Expanding a goal mediational model: the Korean elementary school math class. (On-going Topics).

Abstract

This study conceptualized students' motivational beliefs and learning strategies in elementary school math class by using a goal mediational model. The sample consisted of 178 fourth graders (boys = 95; girls = 83) from two Korean elementary schools. Structural equation modeling showed that a modified goal mediational model was applicable to Korean elementary school math class. Students' goal orientations directly influenced their learning strategies and mediated the effects given by motivational variables, such as math attitudes, effort, and competence beliefs. Students with learning goal orientation had positive math attitudes and believed that their success followed from their effort; these students used effective learning strategies. Students with performance goal orientation focused on their ability and sought to demonstrate high ability; these students also reported significant use of learning strategies. Furthermore, results indicate that the Korean mothers uniquely influence their children's math learning. The implications of students' motivational beliefs and learning strategies in math class were discussed.

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Students must be involved in an active process of integrating and organizing new information, constructing meaning, and monitoring comprehension so that they can develop a sound understanding of a subject matter. However, students have difficulties in activating effectively their appropriate knowledge and strategies in their class. These problems may be attributable to both cognitive and motivational variables that play an important role in students' learning (Ames, 1992; Meece, Blumenfeld, & Hoyle, 1988; Pintrich & De Groot, 1990; Weinstein & Mayer, 1986; Wittrock, 1991). To conceptualize these difficulties, Meece et al. (1988) used a goal mediational model as a conceptual framework.

The International Association for the Evaluation of Educational Achievement (lEA) conducted the Third International Mathematics and Science Study (TIMSS) in 1995 across more than 40 counties. The Korean fourth graders had the highest mean scores in mathematics and science achievement tests compared to all fourth graders worldwide (Mullis et al., 1997). In fact, the Korean mothers ask their children from their early days to realize how important mathematics is in their school life. Therefore, it is predictable that mothers would be uniquely involved in their children's math learning (Stevenson, Chen, & Lee, 1994). In the present study, we investigate whether a goal mediational model is useful in conceptualizing students' motivational beliefs and learning strategies in Korean elementary school math class.

Students' Learning Strategies and Goal Orientations

Recent cognitive researchers have argued that students make meaningful connections between new information and what they have already learned in their class. The outcomes of learning depend on what information is presented to students and how they deal with that information (Weinstein & Mayer, 1986; Wittrock, 1991). Generally, students used two learning strategies in their class. Cognitive strategies refer to integrating new material with prior knowledge, and metacognitive strategies refer to planning, monitoring, and evaluating their own cognition (Pintrich & De Groot, 1990; Weinstein & Mayer, 1986; Wittrock, 1991).

The research has suggested that students' learning strategies are motivated by their achievement goal orientations (Ames & Archer, 1988; Anderman & Young, 1994; Meece et al. 1988; Pintrich & De Groot, 1990; Pintrich & Schrauben, 1992). Students with learning, task-involvement, and mastery goal orientations were more cognitively engaged in trying to learn and comprehend the material. They were oriented toward improving new skills and attaining a sense of mastery by their standards. On the other hand, students with performance and ego-involvement goal orientations concentrated on their ability and self-worth. They were oriented toward achieving normatively defined goal focused on public recognition (Ames, 1992; Ames & Archer, 1988; Elliot & Dweck, 1988; Meece et al, 1988; Nicholls, 1984). In this study, we predicted that students' learning goal orientation would positively relate to their learning strategies, and that their performance goal orientation would negatively relate to their learning strategies.

Students' Motivational Beliefs and Goal Orientations

It has been reported that both students' competence beliefs and effort positively related to their learning goal orientation. Students believing that they can succeed by their effort increased their competence beliefs and adopted learning goal orientation (Ames & Archer, 1988; Ames, 1992; Dweck & Bempechat, 1983; Harter, 1982; Kloosterman, 1988; Kloosterman & Cougan, 1994; Wigfield et al., 1997). In the present study, we predicted that both students' competence beliefs and effort would positively relate to their learning goal orientation.

Parents' interactions with their children predicted children's expectancy for academic success, and students had a tendency to work harder and achieved more in school when their parents had high expectations for academic success. There was evidence of cultural differences. For example, Chinese and Japanese fifth graders and their mothers stressed the importance of hard work as the route to success (Stevenson et al., 1993). The TIMSS (1995) reported that 70% of the Korean fourth graders agreed that their mothers thought that it was important for them to do well in mathematics. More than 90% of them perceived that individual ability was necessary to do well in mathematics, and more than 95% of them also believed that individual effort was necessary to do so (TIMSS, 1995). In this study, we expected that mothers' influence would positively relate to their children's competence beliefs and effort.

We included students' general attitudes toward mathematics because this study takes place in math class. Previous research has reported that students' attitudes toward class positively related to their learning goal orientation and competence beliefs (Ames & Archer, 1988; Kloosterman & Cougan, 1994; Meece et al., 1988). The TIMSS (1995) reported that more than one-quarter of the Korean fourth graders reported that they did not like mathematics. In the present study, we predicted that Korean students' math attitudes would positively relate to their learning goal orientation and their competence beliefs.

