achievement (Lazowski & Hulleman, 2016). Yet, further research is warranted to test how such interventions can be successfully implemented in practice. We conducted a cluster-randomized trial in ninth-grade mathematics classrooms to test the effectiveness of a relevance intervention, which was shown to be efficacious when implemented by researchers, for fostering motivation and achievement under real-world conditions. The 78 participating classrooms (N = 1,744 students) were randomly assigned to one of two intervention conditions or a waitlist control condition. The intervention was implemented by master’s students or the regular math teachers. Intervention effects were evaluated using self-reports, teacher ratings, and achievement tests 4 weeks and 3 months after the intervention, controlling for the initial levels of the outcomes. Compared with the control condition, both intervention conditions showed similar positive effects on utility value. Unexpectedly, students in both intervention conditions also reported higher perceived cost compared with students in the control condition after the intervention. When implemented by master’s students, additional intervention effects on students’ growth mindsets and a standardized achievement test could be observed. Only small differences in effectiveness were observed between the intervention conditions, although master’s students showed a higher level of adherence. In both intervention conditions, higher levels of adherence and lower levels of discipline problems were associated with more positive changes in utility value. Overall, the intervention thus showed mixed effects. Future research should therefore continue to examine the conditions under which relevance interventions work in practice.
To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students’ situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students’ interest in modelling improved more in Germany. An in-depth quantitative analysis of students’ responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.
The need to enhance the STEM workforce and, in turn, the STEM educational pipeline is a prevailing issue in the U.S. One critical component in this pipeline is students’ interest in STEM majors and their persistence in such majors, theorized to be a function of both students’ perceived value and expectancy beliefs in the subject matter. Using an expectancy-value lens, we examined cross-domain patterns of high school students’ expectancy beliefs and values in both mathematics and science using a person-centered or profile approach. With data from the High School Longitudinal Study, latent profile analysis revealed five profiles characterized as Low Math/Low Science (i.e., endorsing low levels of expectancy and value beliefs in math and science), Moderate Math/Moderate Science, High Math/High Science, Low Math/High Science, and High Math/Low Science. Taking into account aspects of students’ background and school context, we found that motivational profile membership predicted math and science high school achievement, college persistence, and both STEM major intentions and decisions. Moreover, there were a number of gender and racial/ethnic differences and contextual variation in profile memberships as well. Implications for theory and educational practice are discussed in relation to study findings.
Most studies utilizing a person-oriented approach to investigating students' achievement goal orientation profiles have been domain-general or focused on a single domain (usually mathematics), thus excluding the possibility of identifying distinct subject-specific motivational profiles. In this study, we looked into this by examining upper secondary school students' subject-specific achievement goal orientation profiles simultaneously in mathematics and English. As distinct profiles might contribute to how students invest time and effort in studying, we also examined differences in perceived subject-specific cost (i.e., effort required, emotional cost, opportunity cost) among students with different profiles and how this was linked with students' more general academic well-being (i.e., school engagement, burnout). The 434 Finnish general upper secondary school students participating in the study were classified based on their achievement goal orientations in the two subjects using latent profile analysis, and the predictions of the latent profile on distal outcomes (i.e., measures of cost and academic well-being) were examined within the mixture model. Five divergent achievement goal orientation profiles were identified: indifferent (29%), success-oriented (26%), mastery-oriented (25%), English-oriented, math-avoidant (14%), and avoidance-oriented (6%). The English-oriented, math-avoidant students showed the most distinct domain-specificity in their profile but, in general, profiles indicated more cross-domain generality than specificity. Overall, mastery-oriented students showed the most adaptive academic well-being, while avoidance-oriented students were the least engaged. Success-oriented students were characterized by high multiple goals in both subjects, elevated costs, and high scores on both positive (engagement) and negative (burnout) well-being indicators. The English-oriented, math-avoidant students perceived studying math as costly. The findings suggest that addressing students' achievement motivation in different subjects may be useful for recognizing factors endangering or fostering student learning and well-being.
