Learning Strategies as Moderators Between Motivation and Mathematics Performance in East Asian Students: Latent Class Analysis

This study applied a three-step latent class analysis (LCA) approach to explore latent classes of learning strategy use and their moderation effects on the relationships between motivation and mathematics performance. The data of 15-year-old students from five East Asian educational systems related to Chinese culture in the Programme of International Student Assessment (PISA) in 2012 were analyzed. The findings indicated that Shanghai, Singapore, Taiwan, and Macau showed three latent classes of learning strategies, whereas Hong Kong had two latent classes. Most students in the five educational systems reported to use the control strategy, some students reported the use of combined learning strategies, and few students reported the use of memorization except for students in Shanghai. Furthermore, we found the moderation effects of learning strategy use on mathematics performance depended on the types of motivation and educational systems. This study provides insights into the advantages of a three-step LCA approach in educational research.


Introduction
Learning strategy use plays a vital role in students' academic performance. Students with high achievement are more likely to use deep learning strategies or a combination of various learning strategies (Greene et al., 2004;Metallidou & Vlachou, 2007;Pintrich, 1999). Researchers have attempted to classify students' learning behaviors into differ ent categories and label them as specific learning strategies (Pintrich, 1999;Weinstein & Mayer, 1986). Learning strate gies are commonly recognized as cognitive and meta cognitive strategies (Weinstein & Mayer, 1986). Cognitive strategies serve to help students process information through remembering, summarizing, and connecting prior and new knowledge. Metacognitive strategies allow students to assess whether they reach their goals, identify a knowledge gap, and adjust their learning behavior (Pintrich, 1999;Weinstein & Mayer, 1986). This established taxonomy of learning strategies in the literature is followed by an international largescale achievement study, named the Programme of International Student Assessment (PISA) 2012, that includes memorization, elaboration, and control strategies (OECD, 2013a). Memorization strategies involve students learning only key terms or learning material repeatedly. In contrast, elaboration strategies involve students making connections to other ideas and developing alternative solutions. Control strategies involve students monitoring and planning throughout the learning process (OECD, 2013a). Generally, elaboration and control strategies are considered deeplevel strategies, while memorization is a surfacelevel strategy (Pintrich, 1999;Weinstein & Mayer, 1986).
Previous studies focusing on learning strategy use have used a variablecentered approach that provides a single set of estimated parameters for a sample, which oversimplifies reality (Metallidou & Vlachou, 2007;Sorić & Palekčić, 2009;Yıldırım, 2012). However, scholars argued that learning strategy use may be a continuous process in which students apply various learning strategies during a learning process (Dinsmore & Alexander, 2016). Moreover, the phases of using learning strategies might be overlapped (Hattie & Donoghue, 2016). For example, students use mem orization to acquire knowledge and then use elaboration to consolidate knowledge. In this process, it is impossible to differentiate when students use a specific strategy.
Given that the use of learning strategy is a dynamic and continuous process, personcentered approaches-latent class analyses (LCAs)-might be more appropriate for the use of learning strategy than variablecentered approaches. Recently, personcentered approaches have become popular in educa tional research (Häfner et al., 2018;Pastor et al., 2007;Shim & Finch, 2014) and were applied to identify different sub groups based on the patterns of responses to measured vari ables. The most appealing advantage of these personcentered approaches is that researchers can include multiple variables at once to investigate the interactions of students' learning behav ior and processes. Personcentered approaches can also iden tify heterogeneous profiles in characteristics of students' learning such as motivation and learning behavior. For exam ple, the interaction between homework time and homework effort (Flunger et al., 2015) and the interaction between achievement goals and motivation (Shim & Finch, 2014) were investigated using personcentered approaches. Thus, apply ing personcentered approaches in learning strategies could reflect theoretical arguments of the use of learning strategies.
Although considerable literature has shown the rela tions among students' learning strategy use, motivation, and academic performance, most studies consider learning strategies as mediators between motivation and academic performance (Metallidou & Vlachou, 2007;Sorić & Palekčić, 2009;Yıldırım, 2012). However, it is unclear whether learning strategies may explain the relationship between motivation and academic performance. Thus, in this study, we attempted to examine the effect of learning strategies as moderators on the relationships between motivation and academic performance.
Only a few studies have examined these relations within East Asian educational systems (Lau & Chan, 2003;Lau & Ho, 2016;Law, 2009;Liu, 2009). Research focusing on an East Asian context is predominant in the reading domain with students from Hong Kong (Lau & Chan, 2003;Lau & Ho, 2016;Law, 2009). Yet, the features of learning reading or languages differ from mathematics, as assignments and tests in mathematics are likely to be multiplechoice or an open format with a specific solution. In the reading domain, students are often asked to write a summary or engage in reading comprehension. Thus, different types of assignments and tests are associated with the use of learning strategies within a specific academic domain (Clare & Aschbacher, 2001;Joyce et al., 2018). Given that motivation is contextual and domainspecific (Schunk et al., 2014), it is likely that students' learning motivation may differ in mathematics compared to other content areas such as reading.
Moreover, mathematical knowledge is coherent, that is, basic mathematical concepts are linearly built upon another so that students can understand more complicated concepts once they master basic concepts (Vanderstoep et al., 1996). Regarding reading, the lists of topics seem to be loosely related. Thus, the features of subjects might result in a dis tinct tendency of learning strategy use (Donker et al., 2014). So far, little is known about the relations among students' learning strategy use, motivation, and performance in math ematics using a wide range of East Asian samples derived from Chineserelated cultures.
Given that East Asian students' outstanding mathematics performance has been documented in international large scale assessments (Leung, 2017;OECD, 2013b), there is a need for more empirical evidence to support East Asian stu dents' outstanding mathematics performance. Focusing on learning strategy use, motivation, and mathematics perfor mance may shed light on how East Asian students achieve high mathematics performance.
The present study makes a unique contribution to the field by applying a threestep LCA approach to explore latent classes of learning strategy use and their moderation effects on the relations between motivation and mathematics performance among students from five East Asian educational systems that are relevant to Chinese culture. A personcentered approach such as LCA is appropriate as learning strategies are a dynamic process, rather than using regression analyses or structural equation modeling. Further, although learning strategies have been examined as mediators, research examining them as mod erating the relationship between motivation and academic per formance is scarce. Lastly, this study examines these relations among students in a wide range of East Asian educational systems. Fifteenyearold students from Shanghai, Singapore, Taiwan, Hong Kong, and Macau in the Programme for International Student Assessment (PISA) in 2012 were used.

