Teacher ability evaluation and changes in elementary student profiles of motivation and performance in mathematics☆
Introduction
Person-centered research has widely shown that different configurations of student motivation and performance can be identified already in elementary school (Corpus & Wormington, 2014; Schwinger, Steinmayr, & Spinath, 2016). These profiles of cognitive and motivational variables emerge in childhood and provide an important basis for students' academic development (Archambault, Eccles, & Vida, 2010; Jurik, Gröschner, & Seidel, 2014). Although there are some studies focusing on the profiles of children in reading (Viljaranta et al., 2017; Farrington-Flint, 2015) and science (Patrick, Mantzicopoulos, Samarapungavan, & French, 2008), research on student profiles of motivation and performance in mathematics is largely missing. It is, however, highly relevant to examine motivation and performance profiles in mathematics because, particularly in the domain of mathematics, students' motivation declines consistently beginning in elementary school (Jacobs, Lanza, Osgood, Eccles, & Wigfield, 2002). Research is also largely missing that examines whether such developmental trends are reflected in children's subject-specific profiles. It is possible, for example, that despite a declining trend in the mean level of mathematics motivation, not all children face declines in their mathematics motivation; instead, the motivation of some students in mathematics might even increase.
Starting from these open research questions, we examined elementary student profiles of motivational and cognitive variables within the domain of mathematics. Focusing on one specific subject allows for a more detailed analysis of the configurations of motivational and cognitive variables (e.g. ‘high interest, low self-concept in math’ instead of ‘high math, low reading motivation’). Consequently, it is possible to explore details of mathematics motivational development that would remain unexplored when including several subjects. Knowledge about individual profiles and their development in mathematics allows teachers to plan their instruction in an individualized manner in order to mitigate the motivational decline. Taken together, the novelty of our study is that it is, to our knowledge, the first study that examines student profiles of motivation and performance in mathematics and the stability and changes of these profiles in early elementary school. The domain-specific focus of our study thereby allows to compare the results to other person-oriented studies focusing elementary school children in reading (Viljaranta et al., 2017) and kindergarteners in science (Patrick et al., 2008). Another important contribution of this study to current work is that we investigate whether teacher-reported ability evaluations and student gender are related to changes in elementary school students' profile membership in mathematics. This approach allows us to better understand the role of socializers and individual characteristics for the emergence of profiles of motivation and performance in mathematics.
The expectancy-value theory of Eccles et al. (1983) and posits that the subjective task value and the academic self-concept of individuals directly predict their achievement-related behaviors and performance. Academic self-concept broadly refers to an individual's self-perception of their general ability in a domain (Marsh & Martin, 2011). Subjective task value is the quality of a task that contributes to the increasing likelihood that an individual will select it (Eccles, 2005). Especially the interest value of a task, that is, the enjoyment one gains or expects to gain when doing the task, is highly correlated with academic self-concept (Marsh, Trautwein, Lüdtke, Köller, & Baumert, 2005). Academic self-concept in particular is closely related to achievement (Spinath, Spinath, Harlaar, & Plomin, 2006). The strong relationships between interest value, self-concept and achievement are reflected in person-centered research identifying student profiles with high, medium and low levels of interest, self-concept and performance (Patrick et al., 2008; Seidel, 2006). The specific value of person-centered research, however, is to identify profiles with inconsistent levels of motivational and cognitive variables. Seidel (2006), for example, identified a profile of ‘uninterested’ learners with high cognitive ability and high self-concept of ability but low interest in secondary school physics classrooms. Knowledge of such student profiles informs teachers on how to plan instruction that addresses the needs of different types of learners. Students with low interest find mathematics activities more interesting when tasks attract their attention (Durik & Harackiewicz, 2007). Learners with a low self-concept of their abilities in mathematics are enhanced by tasks emphasizing their utility for students' lives (Hulleman, 2007). Research based on Eccles et al.'s (1983) and Wigfield and Eccles's (2000) expectancy-value theory shows that elementary school students receive different feedback and support from their socializers, which may contribute to the emergence of different profiles in elementary school. Elementary school children distinguish between competence beliefs and task values (see Wigfield, 1994) and have differentiated activity-related competence beliefs and subjective task values (Eccles, Wigfield, Harold, & Blumenfeld, 1993). In this study, therefore, we expected to identify different profiles of self-concept of ability, performance and interest among elementary school students in mathematics. Referring to theoretical assumptions about the strong relationship between self-concept of ability and interest (Eccles & Wigfield, 2002), we expected to find profiles in which the motivational and cognitive variables were on the same level in relation to one another (i.e., high, medium, low levels of self-concept, performance and interest value). Because competence beliefs and task values are not strongly correlated in elementary school (Wigfield et al., 1997), we also expected to find motivational profiles with pronounced differences in interest value and self-concept. Specifically, we expected to find a group of students with high levels of interest and low levels of self-concept and performance as well as a group of students with low levels of interest and low levels of self-concept and performance. These groups were expected to exist due to different socialization experiences. Some students may have parents who are involved in school, but do not feel competent in mathematics – which is associated with low levels of mathematics self-concept, but not with low interest (Häfner et al., 2017), while other children may have parents who are math-motivated, but they might perceive a lack of relevance of the mathematics tasks in class, which has been shown to be associated with a ‘uninterested’ pattern of motivational and cognitive characteristics (Seidel, 2006).