Self-determination theory (SDT) is a broad framework for understanding factors that facilitate or undermine intrinsic motivation, autonomous extrinsic motivation, and psychological wellness, all issues of direct relevance to educational settings. We review research from SDT showing that both intrinsic motivation and well-internalized (and thus autonomous) forms of extrinsic motivation predict an array of positive outcomes across varied educational levels and cultural contexts and are enhanced by supports for students’ basic psychological needs for autonomy, competence, and relatedness. Findings also show a dynamic link between teacher and student motivation, as teachers are themselves impacted and constrained by controlling mandates, institutional pressures, and leadership styles. Ironically, despite substantial evidence for the importance of psychological need satisfactions in learning contexts, many current educational policies and practices around the globe remain anchored in traditional motivational models that fail to support students’ and teachers’ needs, a knowledge versus policy gap we should aspire to close.
Motivation is an essential determinant of academic learning, educational choices, and career decisions during adolescence and early adulthood. While achievement motivation has been widely studied across Western populations, recent work has emphasized the importance of examining the universality versus cultural specificity of motivation constructs across countries or diverse cultures. This article is a systematic review of the current discourse surrounding developmental and gender differences in student motivation in the disciplines of mathematics and English, offering comparisons of how these patterns are deployed within Western and East Asian countries. Guided by expectancy–value theory, this review focuses on ability self-concept and task values as two prominent motivational constructs. The authors first examine age and gender differences in the development of ability self-concept and task values among those from Western and East Asian countries from primary school to secondary school. Next, the sociocultural and contextual factors driving developmental and gender differences in motivation are discussed. The article concludes by summarizing the limitations of existing literature and suggesting new lines of inquiry to advance knowledge in cross-cultural studies on student achievement motivation.
This paper attempts to engage the field in a discussion about what mathematics is needed for students to engage in society, especially with an increase in technology and digitalization. In this respect, mathematics holds a special place in STEM as machines do most of the calculations that students are taught in K-12. We raise questions about what mathematical proficiency means in today’s world and what shifts need to be made in both content and pedagogy to prepare students for 21st Century Skills and mathematical reasoning.
Students’ interest in mathematics is important for their learning of mathematics, and the ability to accurately judge students’ motivational orientation is important for mathematics teachers. The aim of this study was to answer the following research questions: (1) Is there a difference in students’ interest in solving problems with and without a connection to reality? (2) Is there a difference in pre-service teachers’ judgments of students’ interest in problems with and without a connection to reality? (3) Can pre-service teachers accurately judge students’ interest in solving problems with and without a connection to reality? To answer these research questions, we administered a questionnaire in which we asked 100 ninth graders about their task-specific interest after they solved problems with and without a connection to reality. We additionally asked 163 pre-service teachers to judge fictitious ninth graders’ interest in solving the same problems. Contrary to our expectations, students’ interest in real-world problems was lower than their interest in problems without a connection to reality when task difficulty was controlled for. Further, our findings indicate an important discrepancy between students’ interest and pre-service teachers’ judgments of students’ interest. Pre-service teachers overrated students’ interest in solving real-world problems, and they underrated students’ interest in solving intra-mathematical problems. Moreover, the accuracy of pre-service teachers’ judgments of students’ interest was low and ranged widely across pre-service teachers. Implications for teacher education and classroom practice are discussed.
This chapter reviews the recent research on motivation, beliefs, values, and goals, focusing on developmental and educational psychology. The authors divide the chapter into four major sections: theories focused on expectancies for success (self-efficacy theory and control theory), theories focused on task value (theories focused on intrinsic motivation, self-determination, flow, interest, and goals), theories that integrate expectancies and values (attribution theory, the expectancy-value models of Eccles et al., Feather, and Heckhausen, and self-worth theory), and theories integrating motivation and cognition (social cognitive theories of self-regulation and motivation, the work by Winne & Marx, Borkowski et al., Pintrich et al., and theories of motivation and volition). The authors end the chapter with a discussion of how to integrate theories of self-regulation and expectancy-value models of motivation and suggest new directions for future research.
The goal of this article is to discuss one of Paul Pintrich's more enduring legacies: the Motivated Strategies for Learning Questionnaire (MSLQ), an 81-item, self-report instrument consisting of 6 motivation subscales and 9 learning strategies scales. The MSLQ has proven to be a reliable and useful tool that can be adapted for a number of different purposes for researchers, instructors, and students. The MSLQ has been translated into multiple languages and has been used by hundreds of researchers and instructors throughout the world. This article reviews the history of the MSLQ and discusses how it has been used to (a) address the nature of motivation and use of learning strategies in different types of content areas and target populations; (b) help refine our theoretical understanding of motivational constructs, how they are distinct from one another, and what individual differences exist in self-regulated learning; and (c) evaluate the motivational and cognitive effects of different aspects of instruction.