Learning Strategies and Motivation Among East Asian Students
There is a stereotype of learning behavior among East Asian students that emphasizes the impact of memorization on high academic performance. Recent studies have challenged this stereotype. Crosscultural studies evidenced that East Asian students used less memorization than other Western coun tries (Chiu et al., 2007;Liu, 2009;Wu et al., 2020). Liu (2009) demonstrated that American students reported greater memorization use than Hong Kong students while learning mathematics. Similarly, Wu et al. (2020) found that American students reported more memorization than Taiwanese stu dents; Taiwanese students reported more elaboration and control strategies while learning mathematics. Building on evidence, East Asian students seem not to be stereotyped as rote learners.
Motivation is often conceptualized as intrinsic and extrin sic motivation. Intrinsic motivation refers to a focus on learn ing and mastery (Duncan & McKeachie, 2005). Students who are intrinsically motivated engage in learning tasks because they perceive them as inherently interesting. In con trast, extrinsic motivation is a focus on performance and approval from others (Duncan & McKeachie, 2005). Students who are extrinsically motivated engage in learning tasks because they view them as essential and useful for the future.
Previous studies have found that intrinsic motivation plays an important role in students' learning in most coun tries (Chiu & Chow, 2010;Mullis et al., 2016;Zhu & Leung, 2011). Extrinsic motivation has revealed different patterns between East Asian and Western countries (Chiu & Chow, 2010;Jerrim, 2015;Liu, 2009;Zhu & Leung, 2011). Jerrim (2015) showed that East Asian students reported higher extrinsic motivation than students in Australia and England. Chiu and Chow (2010) found that the effects of extrinsic motivation on academic performance were lower for American students than Hong Kong students. Moreover, intrinsic and extrinsic motivation positively predicted math ematics performance in East Asian countries, but extrinsic motivation negatively predicted mathematics performance in Western countries (i.e., Australia, England, Netherlands, and USA) in the Trends in International Mathematics and Science Studies (TIMSS) 2003 (Zhu & Leung, 2011).

Effects of Learning Strategy Use on the Relations Between Motivation and Mathematics Performance
Selfregulated theory (SRL) hypothesizes students set goals and motivation that influences their learning behavior (phase 1), students evaluate their performance (phase 2), and stu dents adjust their goals and motivation based on their self reflection (phase 3; Zimmerman, 2000). Thus, motivation is related to the selection of learning strategies, and indirectly linked to performance. Aligned with this conceptualization, several studies have examined the extent to which motiva tion predicts academic performance through the mediation effects of learning strategies to understand the mechanisms underlying these associations (Chung, 2000;Lee et al., 2014;Metallidou & Vlachou, 2007;Sorić & Palekčić, 2009;Yıldırım, 2012). However, most studies have not found that the use of learning strategies was a potential mediator to explain the relationship between motivation and academic performance. Chung (2000) found that intrinsic motivation did not significantly predict language and mathematics per formance through several mediators including learning strat egies among fifthgrade Korean students. Similarly, Yıldırım (2012) showed that learning strategies did not mediate the relations of intrinsic and extrinsic motivation with students' mathematics performance in a Turkish sample. In contrast, Metallidou and Vlachou (2007) found cognitive learning strategies as well as control strategies positively mediated the relations of motivation with language and mathematics performance. Although Lee et al. (2014) had similar findings as Metallidou and Vlachou (2007), their findings showed small positive to null relations between control strategies and academic performance, when control strategies were media tors between intrinsic motivation and achievement.
However, SRL only suggests the reciprocal relationships among motivation, learning strategies, and performance and does not explicitly state that learning strategies can only serve as a mediator. Conceptually, one might also expect that students with high levels of motivation and the use of deep level strategies would perform well academically. Thus, it is reasonable to hypothesize that motivation may play a stron ger role in predicting academic performance for students who use highlevel learning strategies (e.g., deeplevel strat egies such as elaboration and control) than those who use lowlevel learning strategies (e.g., surfacelevel strategies such as memorization). Learning strategies may serve as a moderator to alter the magnitude of association between motivation and academic performance. (Baron & Kenny, 1986). Given that limited evidence exists regarding the role of a mediator for learning strategies, learning strategies may interact with motivation to moderate the strengths and direc tions of these relations. Considering learning strategies as moderators may help educational practitioners identify which type of learning strategies may enhance performance when students' motivation is high.