Variable-centered longitudinal research has shown that the average level of motivation decreases over the elementary school years (Eccles et al., 1993; Jacobs et al., 2002; Spinath & Spinath, 2005b). The knowledge gained through such variable-centered studies is limited to information about the average motivational development of students and cannot provide information about inconsistencies in students' motivation – about the different patterns of motivation that exist among a student population, for example – and about the changes in such patterns. Variable-centered longitudinal research shows that the average level of students' perceived task value and competence beliefs decreases throughout the school years (Gottfried, 1990). However, this average decline of motivation in the student population does not cover the motivational changes of specific subgroups of students. For example, person-centered longitudinal research suggests that while for many students the motivation in school decreases during adolescence, a small percentage of students increased their motivation across the academic year (Bråten & Olaussen, 2005; Hayenga & Corpus, 2010). Consequently, person-centered research extends the knowledge provided by variable-centered motivational research by identifying meaningful subtypes that exist in the student population and by enhancing our understanding of the stability and changes of such subtypes across time. Knowledge about different patterns in the development of students' motivation is important for educational research because it shows that motivation does not develop equally for all students and that we therefore need instructional approaches that match the needs of different types of learners in class when aiming to increase or maintain students' motivation throughout the school years.
On a theoretical level, the different changes in student profiles can be explained by different socialization experiences as well as by individual psychological processes. Depending on their motivational and cognitive characteristics, students are confronted with different ability expectations from their teachers (Jussim & Harber, 2005). Furthermore, learners respond differently to instruction depending on their level of individual interest and on their self-concept of their ability (Durik, Hulleman, & Harackiewicz, 2015). Person-centered research has shown an increasing intraindividual stability of student motivational profiles with consistent levels of motivational and cognitive variables (Hayenga & Corpus, 2010) and a low stability of profiles with inconsistent levels of cognitive and motivational variables (Alexander & Murphy, 1998; Viljaranta et al., 2017). The low stability of profiles with inconsistent profiles may result from differential teacher behaviors. Teacher expectancy research has impressively shown differential treatment by teachers of high- and low-achieving students (Babad, 2009; Brophy & Good, 1970). It is well known, for example, that teachers provide more learning support to low-achievers, but that they provide high-achievers with more positive emotional support. One may assume that such non-verbal teaching behaviors lead to an increase in interest in learning for those students who have low interest but high performance and competence beliefs. In the same vein, one may assume that students with high interest in mathematics but low self-concept and performance may be confronted with their teachers' low ability expectations of their ability and are therefore likely to experience a decline in interest.
Another theoretical explanation of the low stability of profiles with inconsistent patterns of motivational and cognitive variables is the cognitive dissonance that students with those profiles experience. Particularly those students with high levels of interest but low self-concept of ability and performance may become frustrated during learning because they are aware of the dissonance between their cognitions and their actions (Festinger, 1957; Harmon-Jones & Harmon-Jones, 2012). For example, they may enjoy working on mathematics tasks, and at the same time they may have difficulties in solving these tasks. Thus, these students might be likely to change to profiles characterized by overall low levels of motivational and cognitive variables. Accordingly, variable-centered research has suggested that the combination of high task value and low self-concept is detrimental for students' academic development in mathematics (Trautwein et al., 2012).