Practical and theoretical issues are discussed for testing (a) the comparability, or measurement equivalence, of psychological constructs and (b) detecting possible sociocultural difference on the constructs in cross-cultural research designs. Specifically, strong factorial invariance (Meredith, 1993) of each variable's loading and intercept (mean-level) parameters implies that constructs are fundamentally the same in each sociocultural group, and thus comparable. Under this condition, hypotheses about the nature of sociocultural differences and similarities can be confidently and meaningfully tested among the constructs' moments in each sociocultural sample. Some of the issues involved in making such tests are reviewed and explicated within the framework of multiple-group mean and covariance structures analyses.
Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models (CSMs). Large-sample theory provides a chi-square goodness-of-fit test for comparing a model (M) against a general alternative M based on correlated variables. It is suggested that this comparison is insufficient for M evaluation. A general null M based on modified independence among variables is proposed as an additional reference point for the statistical and scientific evaluation of CSMs. Use of the null M in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal Ms and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical Ms is also emphasized. Normed and nonnormed fit indices are developed and illustrated. (43 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Mixture modeling is a widely applied data analysis technique used to identify unobserved heterogeneity in a population. Despite mixture models' usefulness in practice, one unresolved issue in the application of mixture models is that there is not one commonly accepted statistical indicator for deciding on the number of classes in a study population. This article presents the results of a simulation study that examines the performance of likelihood-based tests and the traditionally used Information Criterion (ICs) used for determining the number of classes in mixture modeling. We look at the performance of these tests and indexes for 3 types of mixture models: latent class analysis (LCA), a factor mixture model (FMA), and a growth mixture models (GMM). We evaluate the ability of the tests and indexes to correctly identify the number of classes at three different sample sizes (n D 200, 500, 1,000). Whereas the Bayesian Information Criterion performed the best of the ICs, the bootstrap likelihood ratio test proved to be a very consistent indicator of classes across all of the models considered.
In this study which was part of the DISUM-project, 224 ninth graders from 14 German classes from middle track schools (Realschule)
were asked about their enjoyment, interest, value and self-efficacy expectations concerning three types of mathematical problems:
intra-mathematical problems, word problems and modelling problems. Enjoyment, interest, value and self-efficacy were assessed
before and after a ten-lesson teaching unit promoting modelling competency related to the topics “Pythagoras’ theorem” and
“linear functions”. The study aimed to answer the following research questions: (1) Do students’ enjoyment, value, interest
and self-efficacy expectations differ depending on the type of task? (2) Does the treatment of modelling problems in classroom
instruction influence these variables? (3) Are there any differential effects for different ways of teaching modelling problems,
including a “directive”, teacher-centred instruction and an “operative-strategic”, more student-centred instruction emphasising
group work and strategic scaffolding by the teacher? The findings show that there were no differences in students’ enjoyment,
interest, value and self-efficacy between the three types of tasks. However, teaching oriented towards modelling problems
had positive effects on some of the student variables, with the student-centred teaching method producing the most beneficial
effects.
KeywordsAffect–Enjoyment–Self-efficacy–Modelling problems–Word problems–Self-regulation–Teaching methods
In this article we present, illustrate, test and refine a framework developed by Galbraith, Stillman, Brown and Edwards (2006)
for identifying student blockages whilst undertaking modelling tasks during transitions in the modelling process. The framework
was developed with 14~15 year old students who were engaging in their first experiences of modelling at the secondary level.