The Selection of PISA 2012
Each PISA cycle focuses on a specific domain: (1)  In 2009, Shanghai joined PISA. Then, four major provinces in China-Beijing, Shanghai, Jiangsu, and Guangdong-started participating in PISA 2015. Since 2009, there has been a growing interest in investigating Chinese students' learning outcomes (Areepattamannil & Caleon, 2013;Jiang et al., 2021;Kılıç Depren & Depren, 2021;Lau & Ho, 2016, 2020Lee, 2014;Meng et al., 2017;Teng, 2020). Most literature focuses on the reading domain (Areepattamannil & Caleon, 2013;Kılıç Depren & Depren, 2021;Lee, 2014;Meng et al., 2017). For example, Kılıç Depren and Depren (2021) found that metacognition about assessing credibility (i.e., how do you rate the usefulness of the following strategies for writing a summary of this two page text) was the most relevant variable to reading performance in the Chinese sample in PISA 2018. Meng et al. (2017) investigated how teaching factors and reading strategies contributed to reading performance in PISA 2009 by comparing the Chinese and American samples. They showed that teachers' morality (e.g., most of my teachers treat me fairly) and simulation (e.g., my teacher gives me enough time to think about my answers) were important to American students, but not Chinese students. However, the reading strategy related to writing own words as a summary was important to Chinese students. One recent study com pared highperforming educational systems-Hong Kong, China, Canada, and Finland-to investigate the association between motivation and science performance in PISA 2015 (Lau & Ho, 2020). Enjoyment of learning science was the strongest predictor of science performance across all coun tries; explicit and adaption instruction was positively related to enjoyment of science (Lau & Ho, 2020).
However, to our best knowledge, fewer studies have investigated the mathematics domain using a Chinese sam ple. Given that educational systems related to Chinese cul tures perform well in mathematics, it is necessary to take Chinese students into account to examine associations among motivation, learning strategies, and mathematics perfor mance. Among PISA datasets, PISA 2012 is the most appro priate for the current study because it directly measured mathematicsrelated motivation and learning strategies and included multiple educational systems related to Chinese cultures.

Latent Class Analysis With a Three-Step Approach
Although previous studies analyzed each type of learning strategy in a sample (Chiu & Chow, 2010;Yıldırım, 2012), this approach implies that students purely use one strategy during learning and that all students use the same strategy. These two assumptions might rarely occur in the real world. According to a model of learning (Dinsmore & Alexander, 2016;Hattie & Donoghue, 2016), the phases of learning processes start with surface learning, then deep learning and transfer of learning. These phases are partially overlapped; thus, students might combine different types of learning strategies simultaneously. Also, within a sample, subgroups might exhibit different typologies of learning strategies, depending on the levels of motivation and performance (NylundGibson & Choi, 2018). Thus, to relax these two theoretical assumptions, a personcentered approach is appropriate.
A personcentered approach can overcome methodolo gical assumptions and limitations of a variablecentered approach. First, a variablecentered method assumes that relations among variables are the same across individuals in a population or sample. Analyses using a variablecentered approach might be difficult to identify unobserved subgroups in a population or sample. Second, linear relations among variables in a variablecentered approach are built on a nor mal distribution assumption for variables. However, such a strong assumption does not always occur in realworld data. For example, the items of learning strategies in PISA use a forcedchoice design (for details, see Method). Students are allowed to choose one learning strategy within an item. Thus, one cannot assume that the distributions of responses are normally distributed.
Given these theoretical and methodological arguments, a personcentered approach, latent class analysis (LCA), may be an alternative and useful approach. A personcentered approach relaxes the assumptions of a variablecentered approach in order to meet the natural features of variables. LCA can be used to identify unobserved subgroups (i.e., latent classes) in a population thereby grouping students with similar response patterns (Collins & Lanza, 2010). Furthermore, LCA does not require a normal distribution assumption for data. Thus, LCA is wellsuited for the pur pose of this study and the nature of learning strategies data.
In many LCA practical applications, latent classes can be used to predict outcomes (Asparouhov & Muthén, 2014). To conduct these analyses, researchers proposed a threestep approach that combines a latent class model and a regression model into a joint model (Asparouhov & Muthén, 2014;Vermunt, 2010). Including predictors or outcomes can cap ture heterogeneity of latent classes. In this study, we aimed to use motivation and mathematics performance to explain heterogeneity of latent classes that obtained from learning strategies.

