Family and motivation effects on mathematics ...

Learning and Instruction 18 (2008) 321e336 www.elsevier.com/locate/learninstruc

Family and motivation effects on mathematics achievement: Analyses of students in 41 countries Ming Ming Chiu*, Zeng Xihua Faculty of Education, The Chinese University of Hong Kong, 314 Ho Tim Building, Shatin, NT, Hong Kong Received 25 June 2006; revised 23 January 2007; accepted 16 June 2007

Abstract This study examines family and motivation effects on student mathematics achievement across 41 countries. The Rasch estimates of PISA mathematics test scores and questionnaire responses of 107,975 15-year-old students were analyzed via multilevel analyses. Students scored higher in richer or more egalitarian countries; when living with two parents, without grandparents, with fewer siblings (especially fewer older siblings); with higher family SES, more books, cultural possessions, or cultural communication; or when they had greater interest in mathematics, more effort and perseverance, and higher self-efficacy or self-concept. Family structure effects were stronger in individualistic or richer countries. Richer countries showed stronger family cultural communication effects, suggesting stronger, intangible resource effects. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Country characteristics; Culture; Family structure; Mathematics; Motivation; PISA results; Secondary school students

1. Introduction Family characteristics and student motivation are associated with academic achievement (Hampden-Thompson & Johnston, 2006; Pintrich & Schunk, 2002). For example, children in single-parent families often have fewer educational resources, which can reduce children’s academic motivation and achievement (Hampden-Thompson & Johnston, 2006). As schooling affects an individual’s life chances, children from disadvantaged families often become adults with lower income and lower job status. These adults’ economic and educational disadvantages in turn affect their children’s schooling, and so on throughout later generations (Amato & Cheadle, 2005). Whether family, individual, or socio-economic status (SES) characteristics have differential effects on children’s academic achievement across richer vs. poorer countries, across countries with differing distributions of household income, or across countries with various cultural values remain open questions.

* Corresponding author. Tel./fax: þ852 2609 6751. E-mail address: [email protected] (M.M. Chiu). 0959-4752/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.learninstruc.2007.06.003

M.M. Chiu, Z. Xihua / Learning and Instruction 18 (2008) 321e336

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1.1. Family characteristics The constitution of family and the number of family members are important characteristics of families. According to Chiu (in press), family members can offer students extra resources (resource provider) or compete for them (resource dilution). Thus, family members (e.g., parents) with more educational resources provide more learning opportunities on which a student can capitalize to achieve more (see Fig. 1, middle column). For example, families with both parents instead of one typically have higher SES, more educational resources (e.g., books), spend more time with their children (e.g., cultural communication about films and political issues), and are more involved in children’s schooling (e.g., parent communication with teacher) (Baker & Stevenson, 1986; Lareau, 2002). In contrast, separated parents have fewer resources and face more challenges in caring for their children, who might receive less attention (e.g., from step-parents; see Fig. 1, middle column). Children who witness conflicts between their separated parents might also suffer emotionally, often resulting in lower academic motivation and thus lower academic achievement (Amato, 2001). Meanwhile, immigrant parents, especially those who speak a different language than the dominant one in the host country, are likely to have less social and cultural capital to share with their children (e.g., cultural possessions such as books and cultural communication), thus limiting their children’s learning opportunities and academic achievement (see Fig. 1, middle column; Portes & MacLeod, 1996). On the other hand, additional family members who primarily compete for family resources (such as grandparents and siblings) may reduce the available resources for a child, yielding fewer learning opportunities and lower student achievement (resource dilution hypothesis; see Fig. 1, middle column; Downey, 2001). Some students might benefit from grandparents’ physical, informational, social, and emotional resources, and thereby show higher achievement (DeLeire & Kalil, 2002; Greenfield, Keller, Fuligni, & Maynard, 2003; Rogoff, 1990). On the other hand, students who live with poor or ill grandparents compete with them for limited family resources (Patillo-McCoy, Kalil, & Payne,

Country Resources GDP per capita (+) Inequality: Gini (–) Cultural Values Egalitarian (+) Individualism (–)

Family Resource provider Living with no parents (–) Single parent (–) Mixed (–) Family SES (+) 1st generation immigrant (–) 2nd generation immigrant (–) Speak foreign language at home (–)

Student Science Achievement

Number of books at home (+) Cultural possessions (+) Cultural communication (+) Resource dilution Grandparent (–) Number of siblings (–) Older siblings (–)

Motivation Intrinsic (+) Extrinsic (–) Effort and perseverance (+) Self-concept (+) Self-efficacy (+)

Fig. 1. Model of country, family and motivation effects on students’ science achievement.