ZDM-ClassificationC70-M10
Empirical research on the development of individual interests is mostly concerned with the analysis of developmental trends in groups or populations. However, there is a distinct lack of theoretical constructs that describe and explain interest development from the perspective of the growing individual. This article presents a collection of theoretical concepts and models that can be used to describe and explore structural and dynamic aspects of interest development from an ontogenetic research perspective. Basic ideas of an educational–psychological conceptualization of interest are outlined that—contrary to many other conceptualizations in this field—is based on a dynamic theory of personality. Such an approach provides an opportunity to analyze and reconstruct the manifold interrelations between the changing structure of a person's pattern of interests and the developing personal “self” during ontogenesis. Exemplary selected theoretical models and ideas are presented, including the question of general stages during the course of interest development from childhood to early adulthood, models to describe and theoretically reconstruct structural changes in an individual's pattern of personal interests over a longer period of time, ideas of how to conceptualize the transition from situational to individual interest, and theoretical considerations about the structure and function of the psychological regulation-system that is assumed to be responsible for establishing and stabilizing motivational preferences. Although these concepts and considerations are not yet integrated into a coherent ontogenetic theory, they may serve as a basis for a theoretical discussion on how to achieve this aim.
This chapter gives an applied introduction to latent profile and latent class analysis (LPA/LCA). LPA/LCA are model-based methods for clustering individuals in unobserved groups. Their primary goals are probing whether and, if so, how many latent classes can be identified in the data and estimating their proportional size and response profiles. Moreover, latent class membership can serve as a predictor or outcome for external variables. Substantively, LPA/LCA adopt a person-centred approach that is useful for analysing individual differences in learning prerequisites, processes, or outcomes. This chapter provides a conceptual overview of LPA/LCA, a nuts-and-bolts discussion of the steps and decisions involved in their application, and illustrative examples using available data and the R statistical environment.KeywordsLatent variable modelsMixture modelsLatent class analysisLatent profile analysis
We discuss the development of Eccles, Wigfield, and colleagues' expectancy-value model of achievement motivation (now called SEVT for situated expectancy value theory) and review the research on the part of the model that concerns the development of children's expectancies and values and their relations to performance and activity choice. We focus primarily on subjective task value (STV), first discussing the definition of its different components (intrinsic value, attainment value, utility value, and perceived cost) and how they develop across the childhood and adolescent years. We discuss relations among these components and the notion of “hierarchies of values” as being especially important for activity choice. We next turn to discussion of sources of influences on task values and processes by which individuals' STVs take shape. Next is a discussion of how individuals' values and expectancies relate to their activity choice; we discuss both variable-centered and person centered research addressing this issue. Then we discuss expectancy-value theory based interventions that have focused primarily on enhancing individuals' utility values. We close with suggestions for future research.
Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and debates that have dominated the field. After a short introduction, we begin with research that has conceived word problems primarily as problems of comprehension, and we describe the various ways in which this complex comprehension process has been conceived theoretically as well as the empirical evidence supporting different theoretical models. Next we review research that has focused on strategies for actually solving the word problem. Strengths and weaknesses of informal and formal solution strategies—at various levels of learners’ mathematical development (i.e., arithmetic, algebra)—are discussed. Fourth, we address research that thinks of word problems as exercises in complex problem solving, requiring the use of cognitive strategies (heuristics) as well as metacognitive (or self-regulatory) strategies. The fifth section concerns the role of graphical representations in word problem solving. The complex and sometimes surprising results of research on representations—both self-made and externally provided ones—are summarized and discussed. As in many other domains of mathematics learning, word problem solving performance has been shown to be significantly associated with a number of general cognitive resources such as working memory capacity and inhibitory skills. Research focusing on the role of these general cognitive resources is reviewed afterwards. The seventh section discusses research that analyzes the complex relationship between (traditional) word problems and (genuine) mathematical modeling tasks. Generally, this research points to the gap between the artificial word problems learners encounter in their mathematics lessons, on the one hand, and the authentic mathematical modeling situations with which they are confronted in real life, on the other hand. Finally, we review research on the impact of three important elements of the teaching/learning environment on the development of learners’ word problem solving competence: textbooks, software, and teachers. It is shown how each of these three environmental elements may support or hinder the development of learners’ word problem solving competence. With this general overview of international research on the various perspectives on this complex and fascinating kind of mathematical problem, we set the scene for the empirical contributions on word problems that appear in this special issue.
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’ modelling performance. However, current studies comparing modelling performance between Western and non-Western students do not consider the differences in students’ knowledge. This gap in research intrigued us and prompted us to investigate whether Taiwanese students can still perform better than German students if students’ 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’ ability to solve holistic modelling problems.
Posing modelling problems in class is supposed to increase students’ 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’ 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’ task values (but not between students’ 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.
