Relationships of Cognitive and Metacognitive Learning Strategies to Mathematics Achievement

The Journal of Genetic Psychology, 2013, 00(00), 1–7 C Taylor & Francis Group, LLC Copyright

BRIEF REPORT Relationships of Cognitive and Metacognitive Learning Strategies to Mathematics Achievement in Four High-Performing East Asian Education Systems SHALJAN AREEPATTAMANNIL IMELDA S. CALEON National Institute of Education, Nanyang Technological University, Singapore

ABSTRACT. The authors examined the relationships of cognitive (i.e., memorization and elaboration) and metacognitive learning strategies (i.e., control strategies) to mathematics achievement among 15-year-old students in 4 high-performing East Asian education systems: Shanghai-China, Hong Kong-China, Korea, and Singapore. In all 4 East Asian education systems, memorization strategies were negatively associated with mathematics achievement, whereas control strategies were positively associated with mathematics achievement. However, the association between elaboration strategies and mathematics achievement was a mixed bag. In Shanghai-China and Korea, elaboration strategies were not associated with mathematics achievement. In Hong Kong-China and Singapore, on the other hand, elaboration strategies were negatively associated with mathematics achievement. Implications of these findings are briefly discussed.

Keywords: cognitive learning strategies, control strategies, elaboration strategies, Hong Kong-China, Korea, mathematics achievement, memorization strategies, metacognitive learning strategies, PISA, Shanghai-China, Singapore

Address correspondence to Shaljan Areepattamannil, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, 637616, Singapore; shaljan.a@nie. edu.sg (e-mail).

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Compared with students with a Western heritage background, students with a Confucian heritage background are generally perceived to be more reliant on memorization (McInerney, 2011), which is often categorized as a surface-level cognitive learning strategy (Weinstein, Acee, & Jung, 2010, 2011). Notwithstanding these claims, the performance of East Asian students on international student assessment tests, such as the Program for International Student Assessment (PISA) and the Trends in International Mathematics and Science Study (TIMSS), was significantly better than their counterparts in Western countries (see Martin, Mullis, Foy, & Stanco, 2012; Mullis, Martin, Foy, & Arora, 2012; Organization for Economic Cooperation and Development [OECD], 2010). The stellar performance of 15year-old students in Shanghai-China, Hong Kong-China, Korea, and Singapore on the PISA 2009 assessment placed these four East Asian education systems on the list of strong performers and successful reformers in education (OECD, 2011).

According to OECD’s PISA 2009 assessment, Shanghai-China, Hong KongChina, Korea, and Singapore are four of the world’s five highest-performing education systems (OECD, 2010). In PISA 2009, Shanghai’s 15-year-old students outscored their counterparts in more than 70 countries and economies in reading, mathematics, and science. The average scores of Shanghai’s 15year-olds in reading, mathematics, and science were 556, 600, and 575, respectively (OECD, 2010). Korea ranked second in reading (fourth and fifth in mathematics and science, respectively), Singapore ranked second in mathematics (fourth and fifth in science and reading, respectively), and Hong KongChina ranked third in mathematics and science and fourth in reading (OECD, 2010).

Given the sterling performance of East Asian students, it is crucial to examine whether or not memorization strategies are significantly associated with achievement among East Asian students. However, there is growing evidence that the use of other cognitive (i.e., elaboration strategies) and metacognitive (i.e., control strategies) learning strategies may also be linked to student learning outcomes (see Chiu, Chow, & McBride-Chang, 2007; Glogger, Schwonke, Holz¨apfel, N¨uckles, & Renkl, 2012; McInerney, Cheng, Mok, & Lam, 2012; Murayama, Pekrun, Lichtenfeld, & vom Hofe, 2012; Rosander & B¨ackstr¨om, 2012). Hence, it is important to examine not only the relationships of memorization strategies to student achievement but also the relationships of elaboration and control strategies to student achievement. In the present study, we are particularly interested in mathematics achievement alone because the East Asian mathematics pedagogy is generally perceived to emphasize memorization as an effective learning strategy (see Hogan et al., 2013). We hypothesized that all the three learning strategies (i.e., memorization, elaboration, and control strategies) would be significantly and positively associated with mathematics achievement among students in Shanghai-China, Hong Kong-China, Korea, and Singapore.