The development of students' competence beliefs and performance has been shown to be substantially affected by the teacher's evaluation of student abilities in class (Bohlmann & Weinstein, 2013; Jussim & Eccles, 1992; Rubie-Davies, 2010). In the early years of school, teacher ability evaluations are important sources of information that contribute to the formation of the students' own expectations of their ability (Kuklinski & Weinstein, 2001; Spinath & Spinath, 2005a). On a theoretical level, it can be assumed that teachers convey their evaluations indirectly to their students through verbal and nonverbal communication (Bohlmann & Weinstein, 2013). Students in turn infer the teachers' ability evaluations from the instructional behaviors (i.e., Babad, 1992; Eccles et al., 1983; Good & Weinstein, 1986) and adapt their evaluation of their own competence (Spinath & Spinath, 2005a). High teacher ability evaluations can function as a social resource in the academic development of elementary students because they positively predict both achievement (Kuklinski & Weinstein, 2001) and self-concept (Zhou & Urhahne, 2013). Students' competence beliefs in turn mediate the effect of student-perceived teacher ability evaluations on student motivation already in elementary school (Freiberger, Steinmayr, & Spinath, 2012). Referring to these theoretical assumptions and empirical findings, we expected that positive teacher ability evaluations would mainly affect students' self-concept of ability and performance and would thus prevent students changing from profiles with high mathematics self-concept and high performance to profiles with low levels of mathematics self-concept and low performance – and support students changing from profiles with low levels of mathematics self-concept and performance to profiles with high levels of mathematics self-concept and performance.
One individual factor that is decisively related to the development of student motivation and performance is gender. From a theoretical perspective, domain-related social stereotypes influence socializers' support behaviors and ability evaluations which in turn affect student motivation (Eccles et al., 1983; Wigfield & Eccles, 2000). The domain of mathematics is often stereotyped as being a male domain (Nosek, Banaji, & Greenwald, 2002). Together with the gender of the child, such domain-specific stereotypes affect socializers' ability perceptions which in turn predict students' competence beliefs and performance (Jacobs, 1991).
Regarding changes across profiles of mathematics self-concept, performance and intrinsic value, we assume that the exposure to gender-role information from socializers may contribute to gender-specific changes across profiles. Already in elementary school, teachers report that mathematics is a domain in which girls excel because they are put forth a lot of effort, but not because they are talented, while boys are perceived as more talented in mathematics than girls even at equal levels of performance (Tiedemann, 2002). Given that early elementary school children are already aware of such math-gender stereotypes (Gunderson, Ramirez, Levine, & Beilock, 2012), we expected that boys might be less likely than girls to change from profiles with high levels of self-concept to profiles with low levels of self-concept in mathematics. We expected similarly that boys would be less likely than girls to change from profiles characterized by high levels of interest to profiles with low levels of interest. We expected such gender-specific changes in profile membership in terms of interest value because, already in elementary school, boys identify with mathematics more strongly than girls (Cvencek, Meltzoff, & Greenwald, 2011). These identification processes may result in high levels of mathematics interest and enjoyment because students most like subjects that they perceive as congruent with their identity (Hannover & Kessels, 2004).
Little is known, currently, about profiles of motivation and performance of elementary students in the domain of mathematics. This is surprising, because mathematical competencies are important preconditions for the development of general capabilities such as systematic problem solving and analytical skills, which are required to understand societal processes (i.e., tax systems and elections) (Ball, Goffney, & Bass, 2005). The present person-centered study examines the stability and changes in the profiles of self-concept of ability, performance and interest value in mathematics from grades 1 to 2. Furthermore, the study investigates the effects of teacher-reported ability evaluations in grade 1 and student gender on changes in the student profiles. We focus on students from elementary schools in Finland. The Finnish school system differs from that in many European countries, as elementary school begins the year children turn 7 years old and the majority of 6-year-olds spend a year in kindergarten before entering primary school. In the Finnish kindergarten, children's arithmetic skills are promoted through the use of various play-like methods and materials (Lerkkanen & Poikkeus, 2006). Furthermore, the Finnish curriculum places special emphasis on enhancing motivation, and providing individual support for each child in order to help students gain positive experiences (Finnish National Board for Education, 2016; Finnish National Board of Education, 2004).