I: Background.- 1. An Introduction.- 2. Conceptualizations of Intrinsic Motivation and Self-Determination.- II: Self-Determination Theory.- 3. Cognitive Evaluation Theory: Perceived Causality and Perceived Competence.- 4. Cognitive Evaluation Theory: Interpersonal Communication and Intrapersonal Regulation.- 5. Toward an Organismic Integration Theory: Motivation and Development.- 6. Causality Orientations Theory: Personality Influences on Motivation.- III: Alternative Approaches.- 7. Operant and Attributional Theories.- 8. Information-Processing Theories.- IV: Applications and Implications.- 9. Education.- 10. Psychotherapy.- 11. Work.- 12. Sports.- References.- Author Index.
There is a recurrent paradox in the data of the Programme for International Student Assessment (PISA): within each participating country, there is a positive correlation between students’ learning motivation and achievement; when aggregating the data at country level, this correlation becomes negative. Using PISA data across 64 countries, we investigate the association of motivation and achievement within and between countries, and attempt to explain the paradox with three measures indicative of culturally preferred scale usage: cultural response style, overclaiming, and anchoring vignettes. We confirmed the paradox and found that the three measures, in particular anchoring vignettes, could partially explain the negative association between motivation and achievement at country level. Our study is intellectually indebted to the tradition, initiated by David Watkins, to go beyond a simple classification of Chinese learners as focusing on rote memory learning. We illustrate how core Chinese values impinge on educational motivation and achievement and can help to explain seemingly paradoxical cross-cultural differences.
In this paper, we shall report on some of the work that has been, and is being, done in the DISUM project. In §, we shall describe the starting point of DISUM, the SINUS project aimed at developing high-quality teaching. In §, we shall briefly describe the DISUM project itself, and in §3 we shall present and analyse a modelling task from DISUM, the “Sugarloaf” problem. How students dealt with this task will be the topic of §4, the core part of this paper. How experienced SINUS teachers dealt with this task in the classroom will be reported in §5. Finally, in §6, we shall briefly describe future plans for the DISUM project.
The advantages of latent class analysis for cross-cultural research in psychology are discussed. The basic principles of multigroup latent class analysis are described and illustrated by an empirical study comparing satisfaction-with-life-domain profiles across two nations (China, United States). In particular, it is shown how various assumptions of measurement invariance across cultures can be tested statistically in the latent class framework.
We demonstrate that, under a theorem proposed by Q.H. Vuong [Econometrica 57, No. 2, 307-333 (1989; Zbl 0701.62106)], the likelihood ratio statistic based on the Kullback-Leibler information criterion or the null hypothesis that a random sample is drawn from a k 0 -component normal mixture distribution against the alternative hypothesis that the sample is drawn from a k 1 -component normal mixture distribution is asymptotically distributed as a weighted sum of independent chi-squared random variables with one degree of freedom, under general regularity conditions. We report simulation studies of two cases where we are testing a single normal versus a two-component normal mixture and a two-component normal mixture versus a three-component normal mixture. An empirical adjustment to the likelihood ratio statistic is proposed that appears to improve the rate of convergence to the limiting distribution.
Who am I? What am I about? What is my place in my social group? What is important to me? What do I value? What do I want to do with my life? These are all questions related to what psychologists call identity. Many theorists have argued that we are driven to answer these questions, particularly during adolescence. In this article, I summarize an expectancy value perspective on identity and identity formation. Within this framework, identity can be conceptualized in terms of two basic sets of self perceptions: (a) perceptions related to skills, characteristics, and competencies, and (b) perceptions related to personal values and goals. Together these two sets of self perceptions inform both individuals' expectations for success and the importance they attach to becoming involved in a wide range of tasks. Within this perspective, then, I focus on the role personal and collective identities can play on motivated action through their influence on expectations for success and subjective task values. I also discuss briefly how personality and collective identities develop over time.