The Present Study

In this study, we tested a conceptual framework describing relations among students' motivational beliefs and learning strategies that were hypothesized earlier. By using structural equation modeling, we examined a goal mediational model in which students' goal orientations were hypothesized to have direct effects on their learning strategies and to mediate effects given by their motivational variables.

Method

Subjects

The sample in this study consisted of 178 fourth graders (male = 95; female = 83) from two elementary schools in Korea. The students were from a middle class small town. Within each classroom, all students were asked to participate. Project staff members administered questionnaires to students who had returned their consent forms indicating their willingness to participate. All questionnaires were administered in the middle of February in 1999. All questions were also read aloud to all the students in mathematics class.

Procedure and Measures

Students completed the questionnaire measuring their perceptions of their mothers' influence, competence beliefs, attitudes toward mathematics, effort, goal orientations, and learning strategies to see how those motivational variables interrelated to each other in students' math learning. All items were answered using a 5-point Likert-style response scale. In addition, we collected two previous mathematics achievement tests administered by the school district in the early spring and fall semesters in 1998.

Mothers' influence. We adapted two items from the TIMSS (1997) asking the students how important their mother thought it was to do well in mathematics in school and how important their mother thought it was to be placed in the high achieving class. The reliability of the scale for this study was .68.

Attitudes toward mathematics. To obtain a general assessment of students' mathematics attitudes, we used 2 items from the TIMSS (1997) assessing interest and enjoyment. The reliability of the scale for this study was .83.

Effort. We used two items developed by Kloosterman (1988), such as "By trying hard I can become smarter in mathematics" and "My ability in mathematics will increase if I study hard." A high score on this scale is indicative of an incremental view of intelligence. A low score on this scale indicates a feeling that mathematical ability is a constant quantity. The reliability of the scale for this study was .83.

Competence beliefs. To scale students' competence beliefs, we adapted three items used by Kloosterman (1988), such as" I can get good grades in mathematics", "Most subjects I can handle O.K, but I often do poorly in mathematics", and "I have a lot of self-confidence when it comes to mathematics". The reliability of the scale for this study was .84.

Goal orientations. We adapted five items developed by Meece et al. (1988). Learning goal orientation contained three items implying that the student's goal was to learn something new, to learn as much as possible, or to learn more than just the answer. The reliability of the scale for this study was .72. Performance goal orientation contained two items implying that the student's goal was to impress others. The reliability of the scale for this study was .57.

Learning strategies. It has been reported that general cognitive and metacognitive strategies highly correlated with each other using factor analysis and that metacognitive strategies were more predictive of students' academic achievement than are general cognitive strategies (Pintrich & De Groot, 1990; Pokay & Blumenfeld, 1990). We adapted three items used by Meece et al. (1988) tapping dimensions of self-regulated leaning strategies, such as planning and monitoring. The reliability of the scale for this study was .61.

Results

See issue's website <http://rapidintellect.com/AEQweb/fallp.htm>.

Correlational Analyses

Table 1 shows the zero-order intercorrelations among students' previous academic achievement, mothers' influence, competence beliefs, math attitudes, effort, and learning strategies [Insert table One]. Mothers' influence positively related to students' academic achievement, learning strategies, competence beliefs, math attitudes, and performance and learning goal orientations, but it did not relate to their effort. Students' learning goal and performance goal orientations positively related to their learning strategies. In addition, positive relation appeared between them. Students' motivational variables were positively correlated to each other: no relation between math attitudes and performance goal orientation.

Structural Equation Modeling

We performed structural equation modeling to further clarify the relations among variables by using EQS (Bentler & Wu, 1995). Confirmatory Factor Analysis (CFA) allows researchers to test more precisely the hypothesized structure of a set of factors. To choose good fit indices, we considered that a good fit index should have a large model misspecification effect accompanied with trivial effects of sample size, distribution, and estimation method (Hu & Bentler, 1998). So, we used fit indices, such as chi-square, TLI (Turket-Lewis Index), CFI (Comparative Fit Index), SRMR (Standardized Root-Mean-Square Residual), and RMSEA (Root Mean-Mean-Square Error of Approximation).

Model specification. In this study, we hypothesized a goal mediational model that was applied to the Korean elementary school math class. First, we hypothesized that students' goal orientations had direct effects on their learning strategies. Second, we hypothesized that students' math attitudes, effort, and competence beliefs had direct effects on their learning goal orientation. Third, we hypothesized that mothers' influence had a direct effect on students' competence beliefs.

Evaluation model fit. The model that appears on Figure 1 had good fit indices (e.g. chi-square = 147.888, df = 107 (p<.001); TLI = 0.954 CFI = 0.963; SRMR = 0.058; RMSEA = 0.047) [Insert figure One]. The empirical hypotheses were generally confirmed. First, students' learning and performance goal orientations had unmediated effects on their learning strategies. Second, students' math attitudes and effort had direct effects on their learning goal orientation. Their competence beliefs had an indirect effect on their learning goal orientation and a direct effect on their performance goal orientation. Third, mothers' influence had a direct effect on students' competence beliefs and their performance goal orientation. In addition, it had indirect effects on their math attitudes and effort through competence beliefs. To keep this paper in an appropriate length, we have dropped table, showing the direct and indirect effects of variables.