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2003). Moreover, many countries only recently instituted compulsory education and, therefore, many grandparents received little schooling. This may have unfavourable implications for children’s academic achievement (PatilloMcCoy et al., 2003). Besides grandparents, siblings also compete for family resources. Thus, students with more siblings living together often share resources at home and achieve less than those with fewer siblings (Downey, 2001). Older siblings initially receive more family resources than do younger siblings because they compete with younger siblings for family resources only after the latter’s births (e.g., parental time, energy, and engagement, Powell & Steelman, 1993). Hence, parents are often resource providers, while family-resident grandparents and siblings often compete for family resources, thereby diluting the resources’ impact. 1.2. Student motivation According to social cognitive theory, student’s academic motivation beliefs include three components: value, expectancy, and affect (Bandura, 1989). Students’ beliefs about the value of mathematics consist of the reasons why students engage in learning and doing mathematics. For example, students who enjoy learning mathematics (‘‘I think math is interesting’’, that is, intrinsic value) often show higher mathematics achievement (Deci & Ryan, 2002). Through their investment in education and involvement with school activities, families can increase students’ intrinsic academic motivation (Pintrich & Schunk, 2002). Specifically, students with more educational resources (e.g., books) at home have more learning opportunities and more intrinsic motivation to learn (Gottfried & Fleming, 1998). Likewise, students who are more involved in family activities (e.g., political, intellectual and cultural discussions) also have greater intrinsic academic motivation (Gottfried & Fleming, 1998). In contrast, students who view mathematics as a useful tool for other goals (‘‘Math will help me get a good job’’, that is, extrinsic value) often show lower mathematics achievement in Western countries (Deci & Ryan, 2002), but not in other cultures (e.g., d’Ailly, 2003). Students who value an activity are more likely to exert greater effort and to perceive a greater likelihood of success (that is, expectancy belief; Seegers & Boekaerts, 1993). Expectancy beliefs include mathematics self-efficacy (belief in one’s capabilities to carry out a task, ‘‘I can do math problems’’) and mathematics self-concept (belief in one’s competence: ‘‘I’m good at math’’; Bandura, 1997). Students in families with higher socio-economic status and greater family investment and involvement tend to have greater expectancy beliefs (Artelt, Baumert, JuliusMcElvaney, & Pescher, 2003), so these students often learn more (Chiu & Khoo, 2005; Marsh & Hau, 2004). Furthermore, expectancy beliefs regarding academic performance can be affected by students’ actual experience, especially their past successes and failures on academic tasks (Pintrich & Schunk, 2002). Past successes are likely to maintain (or increase) perceived activity value and expectations. Mean while past failures may lead students to lower their expectations and devalue the activity to protect their self-esteem from the damage of a likely future failure (Pintrich & Schunk, 2002). Besides expectancy beliefs, both students’ emotional reactions to the task and their task performance (that is, affect; Pintrich & Schunk, 2002) influence their persistence and performance. Students who have more positive affect when they work on academic tasks tend to keep exerting effort on them, which fosters higher academic achievement. 1.3. Country resources and cultural values Country characteristics, such as average income, social inequality, and cultural values might be associated with student achievement directly, or indirectly via family or motivation (see Fig. 1). Students in countries with higher gross domestic product (GDP) per capita generally show higher academic achievement (see Fig. 1, left column; Baker, Goesling, & Letendre, 2002; Heyneman & Loxley, 1982). Richer countries can raise student achievement directly through education spending (e.g., books, teacher training, better curricula) or indirectly through higher nutritional standards or better health care (UNICEF, 2001). For example, children in poorer countries often lack basic nutrition, are born prematurely, or face exposure to potentially harmful environments (e.g., lead poisoning) e all associated with learning difficulties (UNICEF, 2001). Besides the amount of resources, student achievement may also be associated with the distribution of those resources. Consider a thirsty person and two glasses of water. The person greatly values the first glass of water