Purpose of the Present Study
Most empirical studies have focused on East Asian students' learning strategies, motivation, and performance, yet little research has addressed these relationships in the mathemat ics domain. To our best knowledge, there is no systematic investigation of East Asian students' mathematical learning using a wide range of educational systems related to the Chinese culture (for details, see Selection of PISA 2012). In addition, there is limited evidence indicating that learning strategies may serve as a potential mediator. Theoretically, SRL implies learning strategies can potentially moderate relations between motivation and performance. Lastly, empirical studies assumed that all students use one learning strategy in a sample; however, this assumption might rarely occur in the real world, as students combine different strate gies and students within a sample might display different learning behavior. Thus, to address previous limitations, this study applied a threestep LCA approach to explore latent classes of learning strategy use among East Asian students and examined their moderation effects on the relations between motivation and mathematics performance among five educational systems that are dominated by Chinese cul ture (i.e., Hong Kong, Macau, Shanghai, Singapore, and Taiwan; Yamamoto & Brinton, 2010). Thus, three research questions were addressed in this study: 1. To what extent do students in five East Asian educa tional systems apply learning strategies? We expected that few students purely used memorization and that many students used deeplevel learning strategies (Chiu et al., 2007;Liu, 2009;Wu et al., 2020). We also expected that some students combined different strategies while learning mathematics (Dinsmore & Alexander, 2016;Donker et al., 2014). We did not make any specific hypotheses regarding how stu dents combined learning strategies; this was explor atory in nature due to limited research. 2. To what extent do learning strategies moderate the relations between students' motivation and mathe matics performance? We expected that when students had high levels of intrinsic and extrinsic motivation, they tended to use deeplevel strategies or combine different strategies to enhance their mathematical performance (Chiu & Chow, 2010;Jerrim, 2015;Zhu & Leung, 2011). In contrast, we expected that when students had low levels of intrinsic and extrinsic motivation, they tended to rely on memorization, which leads to low performance.

To what extent do five East Asian educational systems
have the similarities and dissimilarities of learning strategies and their moderation effects? Given the lim ited number of studies focusing on East Asian students from a wide range of Chineserelated educational sys tems, this research question was exploratory.

Participants
Participants in this study were 15yearold students in PISA 2012. The sampling design was a twostage stratified sample design (OECD, 2014). In the first stage, schools were sys tematically sampled based on probabilities proportional to the school size. Once schools were selected, students within the schools were randomly selected. PISA 2012 used a rotated design to distribute students' questionnaires ran domly (OECD, 2014). This twostage stratified sample design aimed to collect a representative sample in each edu cational system. Three forms of student questionnaires (i.e., Forms A, B, and C) were distributed to students randomly. Form C was selected in this study because this form included learning strategy use and motivation variables. Choosing

Measures
Three measures used in this study were from PISA 2012: learning strategy use, motivation, and mathematics performance.
Learning strategy use. Three learning strategies (i.e., memori zation, elaboration, and control) were used to assess student mathematics learning behavior. PISA 2012 adopted a forced choice format for learning strategy items (OECD, 2013a), which allowed each student to choose only one strategy to best describe their learning behavior. There were four items in the questionnaire, and each item included three mutually exclusive learning strategies: memorization, elaboration, and control strategies (see Table 1 for items). It is not recom mended to calculate the reliability of a forcedchoice format due to a violation of a basic assumption of independent errors between items (Brown & MaydeuOlivares, 2013). Thus, we did not provide the reliability of learning strategy items.
Motivation. Intrinsic and extrinsic motivation were measured using a fourpoint Likert scale with four items, respectively (see Table 1 for items). PISA 2012 provides indices of intrin sic and extrinsic motivation for each educational system. These indices are scaled with a mean of 0 and a standard deviation of 1 using an item response theory framework (IRT) (OECD, 2014). The reliabilities of indices of intrinsic and extrinsic motivation were high in OECD countries and partner countries. In our study, among the five East Asian countries, the range of reliability of intrinsic motivation was from .90 to .91; the range of reliability of extrinsic motiva tion was from .87 to .91 (OECD, 2014).
Mathematics performance. In the PISA assessment, mathe matical contents cover: (a) change and relationships, (b) space and shape, (c) quantity, and (d) uncertainty and data. PISA 2012 adopted a booklet design whereby each student was randomly assigned to one of thirteen booklets and tested on a portion of items from the entire item pool. Thus, rather than using raw scores, five plausible values with a mean of 500 and a standard deviation of 100 across countries were provided to represent student mathematics performance in PISA 2012. These plausible values were drawn from the esti mated posterior distributions using an IRT framework (OECD, 2014

