Analysis of the relationship of students' self-efficacy, test anxiety, andparental involvement toward learning strategy and achievement
in Korean middle school mathematics
Youngju Joo
Ewha Womans University, South Korea
youngju@ewha.ac.kr

Jae-Eun Joo
University of Connecticut, U.S.A.
jae-eun.joo@uconn.edu

BoKyung Jung
Ewha Womans University, South Korea
bokj0923@gmail.com

YooKyung Ham
Ewha Womans University, South Korea
hamuhamu89@gmail.com

Se-Bin Choi
Ewha Womans University, South Korea
kssky0712@naver.com

Abstract: This research used the third year survey data of 6,212 ninth graders from the 3-year
Korea Educational Longitudinal Study (2005-2007) in order to examine the relationship ofstudents' self-efficacy, test anxiety, and parental academic involvement toward learning
strategy and academic achievement in middle school mathematics in South Korea by applying
structural equation modeling. After satisfying the standard fit of both the measurement model(TLI=.979, CFI=.989 RMSEA=.040) and the structural model (TLI=.969, CFI=.983
RMSEA=.046), the authors verified the positive effect of academic self-efficacy (B=.21, β=.47) and parental academic involvement (B=.06, β =.15) as well as the negative effect of test
anxiety (B=-.05, β =-.13) on learning strategy. Moreover, the positive effect of all variables onacademic achievement proved to be statistically significant based on the following results:
academic self-efficacy (B=33.51, β =.36), test anxiety (B=3.35, β =.04), parental academic
involvement (B=9.81, β =.12), and learning strategy(B=7.89, β =.04). These results show thatstudents' academic self-efficacy had the greatest effect on learning strategy and academic
achievement, suggesting that educators should increase students' academic self-efficacy,
promote parental academic involvement, and decrease test anxiety in order to improvelearning strategy and academic achievement in middle school mathematics in South Korea.

Keywords: self-efficacy, test anxiety, parental academic involvement, mathematics
education, structural equation modelingAnalysis of the relationship of students' self-efficacy, test anxiety, andparental involvement toward learning strategy and achievement
in Korean middle school mathematics

I. Purpose of study
The evaluation of the students’ educational achievement is very important in measuring the extent to which thestudents achieve the educational objectives guided by the curricula and to improve teaching and learning
methods. In South Korea, the Korea Institute of Curriculum and Evaluation has been nationally evaluating
academic achievement since 2008. At an international level, most notable examples are the PISA (Program forInternational Student Assessment), an international comparative study of academic achievement on reading,mathematics, and science for students under 15 years of age administered by the Economic Cooperation andDevelopment, and the TIMSS (Trends in International Mathematics and Science Study), an international
comparative study of mathematics and science achievement by the International Association for the Evaluationof Educational Achievement.
Upon examination of these international evaluations, however, Korean students demonstratesignificant weakness in affective aspects of learning compared to their higher test results. Although Korean
students achieved high scores in TIMSS’ mathematics, they ranked only in the low-to-middle group concerning
academic competency among the nations represented in the test (Park, 2007). Korean students also achieved
top-level performance in PISA’s mathematics, but they also ranked low in affective aspects of their academic
literacy such as academic competency, participation, and anxiety (Nah, 2005).
Researchers have paid close attention to academic self-efficacy as an influential affective factor onmathematics achievement because academic self-efficacy is an indicator of competency in learning (Cha & Kim,
2009). Moreover, test anxiety in mathematics has been studied as an influential affective variable on academic
achievement (Kim, 2009) as well as parental academic involvement as both an environmental and psychologicalfactor (Shin & Lee, 2010, Kohl, Leuna & McMahon, 2007). Self-directed learning can also be examined byusing cognitive strategy like elaboration (Rush, 2000) and meta-cognitive strategy like self-monitoring (Shin,2008).
However, much of the previous research on the learner’s academic achievement in relation to academic
self-efficacy, test anxiety and parental academic involvement focused on a single variable or simply therelevance between them rather than the causal relationship. Therefore, the purpose of this study is to examine theintegrative and structural causal relationship among these variables to empirically verify their effects on one
another using the Structural Equation Modeling (SEM).
More specific research questions are as follows:
1. In Korean middle school mathematics, do academic self-efficacy, test anxiety, parental academic
involvement influence learning strategy?
2. In Korean middle school mathematics, do academic self-efficacy, test anxiety, parental academic
involvement and learning strategy influence academic achievement?