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Method Data Data for the study were drawn from the PISA 2009 database. The sample comprised 20,224 individuals, including 15-year-old students from ShanghaiChina (n = 5,115; male = 2,528, female = 2,587), Hong Kong-China (n = 4,837; male = 2,557, female = 2,280), Korea (n = 4,989; male = 2,590, female = 2,399), and Singapore (n = 5,283; male = 2,626, female = 2,657).

Measures Mathematics achievement.. The PISA 2009 mathematics achievement scale was the outcome measure in the study. This scale was based on 35 test items. The test items included a combination of multiple-choice and open-ended questions, and were drawn from broad content areas such as space and shape, quantity, change and relationships, and uncertainty (OECD, 2012).

Cognitive and metacognitive learning strategies.. The PISA 2009 indices of memorization, elaboration, and control strategies were the independent variables in the study. Memorization and elaboration strategies assessed students’ cognitive learning strategies, while control strategies measured students’ metacognitive learning strategies (OECD, 2012). All items were rated on a 4-point Likert-type scale ranging from 1 (almost never) to 4 (almost always), and were scaled using item response theory scaling techniques (OECD, 2012).

In addition to these measures, student background characteristics such as gender (0 = male, 1 = female), language spoken at home (0 = another language, 1 = language of test), and family socioeconomic status (i.e., PISA index of economic, social, and cultural status; see OECD, 2012) were included as covariates in the study.

Results and Discussion Hierarchical regression analyses were conducted to examine the relationships of cognitive and metacognitive learning strategies to mathematics achievement (see Table 1). The results of the study revealed three things. First and foremost, memorization strategies were significantly negatively associated with mathematics achievement in all the four East Asian education systems: Shanghai-China (B = –18.41, p < .001), Hong Kong-China (B = –20.86, p < .001), Korea (B = –5.54, p < .05), and Singapore (B = –24.61, p < .001). Although there are assertions that students hailing from the Confucian heritage culture regard memorization as a prelude to understanding (Kember, Biggs, & Leung, 2004), students who reported greater use of memorization strategies scored significantly lower on the PISA mathematics assessment than did their peers who reported lesser use of

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494.03∗∗∗ −5.68 61.46 38.43∗∗

−0.19 38.15 32.94∗∗

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34.90 6.13 34.97 3.14

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12.70 3.37 12.64 2.83

SE B

— −.03 .02 .35

— .00 .05 .33

β

— −.05 .01 .26 −.06 .03 .34

579.66∗∗∗ −6.92 17.83∗ 44.10∗∗∗

−14.25 56.88∗∗ 24.23∗∗

529.53∗∗∗

B

.12

527.73∗∗∗ −8.44 36.31 27.95∗∗∗ −5.54∗ 2.37 30.51∗∗∗ .15

2.62 2.60 3.14 2.08

.10

7.97 4.72 7.67 1.91

SE B — −.08 .16 .26

β −15.49∗ 60.63∗∗∗ 18.68∗∗∗ −20.86∗∗∗ −9.55∗∗ 43.18∗∗∗

— −.03 .09 .34

.09

B 530.89∗∗∗

574.18∗∗∗ −9.54∗ 14.38∗∗ 38.64∗∗∗ −24.60∗∗∗ −8.63∗∗ 31.24∗∗∗

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27.27 5.65 27.59 2.84 2.11 1.69 2.16 .22

— .00 .04 .28 −.14 .03 .26

β

Singapore

12.27 3.47 12.22 2.83 2.18 2.64 2.79 .17

SE B

Model 1

Korea

0.41 37.00∗ 27.43∗∗∗ −18.41∗∗∗ 3.88 31.97∗∗∗

584.26∗∗∗

B

Model 2

Hong Kong-China

.06

Note. ESCS = economic, social, and cultural status. ∗ p < .05. ∗∗ p < .01. ∗∗∗ p < .001.