Statistical Analyses
A three-step LCA approach. The threestep LCA approach is developed under the structural equation modeling (SEM) framework (see Asparouhov & Muthén, 2014;Vermunt, 2010). A threestep LCA approach was applied to explore latent classes in each educational system and to examine the moderating effects of learning strategy use on the relations between motivation and mathematics performance. The model specification of a threestep LCA approach involves three steps. The first step is an unconditional model without predictors and outcomes, with the aim to find a measurement model that fits the data well. In this step, we searched for the best fit model (i.e., class enumeration). The second step is to obtain the estimated parameters in the unconditional model that provided the fixed values for accounting for estimated errors of the assignment of a class. The third step is to include predictors and an outcome while fixing the estimated param eters in the unconditional model. This step is similar to a standard SEM approach where researchers include the struc ture part after finding the fitted measurement model. We describe the details of the threestep model specification in the following subsections.
Step 1: Class enumeration. In the first step, latent classes were explored using students' responses to four learning strat egy items. To explore latent classes in each educational sys tem, the LCA models with 1, 2, 3, and 4class solutions were fitted to each of the seven education systems separately. The Akaike information criterion (AIC; Akaike, 1987), Bayesian information criterion (BIC; Schwarz, 1978) and adjusted BIC (a_BIC; Sclove, 1987), were used to select the optimal num ber of latent classes, because LCA models are not nested with each other. BIC and a_BIC have shown better performance in the LCA simulation compared with AIC (Nylund et al., 2007); thus, BIC and a_BIC were referred to model selec tion. BIC and a_BIC with lower values suggest a better model fit. In addition, the Lo-Mendell-Rubin (LMR) test was used to select the number of latent classes. The LMR compares a model with k classes against an alternative model with k1 classes. If an LMR result has a significant pvalue, it suggests that a model with k classes is favored. In addition to statistical evidence, we also considered the meaningful interpretations of latent classes in each educational system in order to make a final decision of the number of latent classes (Marsh et al., 2009). The interpretations of latent classes were based on the maximum number of highest conditional probabilities of the respective type of learning strategies. For example, if three or four out of four items have the highest conditional prob abilities on the "Control strategy" option within one class, that class is labeled as the "Control" class. If one latent class has two items with the highest probabilities on two or Intrinsic I am interested in the things I learn in mathematics.
Intrinsic Making an effort in mathematics is worth it because it will help me in the work that I want to do later on. Extrinsic Learning mathematics is worthwhile for me because it will improve my career prospects. Extrinsic Mathematics is an important subject for me because I need it for what I want to study later on. Extrinsic I will learn many things in mathematics that will help me get a job. Extrinsic three different strategy options, that class is categorized as the "Combination" class.
Step 2: Estimated parameters for a class. In the second step, each student was classified into one of the identified latent classes of learning strategy use based on the highest probability of class membership obtained from the first step. We obtained the estimated parameters of the final model from the first step. The estimated parameters that account for the measurement error can be found in the Mplus output. The estimated parameter of the last class is fixed 0 as a reference group. The details of manual calculations can be referred to Formula One in Asparouhov and Muthen (2014). These esti mated parameters would be fixed in the third step to avoid the shift of class membership.
Step 3: Including predictors and an outcome. In the third step, we included intrinsic motivation and extrinsic moti vation as predictors and mathematics performance as a dependent variable in the regression model. Latent classes of learning strategy use were moderators. In addition, we fixed the estimated parameters for each class. Figure 1 depicts the threestep LCA model to explain the relations between motivation, learning strategy use, and mathemat ics performance.
In the threestep LCA approach as shown in Figure 1, stu dents' five mathematics plausible values were dependent variables; intrinsic motivation and extrinsic motivation were two predictors; the types of learning strategy use as latent classes were moderators. Analyses were conducted with Mplus 7.4 (Muthén & Muthén, 2015). To include five math ematics plausible values, "Type=imputation" syntax was used in the Mplus. Table 2 presents descriptive statistics for motivation and learning strategies items. At the top of the table, the means and standard deviations of intrinsic and extrinsic motivation among the five educational systems are presented. Macau had the highest levels of intrinsic and extrinsic motivation, followed by Taiwan, Shanghai, and Singapore. Hong Kong had the lowest levels of intrinsic and extrinsic motivation. Across the five educational systems, the means of intrinsic  Note.

Descriptive Statistics
The means and standard deviation for learning strategies items are not available due to the forced-choice format. The proportions of each type of a learning strategy are presented within an item. motivation were higher than those of extrinsic motivation. The rest of Table 2 presents the proportions of students endorsing one of three learning strategies for four items of learning strategy use across the five educational systems. In the five educational systems, there were consistently the largest proportions of students endorsing the control strategy for Items 1, 2, and 3 of learning strategy use. For instance, excluding the missing data (i.e., 2.5%), there were 58.90%, 27.40%, and 11.20% of students endorsing learning strate gies of control, elaboration, and memorization, respectively, in Shanghai. For Item 4, there were the largest proportions of students endorsing memorization in all educational systems except for Singapore. The missing data information is pre sented in Table 2 as well. Overall, there were extremely low missing data in the five educational systems in East Asia, ranging from 2.5% (Item 1 in Shanghai) to 0.20% (motiva tion items in Taiwan). Descriptive statistics for mathematical scores were not provided in Table 2 because mathematical scores were derived from five plausible values. Table 3 shows the outputs of selection criteria for one, two, three, and fourclass solutions for five East Asian educa tional systems. As seen in Table 3 The interpretations of the latent classes of learning strate gies were defined based on the number of highest endorse ment probabilities of the three types of learning strategies (i.e., control, elaboration, and memorization) for four items. Table 4 presents endorsement probabilities of the use of three different strategies and class sizes for latent classes for the five educational systems. The substantive interpretations of latent class characteristics based on the endorsement proba bilities of three types of learning strategy are presented at the bottom of Table 4.