II. Theoretical Framework
Academic strategy is a concept that covers information processing activities that influence the learner’s
learning process (Han, 2004). This research examines learning strategy as cognitive strategy that signifies thepromotion of information acquisition, organization, storage and utilization, and meta-cognitive strategy. Selfefficacy which is the variable that affects academic achievement and learning strategy is defined as the judgmentof the self’s ability to organize and implement the actions he intended to perform (Bandura, 1986). According to
Pintrich and De Groot (1990), test anxiety is an intermediary that lowers performance by interfering withconcentration of attention. Test anxiety in most research shows that students with low propensity toward anxiety
tend to be more proactive and do their best in test while students with high propensity for anxiety tend to lose
efficiency greatly due to worrying. Concerning parental academic involvement, Coleman (1988) explained
family environment as a concept that covers the parents’ economic ability, intellectual level or educational
background, and interest and investment of time on the child’s education. In this study, however, only parental
involvement in the learning activities at home is examined.

Based on the previous study results, this study has set the following hypothesis: Hypothesis 1. In Korean middle school mathematics, academic self-efficacy, test anxiety, and parental
academic involvement will influence learning strategy.
 Hypothesis 2. In Korean middle school mathematics, academic self-efficacy, test anxiety, parental academic
involvement, and learning strategy will influence academic achievement.

III. Research Methods
Data sources
This study examined the third year (2007) survey data of 6,212 9 th graders, 3,229 male (52%) and 2,983 female(48%). from the 3-year Korea Educational Longitudinal Study (2005-2007).
Measurement instruments
The student’s academic achievement was measured by using the assessment scores of the math curriculum in the
Korea Educational Longitudinal Study. Academic strategy consists of demonstration, elaboration, organization,and meta-cognition. The Cronbach's α of the internal consistency reliability in each variable was as follows:demonstration (4 questions, Cronbach's α =. 773), elaboration (4 questions, Cronbach's α = .802), organization
with 5 questions (Cronbach's α = .832), and meta-cognition with 5 questions (Cronbach's α = .834). Self-efficacy
was measured in 5 questions (Cronbach's α = .922), test anxiety questions had 9 questions (Cronbach's α = .918),
and parental academic involvement had 8 questions (Cronbach's α = .837).
-

Data analysis
To examine causal and structural relationship between the variables, the authors set the statistical model
based on the hypothetical research model as shown in Figure 1. To set the model, upon the result of explorative
factor analysis, the measurement variables proved to be single-factor measurement variable. Our explorative
factor analysis of academic strategy showed its four sub-factors: demonstration, elaboration, organization, andmeta-cognition, and to prevent the excessive importance from being attributed to the measurement model, an
item parcel was used for academic self-efficacy, test anxiety, and parental academic involvement. Item parcelinguses the total or the average value of uni-dimensionally combined one-dimensional measured variables thatmeasure the same factor (Kishton & Widamn, 1994) and can decrease measurement error. Item parceling canalso achieve multivariate normal distribution rather than using individual questions (Bandalos, 2002). In order todetermine the estimation method for the statistical model, AMOS was used to verify the multivariate normal
distribution of the measurement variables of the structural equation model and each model’s goodness-of-fit andparameters were estimated by the Maximum Likelihood Estimation procedures.
[Figure 1] Hypothetical Research Model

IV. Results
Correlation matrix between measurement variables and descriptive statistics
Table 1 shows the mean, the standard variation, and the correlation analysis result for each variable, which
confirmed a significant correlation of all variables at the significant level of .05. Since the conditions of thenormal distribution is satisfied when the average skewness of the measurement variable in SEM is less than 3
and the average kurtosis is less than 10 (Kline, 2005), the basic hypothesis of the multivariate normal distribution
is satisfied in our model.

[Table 1] Matrix of Mean, Standard Deviation, Skewness and Kurtosis of the measurement variables (n=6212)
Measurement variables