A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we stress the relationship of confidence intervals to a framework for hypothesis testing. The approach allows for testing null hypotheses of not-good fit, reversing the role of the null hypothesis in conventional tests of model fit, so that a significant result provides strong support for good fit. The approach also allows for direct estimation of power, where effect size is defined in terms of a null and alternative value of the root-mean-square error of approximation fit index proposed by J. H. Steiger and J. M. Lind (1980). It is also feasible to determine minimum sample size required to achieve a given level of power for any test of fit in this framework. Computer programs and examples are provided for power analyses and calculation of minimum sample sizes. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Students’ achievement task values, goal orientations, and interest are motivation-related constructs which concern students’ purposes and reasons for doing achievement activities. The authors review the extant research on these constructs and describe and compare many of the most frequently used measures of these constructs. They also discuss their development during childhood and adolescence. They review the research on the relations of these constructs to achievement outcomes, and their relations to each other both contiguously and over time. Suggestions for future research include testing theoretically derived predictions about how students’ achievement values, goal orientations, and interest together predict various achievement outcomes; and examining how their relations with one another become established and change over time.
An abstract is not available.
The establishment of measurement invariance across groups is a logical prerequisite to conducting substantive cross-group comparisons (e.g., tests of group mean differences, invariance of structural parameter estimates), but measurement invariance is rarely tested in organizational research. In this article, the authors (a) elaborate the importance of conducting tests of measurement invariance across groups, (b) review recommended practices for conducting tests of measurement invariance, (c) review applications of measurement invariance tests in substantive applications, (d) discuss issues involved in tests of various aspects of measurement invariance, (e) present an empirical example of the analysis of longitudinal measurement invariance, and (f) propose an integrative paradigm for conducting sequences of measurement invariance tests.
Two Monte Carlo studies were conducted to examine the sensitivity of goodness of fit indexes to lack of measurement invariance at 3 commonly tested levels: factor loadings, intercepts, and residual variances. Standardized root mean square residual (SRMR) appears to be more sensitive to lack of invariance in factor loadings than in intercepts or residual variances. Comparative fit index (CFI) and root mean square error of approximation (RMSEA) appear to be equally sensitive to all 3 types of lack of invariance. The most intriguing finding is that changes in fit statistics are affected by the interaction between the pattern of invariance and the proportion of invariant items: when the pattern of lack of invariance is uniform, the relation is nonmonotonic, whereas when the pattern of lack of invariance is mixed, the relation is monotonic. Unequal sample sizes affect changes across all 3 levels of invariance: Changes are bigger when sample sizes are equal rather than when they are unequal. Cutoff points for testing invariance at different levels are recommended.
In this chapter, the author discusses interest researchers' conceptualization of interest and how interest relates to intrinsic motivation. She reviews changes in motivational aspects of school activities and suggests that extrinsic factors may play an inevitable and increasingly more important role in motivating students as they progress through their education. The author considers research examining how rewards affect individuals' behavior and motivation, and the relation of this literature to research on interest. Specifically, it is argued that the questions raised, the research conducted, and the conclusions reached in the intrinsic-motivation literature have not taken into account critical issues, some of which are implicit in interest research. Therefore, the studies may not sufficiently inform researchers about how rewards affect individuals' interests and real-life academic performance. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
The importance of motivation in learning has been widely recognized. However, due to its multidimensional and complex nature,
it appears difficult to synthesize research findings on motivation across studies. Heated debates about the effects of intrinsic
and extrinsic motivation on learning and their interaction have been going on since the terms started to be used. Moreover,
cultural difference acts as another crucial factor in the field. Using the Trends in International Mathematics and Science
Studies 2003 eighth grade mathematics data, this study scrutinized the relationship between pleasure-oriented (intrinsic-related)
and productivity-oriented (extrinsic-related) motivation and how they collectively affect students’ academic performance in
East Asian education systems compared with those from Australia, England, The Netherlands, and the USA. The study found that
both types of motivation contributed to East Asian students’ mathematics achievement in an additive fashion, whereas extrinsic-related
motivation appeared to have a detrimental effect on their Western counterparts’ learning. Possible reasons were explored from
a cultural perspective.
KEY WORDSEast Asia–extrinsic motivation–intrinsic motivation–mathematics achievement–pleasure-oriented motivation–productivity-oriented motivation–TIMSS
The problem of selecting one of a number of models of different dimensions is treated by finding its Bayes solution, and evaluating the leading terms of its asymptotic expansion. These terms are a valid large-sample criterion beyond the Bayesian context, since they do not depend on the a priori distribution.
The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.