Typology of Learning Strategy Use
As seen in Table 4, Shanghai, Singapore, and Taiwan had the same characteristics of three latent classes: the memori zation, elaboration, and control classes. In these educational systems, students in the control class reported three out of four items with the highest endorsing probabilities on control strategies, and one item on memorization (Item 4). In other words, students in the control class in Shanghai, Singapore, and Taiwan showed consistent response patterns. Students in the elaboration class had three items with the highest endors ing probabilities on elaboration, and one item on a control strategy (Item 2 for Singapore and Taiwan, Item 4 for Shanghai). Shanghai, Singapore, and Taiwan had a memori zation class and Singapore had the highest probabilities endorsing on memorization across four items. Taiwanese and Shanghai students had three items on memorization and one item on control (Item 4 for Taiwan, Item 3 for Shanghai). Based on response patterns in these three latent classes, the use of learning strategies from Singaporean and Taiwanese students exhibited more similar than Shanghai students. Macau also had three latent classes that involved the same control and memorization classes and the combination class of control and elaboration. In the control class, three items had the highest endorsing probabilities on control and one on memori zation (Item 4), same as those in Shanghai, Singapore, and Taiwan. In the memorization class, three items had the highest probabilities endorsing on memorization and one on control (Item 3), same as those in Shanghai. In the combination class, two items had the highest endorsing probabilities on control (Items 2 and 3) and two items on elaboration (Items 1 and 4).
Hong Kong possessed the control class and the combina tion class. Like other four educational systems, the response pattern for the control class was that three items had the high est endorsing probabilities on control and one on memoriza tion (Item 4). The combination class for Hong Kong was also the combination of control and elaboration with the two highest endorsing probabilities on control (Items 2 and 4) and the two highest endorsing probabilities on elaboration (Items 1 and 3). The control and elaboration combination classes were the same as that in Macau but were partially different in response patterns.
At the top of Table 4 shows the proportions of students in latent classes for the five educational systems. In the four educational systems with three latent classes, more students (45%-78%) were classified into the control class, and fewer students (10%-15%) were in the memorization class except for students from Shanghai (30%). Few students from Singapore (12%) and more students from Taiwan and Shanghai (30% and 25%, respectively) reported the use of elaboration. Approximately 20% of students in Macau reported the combined use of the control and elaboration strategies. As for Hong Kong with two latent classes, most students (77%) were classified in the control class, and fewer students (23%) reported a combined use of strategies, like those distributions in other four educational systems. Table 5 presents the estimated standardized coefficients and standard errors of estimates of two predictors (i.e., intrinsic motivation and extrinsic motivation). For students who were classified in the control class, intrinsic motivation had sig nificant and positive effects on mathematics performance in Hong Kong, Macau, and Taiwan, but not in Shanghai and Singapore. This result indicated that students who reported more control strategies with higher intrinsic motivation tended to have higher mathematics performance in Hong Kong, Macau, and Taiwan. For Shanghai and Singaporean students in the control class, intrinsic motivation did not sig nificantly predict mathematics performance. Extrinsic moti vation significantly and positively predicted mathematics performance when students were in the control class only in Note. The bold value represents the highest probability on a strategy option in an item. CTL = control class; ELA = elaboration class; MEM = memorization class; Com = combination class.

Moderation Effects of Learning Strategy Use
Taiwan and Hong Kong, but it showed a significantly nega tive prediction for Singaporean students who were in the control class. Extrinsic motivation did not have significant predictions on mathematics performance for students from the control class in Shanghai and Macau. Only Shanghai, Singapore, and Taiwan showed the elabo ration class. For all three educational systems, intrinsic moti vation significantly and positively predicted mathematics performance. However, only Taiwanese students in the elab oration class showed a significant and positive impact of extrinsic motivation on mathematics performance. Students in Shanghai and Singapore did not show significant effects of extrinsic motivation on mathematics performance.
Four educational systems had the memorization class, including Shanghai, Singapore, Taiwan, and Macau. Both types of motivation had no impact on mathematics perfor mance in Taiwan and Macau. In Shanghai, only intrinsic motivation showed a significantly positive impact on math ematics performance. For Singaporean students in the mem orization class, both types of motivation had significant impacts on mathematics performance. Intrinsic motivation positively predicted mathematics performance, whereas extrinsic motivation negatively predicted mathematics performance.
Macau and Hong Kong had the combination class of the control and elaborations strategies. As shown in Table 5, intrinsic motivation significantly and positively predicted mathematics performance in these two educational systems, while extrinsic motivation had no significant impacts on mathematics performance.