Discussion

The results of this study show that a goal mediational model is useful in conceptualizing students' motivational beliefs and learning strategies. Students' learning goal orientation has the biggest direct effect on their learning strategies. Consistent with previous research, students' learning goal orientation positively relates to their learning strategies, math attitudes, effort, and competence beliefs (Ames, 1992; Ames & Archer, 1988; Anderman & Young, 1994; Meece et al., 1988; Pintrich & De Groot, 1990; Pintrich & Schrauben, 1992).

Students' performance goal orientation positively relates to their learning strategies. In addition, structural equation modeling reveals that students' performance goal orientation has a direct effect on their learning strategies, as reported by Meece et al. (1988). Midgley et al. (1998) argued that previous research has been done without separating performance goal orientation into the two constructs of ability-approach and ability-avoid. Accordingly, performance goal orientation was sometimes linked to adaptive patterns of learning strategies and other times to maladaptive patterns of learning strategies. The present study also focus only on the ability-approach construct of performance goal orientation. We will separate achievement goal orientations into three conceptual constructs for future work. It is also notable that students' performance goal orientations positively related to learning goal orientation (r=.24), as Medgly et al. (1998) suggested. Of course, learning goal orientation leads to deeper levels of cognitive engagement. However, it is important for students to be motivated extrinsically and to participate in their class (Pintrich & Schrauben, 1992; Pintrich & Schunk, 1996).

Students' math attitudes, effort, and competence beliefs have indirect effects on their learning strategies through learning goal orientation, and their competence beliefs have an indirect effect on their learning strategies through performance goal orientation. Consistent with previous research, students' math attitudes, effort, and competence beliefs positively relate to their learning goal orientation, learning strategies, and academic achievement (Ames, 1992; Dweck & Bempechat, 1983; Kloosterman, 1988; Kloosterman & Cougan, 1994). Therefore, students' learning goal orientation mediates math attitudes, effort, and competence beliefs, and their performance goal orientation mediates competence beliefs.

Interestingly, students' math attitudes and effort play mediating roles in learning goal orientation. Their math attitudes and effort have direct effects on their learning goal orientation, and competence beliefs have indirect effect on learning goal orientation through math attitudes and effort. On the other hand, students' competence beliefs have direct effect on their performance goal orientation, and mothers' influence has an indirect effect on students' performance goal orientation through their competence beliefs. So, students' competence beliefs play a mediating role in their performance goal orientation.

The results of this study show that a modified goal mediational model is applicable to the Korean elementary school math class. As predicted, Korean mothers' influence has a positive relation with their children' competence beliefs (Eccles et al., 1983; Kloosterman & Cougan, 1994; Stevenson et al., 1994; Wigfield, 1994; Wigfield et al., 1997). Structural equation modeling shows that Korean mothers' influence has a direct effect on their student's competence beliefs and performance goal orientation. It also has indirect effects on math attitudes and effort through their competence beliefs. Thus, Korean mothers play a unique role in their children's math learning. For future work, however, we will need to interview directly students' mothers because the present study uses students' perceptions of their mothers' influence.

In summary, a modified goal mediational model conceptualizes students' motivational beliefs and learning strategies in Korean elementary school math class. Students' learning goal orientation mediates math attitudes, effort, and competence beliefs, and their performance goal orientation mediates competence beliefs. Furthermore, their math attitudes and effort play major roles in their learning goal orientation, and their competence beliefs take an important role in their performance goal orientation. The Korean mothers are closely involved in their students' math learning and help them to develop their competence beliefs. Accordingly, students who are competent with their math ability and have positive math attitudes are oriented toward learning goal and use effective learning strategies. On the other, students who are competent with their math ability and perceive that their mothers think that it is important to get good grades take performance goal orientation; these students also use effective learning strategies.

In term of the limitation of this study, we used only the two elementary schools in a small school district and did not validate whether or not this model was applicable to a different context, such as different schools and different subject matter. Thus, we will conduct a validation study using a bigger sample size for future work. Stevenson et al. (1994) reported that there were cultural differences between Asian and American mothers' supports for their children's math learning. Thus, we ask researchers to do a study of how mothers' influence had an influence on their children's math learning in different cultural context. It has been reported that metacognitive strategies were more predictive of students' academic achievement than are general cognitive strategies (Pintrich & De Groot, 1990; Pokay & Blumenfeld, 1990). Accordingly, we used only metacognitive strategies in the present study. However, we will include these two kinds of general learning strategies for future study. Finally, previous research has suggested that students' task values have not been highlighted by motivational researchers even if they are important variables to explain students' motivational beliefs (Eccles et al., 1983; Eccles & Wigfeld, 1995; Wigfield, 1994; Wigfield & Eccles, 1992). For future work, we will include student's task values in a goal mediational model.

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Daeryong Seo, The Pennsylvania State University, PA

Jeong Hwan Kim, The Korea National University of Education, Seoul, Korea

Daeryong is a Ph.D. candidate of the department of educational psychology. Jeong is a professor of the department of educational psychology.