1

2

3

4

5

6

7

8

9

10

11

1. Academic self-efficacy 1-

2. Academic self-efficacy 2

.82*

-

3. Test anxiety 1

.06

*

.04*

-

4. Test anxiety 2

.05*

.05*

.79*

-

5. Parental academic involvement 1

.21*

.23*

-.13*

-.13*

-

6. Parental academic involvement 2

.26*

.29*

-.18*

-.16*

.62*

-

7. Demonstration

.18

*

.20

*

.18

*

-.17

*

.16

*

.15*

-

8. Elaboration

.38*

.40*

-.07*

-.07*

.20*

.22*

.37*

-

9. Organization

.30*

.32*

-.10*

-.09*

.19*

.22*

.44*

.53*

-

10. Meta-cognition

.38*

.41*

-.09*

-.07*

.21*

.25*

.44*

.59*

.61*

-

11. Academic achievement

.37

*

.39

*

.03

*

.04

*

.16

*

.24

*

.03

*

.24

*

.14

*

.25*

Mean

2.48

2.50

3.11

3.27

2.69

3.20

2.41

2.63

2.61

2.65 508.84

Standard Deviation

.73

.69

.85

.89

.75

.80

.53

.58

.59

.55 59.51

Skewness

.09

.04

.10

-.04

-.06

-.30

.00

-.26

-.26

-.38

Kurtosis

-.32

-.03

.06

-.17

.18

.27

.96

.57
.61
*
p<.05

-

.79

.88 1.60

Verification of the Measurement Model
Based on the verification process via 2-Level possibility of a measurement model (Kline, 2005), its goodness-offit was tested by the Maximum Likelihood Estimation and all measurement variables were appropriately
measuring the applicable latent variables as indicated in Table 2 and Figure 2.
[Table 2] Results of the Goodness-of-Fit Test on the Measurement Model (n=6212)
CMIN
p
Df
TLI
CFI
RMSEA (90% C.I.)
Measurement Model
11.022
.000
29
.979
.989
.040 (.036～.044)[Figure 2] Results of Parameter Estimation of the Measurement Model

Verification of the Structural ModelAll the goodness-of-fit index of the measurement model were shown to satisfy the standard fit, and since theestimation possibility of the structural model has been theoretically verified, the goodness-of-fit of the researchmodel was tested by the Maximum Likelihood Estimation, proving that it is a statistically proper model as shownin Table 3.
[Table 3] Results of the Goodness-of-fit Test for the Structural Model (n=6212)
CMIN
p
df
TLI
CFI
Structural Model

14.782

.000

35

.969

.983

RMSEA (90% C.I.).046 (.043～.050)

Based on these findings, the results of the effect verification between the measurement variables are as shown in
Figure 3. Since the correlations among all variables were statistically significant, the structural model was
selected as the final model described in Picture 3.
[Picture 3] Unstandardized (standardized) path coefficients of the structural model

Since academic self-efficacy, test anxiety, and parental academic involvement influences learning strategy, andconcurrently, learning strategy was shown to influence academic achievement; it is necessary to examine thesignificance of the mediating effects between them (Baron & Kenny, 1986). Table 4 shows that learning strategy
can be seen as mediating between academic self-efficacy and academic achievement, between test anxiety andacademic achievement, and between parental academic involvement and academic achievement in middle schoolmathematics.
[Table 4] The Breakdown of the Direct/Indirect Effects (n=6212)
Unstandardized coefficient (B)wholedirectindirect
.210
.210
-

Standardized coefficient(β)
wholedirectindirect
.471
.471
-

learning strategy← academic self-efficacy

learning strategy← test anxiety

-.049

-.049

-

-.133

-.132

-

learning strategy← parental academic involvement

.061

.061

-

.153

.153

-

academic achievement ← academic self-efficacy

35.16833.509

1.659

.378

.360

.018

academic achievement ← test anxiety

2.959

3.349

-.390

.038

.043

-.005

academic achievement ← parental academic involvement

10.287

9.809

.478

.124

.119

.005

academic achievement ← learning strategy

7.888

7.888

-

.038

.038

-

V. Discussions and Implications
This research aimed to identify the structural relationship among academic self-efficacy, test anxiety, parental
academic involvement, learning strategy and academic achievement in Korean middle school mathematics.
Firstly, there were the positive effect of academic self-efficacy and the negative effect of test anxiety on learning
strategy, confirming the existing research results that the students who possess high level of academic selfefficacy and low test anxiety employ effective learning strategy (Pintrich & De Groot, 1990). Secondly, upon theexamination of the effect of academic self-efficacy, test anxiety, parental academic involvement, and learning
strategy on academic achievement, all variables positively influenced academic achievement. One interesting
result was that the test anxiety had a negative effect on learning strategy but a positive effect on academic
achievement. These results can be explained by the Korean educational culture. Since mathematics is considered
as a major subject and private tutoring on mathematic is prevalent in Korea, students can learn the contents ofmathematics by memorization. Hence, it is possible that Korean students with high test anxiety can achieve
highly on mathematics performance without developing deeper learning strategies, as verified by learning
strategy’s minor influence on academic achievement. Moreover, parental academic involvement had a positiveeffect on academic achievement and also indirectly influenced it, suggesting that it is important for parents tohave a high expectation of their children’s academic competency and provide intellectual and emotional stimuli
for their children. Learning strategy also influenced academic achievement; so Korean students should haveappropriate learning activities to improve learning strategy. Academic self-efficacy had the greatest effect onlearning strategy and academic achievement in this research, suggesting that educational policy and practices
should consider effective ways to increase students’ academic self-efficacy.
This research is significant in that it has structurally verified the causal relationship between academic
self-efficacy, test anxiety, parental academic involvement, learning strategy and academic achievement in Korean
middle school mathematics. Unlike previous research, this research has expanded the variables influencing
academic achievement to not only the learner variable, but also the causal relationship between the learner
variable, the environmental variables and learning strategy. The fact that this study utilized the third-year datafrom the Korean Education Longitudinal Study can support the generalization of its results.
Acknowledgement: This work was supported by the National Research Foundation of Korea Grant of the Korean Government(2012-045331).

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