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and drinks it all. Thirst quenched, the second glass of water is not valued as much as the first one, and the person does not finish it. This relatively lower value of the additional resource is diminishing marginal returns (Mankiw, 2004). Hence, poorer students typically benefit more from an extra book than richer students do. With greater equality in resources, poorer students have more resources and benefit more from them, resulting in higher education outcomes overall (Chiu & Khoo, 2005). Furthermore, the associations between family variables and student achievement may differ in richer vs. poorer countries (Baker et al., 2002; Heyneman & Loxley, 1982). Specifically, there are three hypotheses that might explain the fact that the associations may be weak, similar, or strong. They are the public resources substitution, the social reproduction, and the complementary intangibles hypotheses, respectively (Blossfeld & Shavit, 1993). Richer countries can provide more public resources (e.g., school teachers, library books) that can substitute for family resources (Blossfeld & Shavit, 1993). These public resources reduce the importance of family resources for providing learning opportunities and thereby weaken the association between family resources and student achievement (public resources substitution hypothesis). For example, subsidized lunches in the USA reduce the nutritional disadvantages of poorer children (Betts, Rueben, & Danenberg, 2000). However, these social changes might only be temporary as high SES families use their superior resources to create advantages for their children (e.g., hiring admissions coaches for their children’s college applications). In this view, associations between family variables and achievement would be similar across poor and rich countries (social reproduction hypothesis). Lastly, family variables may have strong associations to student achievement in richer countries e as shown in the 1970s (Heyneman & Loxley, 1982) and in the 1990s (Baker et al., 2002). We propose the following hypothesis to explain the strong associations between family variables and student achievement in richer countries: the widespread availability of physical resources (such as public libraries and museums) may increase the value of less tangible resources (such as parent time and attention). For example, a student benefits from reading an extra book, but that benefit can be substantially magnified by discussing the book with a parent, especially a well-educated one. As physical resources are relatively abundant and accessible in richer countries, richer and poorer students might differ more because of family involvement and less by access to physical resources. In richer countries, compulsory public schooling starts earlier and offers more years of subsidized schooling. Thus, parents in richer countries often have more years of schooling, possibly yielding higher quality academic discussions with their children (Blossfeld & Shavit, 1993; OECD, 2000). Furthermore, children in richer countries often spend more time with their parents due to fewer competing siblings, less parent time on housework, and multi-tasking parents (Sandberg & Hofferth, 2001). Thus, parental involvement and other intangible family resources might be more strongly associated with academic outcomes in richer countries (complementary intangibles hypothesis). Countries differ not only in wealth and degree of social equality but also in their cultural values. Nations that address basic societal issues differently have different cultural values (Schwartz & Ros, 1995). As these values shape the behaviours of a country’s citizens, they may also be associated with students’ behaviours and academic achievement. Consider two basic societal issues: (a) inducing responsible individual behaviour to preserve the fabric of a society and (b) prioritizing the interests of individuals vs. groups. A society may encourage responsible behaviour by assigning clear, fixed hierarchical roles and by teaching its citizens to obey authority (hierarchical structure). Or, a society may teach its members to view, value, and act towards one another as equals based on their common humanity (egalitarian structure). Likewise, a society may favour group interest over individual interest (collectivist), or it may favour individual interest over collective interest (individualist). Many researchers have organized their theoretical frameworks of cultural values along two dimensions according to these basic dichotomies, that is, hierarchical vs. egalitarian and collective vs. individual (Hofstede, 2003; Inglehart & Baker, 2000; Schwartz & Ros, 1995). Although their terminologies differ, their frameworks are conceptually similar (Smith & Bond, 1998). Furthermore, cultural values tend to differ mostly across countries, and less so within countries, as cultural values are associated more strongly with one’s nation than with religion, employer organization, or individual personality (Hofstede, 2003; Inglehart & Baker, 2000). People learn these values through both formal socialization (via direct teachings of parents, teachers, and religious leaders) and informally (via everyday exposure to customs, laws, norms and practices shaped by and expressing cultural values; Markus & Kitayama, 1994). Thus, these cultural values might be associated with students’ behaviours and subsequent learning.