Intercept Gender Language ESCS Memorization Elaboration Control Adjusted R2 f2

578.87∗∗∗

B

Model 1

Shanghai-China

TABLE 1. Results of Regression Analyses Predicting Mathematics Achievement

2.83 2.66 2.98 2.17 1.61 1.85 2.22 .22

8.17 4.21 7.89 1.83 1.94 1.86 2.15 .20

SE B

Model 2

— −.05 .07 .30 −.22 −.08 .28

— −.08 .17 .20 −.19 −.09 .42

β

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memorization strategies. Thus, even in countries that have been commonly stereotyped as prone to memorization (see Hogan et al., 2013; McInerney, 2011), the use of this learning strategy can prove to be counterproductive. The increased use of memorization, which effectively reduces the processing time that can be allotted for deep learning strategies, can be one key reason why memorization strategies may have negative relations with mathematics achievement (see Weinstein et al., 2010, 2011; Weinstein & Mayer, 1986). Our findings, however, do not discount the possibility that the use of memorization strategies may be useful in learning introductory concepts in mathematics and in building up background knowledge that can facilitate the application of deep learning strategies (see Weinstein & Mayer, 1986).

Second, elaboration strategies were not significantly associated with mathematics achievement in Shanghai-China and Korea, whereas such learning strategies were significantly negatively linked to mathematics achievement in Hong Kong-China (B = –9.55, p < .01) and Singapore (B = –8.63, p < .01). Although a substantial body of research has documented that students who use elaboration strategies tend to think deeply about concepts, integrate what they learn with other material, and transfer concepts to different situations (Seaton, Marsh, & Craven, 2010), the results of the present study indicated that elaboration strategies may not be a significant determinant of student achievement in mathematics, especially in Shanghai-China and Korea. In contrast, greater use of elaboration strategies proved to be counterproductive in enhancing student mathematics achievement in Hong Kong-China and Singapore. Both nonsignificant and negative relationships between the use of elaboration strategies and mathematics performance can be an artifact of the poor quality of elaboration techniques that the students applied.

Elaboration strategies take up considerable time, and may slow down the learners’ generation of ideas (Czuchry & Dansereau, 1998). It is also possible that the effect of elaboration strategies was overshadowed by the use of metacognitive control strategies, that is, a decrease in elaboration may be accompanied by an increase in achievement due to the positive effect of metacognitive control strategies.

Third, as expected, the use of control strategies was significantly positively associated with mathematics achievement in Shanghai-China (B = 31.97, p < .001), Hong Kong-China (B = 43.18, p < .001), Korea (B = 30.51, p < .05), and Singapore (B = 31.24, p < .001). Indeed, students who are adept at regulating their own learning are able to identify or discern feasible objectives, choose suitable approaches to achieve their objectives, transcend their other goals and remain motivated to learn (Marsh, Hau, Artelt, Baumert, & Peschar, 2006). Hence, the use of control strategies has generally been associated with positive educational outcomes (Marsh et al., 2006; Seaton et al., 2010).

In conclusion, the findings of the present study suggest that East Asian students’ greater reliance on memorization strategies may not be helpful in improving their performance on the PISA mathematics assessment; but greater utilization of control strategies may be more beneficial. However, the findings in regard to the

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relations of elaboration strategies to mathematics achievement were mixed. Indeed, the nuanced relationship between elaboration strategies and mathematics achievement warrant further research. Because there are individual differences in students’ learning strategies, it is crucial to identify students’ knowledge and use of learning strategies (Weinstein et al., 2010, 2011). However, some type of training or educational intervention in the form of an adjunct learning strategies course combined with a metacurriculum (i.e., teaching learning strategies as part of content courses) intervention approach may be required to help students develop an effective and efficient repertoire of learning strategies (Weinstein et al., 2010, 2011).

AUTHOR NOTES Shaljan Areepattamannil is a research scientist at the Centre for International Comparative Studies, Office of Education Research, National Institute of Education, Nanyang Technological University, Singapore. His research interests primarily revolve around psychosocial correlates and antecedents of student achievement and engagement across cultures. Imelda S. Caleon is a research scientist at the Office of Education Research, National Institute of Education, Nanyang Technological University, Singapore. Her research interests include students’ conceptual development, teacher professional development, and the assessment and development of 21st century skills.

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Original manuscript received July 21, 2012 Final version accepted March 29, 2013