In this study, we tested the following hypotheses.
- (1)
In addition to profiles characterized by consistent levels of interest value, self-concept, and performance in mathematics (e.g., high, medium, or low), we expected to find profiles of elementary students with inconsistent configurations of self-concept and interest value (i.e., low self-concept and performance but high interest value as well as high self-concept and performance but low interest value). Despite strong intercorrelations of these variables (Marsh et al., 2005), previous person-centered studies (Seidel, 2006) have shown profiles characterized by theoretically unexpected configurations of self-concept and interest.
- (2)
We expected the motivational profiles an increasing stability of motivational profiles from grades 1 to 2 (Viljaranta et al., 2017). However, we did not assume an absolute stability and rather expected that students would remain particularly in those profiles in which the motivational and cognitive variables were on the same level in relation to each other (i.e., high, medium, low levels of self-concept, performance and interest value) (Hayenga & Corpus, 2010), while we hypothezised that students in profiles characterized by inconsistent configurations of cognitive and motivational variables would be likely to change to other profiles (Alexander & Murphy, 1998). We expected, however, that particularly the combination of high interest value and low self-concept might be detrimental to students' motivational development by making them likely to change to profiles characterized by overall low levels of motivational and cognitive variables.
- (3)
From a theoretical perspective, it can be assumed that teachers convey their evaluations indirectly through communication and teaching behaviors to their students (i.e., Babad, 1992; Eccles et al., 1983; Good & Weinstein, 1986) and that students infer the teachers' ability evaluations from the instructional behaviors (Kuklinski & Weinstein, 2000) and adapt their evaluation of their own competence (Spinath & Spinath, 2005a). In this study, therefore, we assumed that positive teacher ability evaluations would prevent students changing from profiles with high mathematics self-concept to profiles with low levels of mathematics self-concept – and support students changing from profiles with low levels of mathematics self-concept to profiles with high levels of mathematics self-concept.
- (4)
According to social math-gender stereotypes, teachers believe that girls perform better than boys in mathematics and attribute this higher performance to girls' greater effort, but not greater talent (Tiedemann, 2002). Related to such stereotypes, boys identify more strongly than girls with mathematics in elementary school (Cvencek et al., 2011). We therefore assumed that girls would be more likely than boys to change from profiles characterized by high levels of mathematics self-concept and performance to profiles with low levels of self-concept and performance and/or from profiles with high levels of interest value in mathematics to profiles with low levels of interest value in mathematics.
Section snippets
Sample
The data used in this study stemmed from the longitudinal JEPS study (Jyväskylä Entrance into Primary School study) (Nurmi & Aunola, 1999b). The aim of the JEPS study is to examine students' academic and motivational development from the beginning of their school career until the end of comprehensive school. The present study focuses on four measurement points during grades 1 and 2. Students were administered questionnaires twice during the school year, once in the fall term and once in the
Motivational profiles
The model fit criteria for the series of latent profile analyses that were conducted to identify the motivational profiles are provided in Table 3. The adjusted LMR LR test showed a significantly better fit of the three-class solution compared to the two-class solution. The entropy score for all profile solutions was above the critical value of 0.80 but showed the highest value for the two- and for the eight-profile solution. The AIC, BIC, and aBIC values decreased consistently and thus did not
Discussion
This person-centered longitudinal study contributes to previous research by examining the changes in elementary student motivation and performance profiles in mathematics. The children's profiles of motivation and performance showed an increasing stability from the beginning of grade 1 to the end of grade 2. Students with overall high motivation at the beginning of grade 1 particularly benefitted from high teacher evaluations of their mathematical performance. These students were less likely to
Acknowledgment
Analyses were based on survey data of the Jyväskylä Entrance into Primary School (JEPS) study (Nurmi & Aunola, 1999–2009) and funded by the Academy of Finland under grant numbers 63099, 63099 and 778230 and by personal funding from the Academy of Finland to Jaana Viljaranta (grant numbers 265817 and 316852).