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In nations with more egalitarian cultures, people perceive one another as more similar and are more likely to be friendly to one another (homophily, Hofstede, 2003). Students with more schoolmate friends tend to share more resources and have higher academic achievement (Crosnoe, Cavanagh, & Elder, 2003). Furthermore, students who view one another as more similar tend to perceive smaller status differences, thereby reducing harmful status effects on student achievement (Cohen, 1994). As a result, students might achieve academically more in egalitarian cultures (egalitarian sharing hypothesis). On the other hand, students in collectivist societies might be more inclined to cooperate, support, and learn from one another, thereby enhancing their academic achievement (see Fig. 1, left column). In more collective societies, people tend to rely more on their extended family members who often live nearby, and so students are more likely to benefit from them (Hofstede, 2003). As extended family resources dilute the effects of immediate family resources, the association between immediate family resources and academic achievement is weaker in more collectivist countries (collectivist dilution hypothesis). 1.4. The present study In this study, we extended the research on the associations between family, student motivation, and mathematics achievement in three ways. First, this study examined whether family effects on mathematics achievement were mediated by student motivation. Second, we tested whether these family or motivation effects were associated with each country’s economic conditions or cultural values. And third, we tested for differences among countries and among schools. Specifically, we tested several hypotheses regarding family effects (resource provider and resource dilution) and country effects (public resources substitution, social reproduction, and complementary intangibles). See Fig. 1 for our model of the possible relations between country, family, and individual student characteristics, as well as the directions of the effects. 2. Method 2.1. Design The Organization for Economic Cooperation and Development’s (OECD) Program for International Student Assessment (PISA) assessed 15-year-olds’ mathematics literacy and asked them to fill out questionnaires. International experts from participating OECD countries defined mathematics literacy, built assessment frameworks, created test items, forward-translated and backward-translated these items, and pilot tested these items to ensure their validity and reliability e for details including sample items, reliability, and validity checks, see Organization for Economic Cooperation and Development (2002) and www.pisa.oecd.org. These experts defined mathematics literacy as the ability to understand, use, and reflect on mathematics concepts to achieve one’s goals, develop one’s knowledge and potential, and participate effectively in society. Each student completed a 2-hour assessment booklet and a 30- to 40-minute questionnaire. Investigating research questions across a large number of countries and schools requires choosing a representative sample of 15-year-olds to test, creating precise tests and questionnaire items for data collection, and modeling the complex relationships in the data (Chiu & McBride-Chang, 2006). OECD used stratified sampling with respect to neighbourhood SES and student intake to select about 150 schools in each country that would represent a broad spectrum of schools. Then, they sampled about 35 students from each of the selected schools. Each country was represented with at least 4500 students. The participant test scores and variables were then weighted by OECD (2002) accordingly to represent the schools and the 15-year-old student populations of each country. 2.2. Sample The sample of the present study comprised 107,975 15-year-old students from 41 countries (see Table 1). They ranged from poor, unequal, hierarchical, collectivist nations (e.g., Indonesia) to rich, equal, egalitarian, individualistic ones (e.g., Switzerland). In the sample, 54,743 girls (50.7%) and 53,232 boys (49.3%) participated.


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Table 1 The participating countries and their characteristics Country

GDP

Gini

Egalitarian

Individualism

Masculinity

Uncertainty avoidance

AL AR AUS AUT BE BR BU CHL CZ DK FI FR GE GR HK HO HU IC IDO IR IS IT KO LIE LV LU FY ME NZ NO PE PL PT RO RU SP SE SZ THA UK USA

2771 8746 15,806 13,278 13,900 4561 6164 5327 12,962 16,736 13,245 13,752 17,494 8979 13,709 14,445 8357 14,644 2050 9835 10,061 12,848 5751 10,303 7029 19,360 4690 5939 14,040 14,822 4148 7032 7797 3389 7780 9963 15,513 19,890 2857 13,714 19,553

31 46 35 31 25 59 32 58 25 25 26 33 38 35 43 33 24 31 30 36 36 36 32 35 32 31 28 52 36 26 46 32 39 31 46 33 25 33 43 36 41

14 55 68 93 39 35 34 41 47 86 71 36 69 44 36 66 58 74 26 76 91 54 44 70 64 64 25 23 82 73 40 36 41 14 11 47 73 70 40 69 64

20 46 90 55 75 38 30 23 58 74 63 71 67 35 25 80 55 60 14 70 54 76 18 68 60 60 26 30 79 69 16 60 27 30 39 51 71 68 20 89 91

80 56 61 79 54 49 40 28 57 16 26 43 66 57 57 14 88 10 46 68 47 70 39 68 30 50 46 69 58 8 42 64 31 42 36 42 5 70 34 66 62

70 86 51 70 94 76 85 86 74 23 59 86 65 112 29 53 82 50 48 35 81 75 85 62 60 70 84 82 49 50 87 93 104 90 95 86 29 58 64 35 46