Discussion
This study used a threestep LCA (i.e., personcentered) approach to explore latent classes of learning strategy use. Specifically, this study examined the moderation effects of learning strategy use on the relations between motivation and mathematics performance (i.e., the effects of the inter actions between learning strategy use and motivation on mathematics performance). The data of 15yearold students from five East Asian educational systems related to Chinese culture in the Programme of International Student Assessment (PISA) in 2012 were analyzed, including Shanghai, Singapore, Taiwan, Macau, and Hong Kong. The results indicated that Shanghai, Singapore, Taiwan, and Macau showed three latent classes of learning strategies, whereas Hong Kong had two latent classes. Most students in the five educational systems reported to use the control strategy, some students reported the use of combined learn ing strategies, and few students reported the use of memori zation except for students in Shanghai. The moderation effects of learning strategy use on mathematics performance depended on the types of motivation and educational sys tems. We discuss how this study provides insights into the advantages of a threestep LCA approach in educational research. Implications and future research directions are also discussed.

Similarities and Dissimilarities of Typology of Learning Strategy Use
The findings indicated that all five educational systems pos sessed the control classes and had similar response patterns in the control class. In addition, most students in these edu cational systems were classified in the control class. These findings reflected the similarities of learning strategy use among these educational systems. With outstanding mathe matics performance among these East Asian educational sys tems in PISA 2012 (OECD, 2014), the use of control strategies may play a key role in promoting high academic performance. Similarly, most educational systems had the memorization classes, but few students (i.e., 14% or less) were classified in this class except for Shanghai (30%). On the one hand, these findings aligned with previous studies suggesting that few East Asian students reported memoriza tion (Chiu et al., 2007;Liu, 2009;Wu et al., 2020). On the other hand, the findings indicated that some educational sys tems related to Chinese culture seem likely to choose memo rization, even though few students reported to use it in this study. Over the past decades, some East Asian educational systems have been reformed to improve students' critical thinking development and to help students to become inde pendent learners (Cheng, 2017). For instance, new curricu lum reforms in China emphasize critical and analytical thinking rather than passive and rote learning (Yin, 2013). A recent reform in Taiwan aims at encouraging students to be motivated and passionate about society, nature, and culture (Cheng, 2017). Recent efforts in these educational systems may have important implications for the learning strategy use among East Asian students and may serve as a plausible explanation of why most students reported using control strategies and few students used memorization strategies in these East Asian educational systems. Although Shanghai, Taiwan, and Singapore had the same latent classes, the characteristics (i.e., response pat terns) of learning strategy use in Singapore and Taiwan were more alike than those in Shanghai. Singapore and Taiwan had almost identical response patterns across three types of learning strategy use, except for one item response in the memorization classes. Likewise, the characteristics of learning strategy use among Shanghai, Macau, and Hong Kong shared many similarities. Both Shanghai and Macau possessed the control and memorization classes and shared the same response patterns. In addition to the con trol class, the response pattern of the elaboration class in Shanghai was similar to the combination class in Hong Kong, except for one item. Finally, Macau and Hong Kong had two same latent classes, and they were only two edu cational systems that exhibited the combination class of the control, and elaboration strategies. These findings revealed that students' learning behaviors were close to Macau, Hong Kong and Shanghai, which might be due to the fact that these educational systems share some same features (Li & Choi, 2014).
Students in these five educational systems consistently reported the partial use of memorization in the control class and the partial use of control in the elaboration and memorization classes, except for Singaporean students in the memorization class. These findings suggested that most students in these educational systems may not consis tently use one strategy in the process of learning mathe matics, which aligned with the hypotheses from Dinsmore and Alexander (2016) as well as Hattie and Donoghue (2016). Both studies hypothesized that learning strategy use is a continuous process so that students may exchange surface and deeplevel strategies in the learning process based on their levels of domain knowledge and the nature of a task. These findings may also align with qualitative crosscultural studies demonstrating that Chinese and Hong Kong students perceived memorization as boosting their understanding and combined memorization with deeplevel strategies (Kember, 2000;Marton et al., 1996).