References (79)
- et al.
Classroom context, teacher expectations, and cognitive level: Predicting children's math ability judgments
Journal of Applied Developmental Psychology
(2013) - et al.
Profiling individual differences in student motivation: A longitudinal cluster-analytic study in different academic contexts
Contemporary Educational Psychology
(2005) Uncovering strategy profiles in young children's reading & spelling
Learning and Individual Differences
(2015)- et al.
Competence beliefs and perceived ability evaluations: How do they contribute to intrinsic motivation and achievement?
Learning and Individual Differences
(2012) - et al.
Self-to-prototype matching as a strategy for making academic choices. Why high school students do not like math and science
Learning and Instruction
(2004) - et al.
Predicting students' cognitive learning activity and intrinsic learning motivation: How powerful are teacher statements, student profiles, and gender?
Learning and Individual Differences
(2014) - et al.
Task-motivation during the first school years: A person-oriented approach to longitudinal data
Learning and Instruction
(2005) - et al.
Achievement goal profiles in elementary school: Antecedents, consequences, and longitudinal trajectories
Contemporary Educational Psychology
(2016) - et al.
Development of self-perceived ability in elementary school: The role of parents' perceptions, teacher evaluations, and intelligence
Cognitive Development
(2005) - et al.
Longitudinal analysis of the link between learning motivation and competence beliefs among elementary school children
Learning and Instruction
(2005)
Predicting school achievement from general cognitive ability, self-perceived ability, and intrinsic value
Intelligence
Expectancy–value theory of achievement motivation
Contemporary Educational Psychology
A new look at the statistical model identification
IEEE Transactions on Automatic Control
Profiling the differences in students' knowledge, interest, and strategic processing
Journal of Educational Psychology
Ability self-concepts and subjective value in literacy: Joint trajectories from grades 1 through 12
Journal of Educational Psychology
The role of parents' self‐esteem, mastery‐orientation and social background in their parenting styles
Scandinavian Journal of Psychology
Developmental dynamics of math performance from preschool to grade 2
Journal of Educational Psychology
Developmental dynamics between mathematical performance, task motivation, and teachers' goals during the transition to primary school
British Journal of Educational Psychology
Teacher expectancies and nonverbal behavior
Teaching and nonverbal behavior in the classroom
Guest editorial. The role of mathematics instruction in building a socially just and diverse democracy
The Mathematics Educator
Studying individual patterns of development using I-states as objects analysis (ISOA)
Biometrical Journal
Studying individual development in an interindividual context: A person-oriented approach
Teachers' communications of differential expectations for children's classroom performance
Journal of Educational Psychology
Multigroup comparisons and the assumption of equivalent construct validity across groups: Methodological and substantive issues
Multivariate Behavioral Research
Profiles of intrinsic and extrinsic motivations in elementary school: A longitudinal analysis
The Journal of Experimental Education
Math–gender stereotypes in elementary school children
Child Development
Different strokes for different folks: How individual interest moderates the effects of situational factors on task interest
Journal of Educational Psychology
One size fits some: Instructional enhancements to promote interest
Subjective task value and the Eccles et al. model of achievement-related choices
Expectancies, values and academic behaviors
Motivational beliefs, values, and goals
Annual Review of Psychology
Age and gender differences in children's self-and task perceptions during elementary school
Child Development
A theory of cognitive dissonance
National core curriculum for basic education 2014
National core curriculum for basic education 2004: National core curriculum for basic education intended for pupils in compulsory education
Fostering adolescents' value beliefs for mathematics with a relevance intervention in the classroom
Developmental Psychology
Teacher expectations: A framework for exploring classrooms
Academic intrinsic motivation in young elementary school children
Journal of Educational Psychology
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Analyses were based on survey data of the Jyväskylä Entrance into Primary School (JEPS) study (Nurmi & Aunola, 1999a–2009) and funded by the Academy of Finland under grant numbers 63099, 778230 and by personal funding from the Academy of Finland to Jaana Viljaranta (grant numbers 265817 and 316852).