AL, Albania; AR, Argentina; AUS, Austria; AUT, Australia; BE, Belgium; BR, Brazil; BU, Bulgaria; CHL, Chile; CZ, Czech Republic; DK, Denmark; FI, Finland; FR, France; GE, Germany; GR, Greece; HO, Holland; HK, Hong Kong; HU, Hungary; IC, Iceland; IDO, Indonesia; IR, Ireland; IS, Israel; IT, Italy; KO, Korea; LV, Latvia; LIE, Liechtenstein; LU, Luxembourg; FY, FYROM; ME, Mexico; NO, Norway; NZ, New Zealand; PE, Peru; PL, Poland; PT, Portugal; RO, Romania; RU, Russian Federation; SP, Spain; SE, Sweden; SZ, Switzerland; THA, Thailand; UK, United Kingdom; USA, United States of America.

2.3. Instruments This representative sample of students was given the mathematics test and the questionnaire. Traditional tests that seek to cover a lot of mathematics content often result in student fatigue and learning effects during the exam. To reduce these effects and to maximize evaluative precision, OECD used a balanced incomplete block (BIB) test. In a BIB test, each student only answered a subtest comprising a subset of questions from the overall test (Baker, 2001). Because each pair of subtests shared overlapping questions, OECD (2002) analyzed the test scores by fitting a graded response Rasch model to the BIB data. The Rasch model estimated the difficulty of each item and the achievement score of each student based on the subtest responses e adjusting for the difficulty of each test item and calibrating all


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test items (Baker, 2001). As the test included multiple choice and open-ended questions, the graded response aspect of the model captures the partial credit on student responses to open-ended questions (Baker, 2001). Like the tests, the questionnaire should also maximize precision. A traditional questionnaire probing an underlying construct with a single question and a limited number of possible responses (e.g., yes and no, or a simple Likert-type scale) often measures the construct coarsely, resulting in substantial measurement error. To minimize this measurement error, OECD (2002) included multiple measures for each theoretical construct and computed a single value from these measures with a graded response Rasch model e mapping the partial credit Rasch model to the partial agreement on a Likert-type scale with Warm’s (1989) estimates. This method is more precise than the traditional method of summing the nonweighted response values of multiple measures (Rowe & Rowe, 1997). Furthermore, reliability tests showed that participants in all countries generally answered consistently each set of questionnaire items that represented a theoretical construct (e.g., intrinsic mathematics motivation, see Appendix A for reliability ranges of variables). This suggests that participants had similar understanding of the underlying theoretical constructs (OECD, 2002). Because students did not answer all questions, there were missing data (6%) that could reduce estimation efficiency, complicate data analyses, and bias results (Peugh & Enders, 2004). Using Markov Chain Monte Carlo multiple imputation in the present study, we addressed these problems more effectively than other approaches (such as deletion, mean substitution, simple imputation, Peugh & Enders, 2004). 2.4. Variables For details of each variable, summary statistics, and order of entry of vectors of variables into the regressions, see Appendix A. Relative grade is a proxy for past achievement that indicates the number of grade levels a student has skipped or was retained. (Readers should cautiously interpret results involving these coarse proxies due to school or country variation in placement of students and in their curricula.) The country-level variables tested were log GDP per capita, GDP Gini,1 and cultural values (egalitarianism, individualism, masculinityefeminity in terms of gender role differentiation, uncertainty avoidance, short-term orientation, harmony, mastery, external dynamism, and social cynicism; Bond et al., 2004; Hofstede, 2003; Inglehart & Baker, 2000; Schwartz & Ros, 1995). Due to space limitations, the nonsignificant results of the cultural value variables are not reported in the analysis, although they were included in the models. Next, family structure variables were added: first generation immigrant, second generation immigrant, foreign language spoken at home, socio-economic status, single parent, mixed parents (one birth parent and one step-parent), living with no parents, living with at least one grandparent, number of siblings, and birth order. Other family characteristics followed: number of books at home, cultural possessions, and cultural communication. Gender was added next (girl), followed by motivation variables: interest in mathematics, instrumental motivation, perseverance and effort, self-efficacy, and self-concept. Lastly, interaction terms were entered. 2.5. Analysis Ordinary least squares regressions often underestimate standard errors in nested data (students within schools within countries). We addressed this concern with multilevel analyses using MLn software (Goldstein, 1995; Rasbash & Woodhouse, 1995; in contrast to Artelt et al., 2003). Multilevel models separate unexplained error into student (Level 1), school (Level 2), and country (Level 3) components, thereby removing the correlation among error terms resulting from the nested data, using the following equation.2 A variance components model tests if the variances are significant at each level: Yijk ¼ b000 þ eijk þ f0jk þ g00k