Similarities and Dissimilarities of Learning Strategies as Moderators
Regarding the moderation effects of learning strategy use, this study showed that these effects on mathematics perfor mance depend on the types of motivation and various edu cational systems. Generally, the moderation effects of learning strategies with intrinsic motivation made more sig nificantly positive impacts on mathematics performance than those with extrinsic motivation across educational sys tems. Especially with the elaboration class, intrinsic moti vation showed consistently positive impacts on mathematics performance across all three educational systems (i.e., Shanghai, Singapore, and Taiwan). In contrast, extrinsic motivation had inconsistent effects on mathematics perfor mance with different types of latent classes across five edu cational systems; that is, most moderations with extrinsic motivation had no impact (e.g., Shanghai and Macau across all latent classes), some showed positive impact (e.g., Taiwan with control and elaboration as well as Hong Kong with control and combination), but some had negative effects (e.g., Singapore with control and memorization). The findings contrasted with previous literature that suggested intrinsic motivation had no or small effect on mathematics performance when learning strategies were mediators (Chung, 2000;Lee et al., 2014;Yıldırım, 2012). The different results might result from learning strategies as moderators in this study, which highlighted that learning strategies could interact with motivation to moderate the strengths and directions of these relations.
From a perspective of an individual educational system, Taiwan and Hong Kong seemed to have consistently posi tive moderation effects of learning strategies with intrinsic and extrinsic motivation for students in most types of learn ing strategies, but not in the memorization class. Taking high proportions of students in the control classes into con sideration, these findings partially supported Zhu and Leung's (2011) study showing that intrinsic and extrinsic motivation positively predicted mathematics performance without taking learning strategies into account in Taiwan, Hong Kong, and other East Asian educational systems (i.e., Korea and Japan). Intrinsic motivation did not have signifi cant impacts for Taiwanese and Macau's students who report using memorization, which was in line with empirical stud ies evidenced that memorization was not an appropriate strategy to help students obtain desirable learning outcomes such as motivation or academic performance (Donker et al., 2014;Sorić & Palekčić, 2009). However, memorization had significantly positive effects on mathematics among Shanghai students, and especially for Singaporean students. Singaporean students with high intrinsic motivation could still obtain high mathematics performance, though they used memorization strategies. These results could indicate that Singaporean teachers do not have concrete concepts between metacognition and cognition learning strategies to teach students (Lee et al., 2019). In turn, students might not understand how to use appropriate learning strategies during learning mathematics, though they have high intrinsic moti vation. Thus, these findings provided instruction implica tions in mathematics in Singapore.
Different patterns of the effect of extrinsic motivation may result from educational system structures and parents' expectations. Most education systems in this study are com petitive due to public examinations for enrolling high schools or universities (Cheng, 2017;Deng & Gopinathan, 2016), and parents often set high expectations on students (Kim & Bang, 2017;Mun & Hertzog, 2019). In the current study, only students in Taiwan and Hong Kong have additively positive impacts of extrinsic motivation that may be resulted from the school and family environment. Surprisingly, the control and memorization classes in Singapore showed nega tive effects of extrinsic motivation on their mathematics per formance. Future research should explore why Singaporean students with higher extrinsic motivation tended to have lower mathematics performance when they use control and memorization strategies.

Conclusions and Future Research Directions
Learning strategy use and motivation are essential to stu dents' academic performance. The present study makes a unique contribution to the field by applying a threestep LCA approach to explore the combination of learning strategies and examine whether latent classes of learning strategy could serve as moderators to explain the relations between motiva tion and mathematics performance. This study captures the use of combined learning strategies and latent classes of learning strategy use as a moderator to explain the relations between motivation and mathematics performance among East Asian educational systems which are dominated by Chinese culture. Our study demonstrates that the use of learning strategies is a continuous process as students inter changed different learning strategies based on the context when learning mathematics. This has implications for math ematics classroom instruction in East Asian educational sys tems. For instance, teachers could instruct which different types of learning strategies are used, as well as how and when they are used, so that students could efficiently switch learning strategies while learning mathematics. Moreover, control strategies and intrinsic motivation appeared to be important for East Asian students to learn mathematics, com pared to other strategies and extrinsic motivation.
There are suggestions for future research based on the limitations of this study. First, due to the nature of PISA data, learning strategies and motivation were assessed with lim ited scales, which might provide limited information on the use of mathematics learning strategies and mathematics motivation. Future studies could use more comprehensive scales possibly accompanied by personal digital assistants (e.g., videotaping) to collect qualitative data during or imme diately following learning events and tasks that may more accurately assess the use of learning strategies and motiva tion. Second, this study used the samples from five East Asian educational systems that are highly related to Chinese culture. To understand the generalizability of the findings in this study, researchers could consider other cultural popula tions (e.g., Englishspeaking educational systems). Moreover, the heterogeneity of the five educational systems is not con sidered in this study, such as differences in economic devel opment or education. Social, economic, and/or educational diversities (e.g., socialeconomic status, parental income, and education) can be incorporated in the future studies of learning strategy use. For instance, these variables can be added in threestep LCA analyses as covariates to examine if the latent class patterns of learning strategy use and/or the moderating patterns across the five educational systems are different. Moreover, to better understand similarities and dif ferences in the use of learning strategies and motivation across these educational systems, teaching practices should be considered. Teaching practices can influence students' psychosocial and learning outcomes. For example, if teachers adopt cooperative learning strategies in the classroom, stu dents tend to be engaged in learning due to social interactions with classmates (Hoek et al., 1999). When teachers provide students with emotional support, students feel connected to the learning environment (Romano et al., 2020). Thus, foster ing a positive learning environment may influence students' motivation and selection of learning strategies. We encourage future studies to investigate how the quality of instruction influences motivation and learning strategies among East Asian students. Finally, the nature of the data in this study is crosssectional. With the use of longitudinal data or repeated measures, the results may display different patterns. Researchers are encouraged to examine the effects of learning strategies as moderators with longitudinal data.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Bamberg Graduate School of Social Sciences which is funded by the German Research Foundation (DFG) under the German Excellence Initiative [GSC1024].