ð1Þ

We modeled students’ mathematics scores with sequential sets of variables (hierarchical sets; Cohen, West, Aiken, & Cohen, 2003) to estimate the variance explained by each set (see Appendix A and Table 2). Past achievement variables (R) were entered first as control variables to predict the improvement between past and present achievement, 1

Gini scores range from 0 (perfect equality with the same incomes for all) to 1 (perfect inequality, where one person has all the income). Yijk is the science score for student i in school j in country k. b000 is the grand mean intercept. Error terms (residuals) at the student-, school-, and country-levels are eijk, f0jk, and g00k, respectively. 2


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Table 2 Multilevel regressions of mathematics scores with unstandardized regression coefficients (N ¼ 107,975) Predictor

Relative grade Any remedial Log GDP per capita GDP Gini Individualism 1st Generation immigrant 2nd Generation immigrant Foreign language at home SES Single parent Mixed parentsa Living with no parents Grandparent Number of siblings Birth order Number of books at home Cultural possessions Cultural communication Girl Interest in mathematics Perseverance and effort Self-efficacy Self-concept Single parent Individualism Mixed parents Log GDP per capita Living with no parents Log GDP per capita Cultural communication Log GDP per capita Variance explained Country School Student Total

Regressions predicting mathematics scores M1

M2

M3

M4

M5

M6

M7

M8

32.60 26.82

32.59 26.8 74.26 1.76 0.16

29.46 25.51 69.98 1.42 0.25 12.36 5.17 10.67 14.79 6.40 5.65 16.10 12.40 3.62 3.49

28.20 25.65 66.26 1.26 0.24 8.57 4.02 8.94 9.42 4.32 3.89 14.26 11.88 4.07 4.07 9.31 2.43 3.19

28.99 25.54 66.27 1.25 0.24 8.17 3.94 9.32 8.66 3.88 2.93 14.68 12.62 3.95 4.18 9.33 2.99 3.64 18.23

29.07 25.17 68.17 1.37 0.24 9.82 4.74 9.69 8.55 3.09 2.16 14.29 12.49 3.90 3.97 9.08 2.56 2.69 17.67 8.59 3.33

28.91 23.02 71.52 1.37 0.36 10.39 4.69 9.37 7.97 2.78 1.60 14.10 12.22 3.71 3.62 8.59 2.03 1.83 16.77 5.00 2.21 4.40 12.57

28.95 22.93 72.38 1.39 0.34 10.37 4.84 9.50 7.99 2.50 0.84 16.07 12.26 3.66 3.62 8.53 1.97 2.00 16.8 5.02 2.25 4.36 12.51 0.12 6.39 8.65 2.17

0.14 0.19 0.06

0.65 0.19 0.06

0.64 0.37 0.09

0.64 0.45 0.11

0.64 0.45 0.11

0.64 0.44 0.13

0.61 0.43 0.15

0.61 0.43 0.16

0.12

0.28

0.33

0.36

0.36

0.36

0.36

0.36

M ¼ Model. All regression coefficients are significant at the 0.05 level except for those in italics. a Mixed parents refer to living with one parent and one step-parent.

namely learning. By focusing on the smaller time period between past achievement and current achievement rather than a student’s entire life, this approach reduces the problems of estimating the effects of variables that might change over time (e.g., parents’ jobs might change from year to year; Hanushek, Cain, Markman, & Rivkin, 2003). Country variables (S) might affect family variables (T, U). All of these might affect student characteristics (W) except for gender (V). Thus, we entered the variables in the order listed in the variables section in Appendix A. To examine the effects of family and motivation variables across different countries, we modeled all two-way interactions of country variables with family variables or with motivation variables (X). We added the explanatory variables one vector at a time, and did a nested hypothesis test (c2 log likelihood; Cohen et al., 2003) for each added vector. Yijk ¼ b000 þ eijk þ f0jk þ g00k þ brjk Rik þ b00s S00k þ btjk Tijk þ bujk Uijk þ bvjk Vijk þ bwjk Wijk þ bxjk Xijk

ð2Þ

To facilitate interpretation of the results, we reported how a 10% increase in each continuous predictor above its mean affected students’ mathematics scores (10% effect ¼ b SD [10%/34%]; 1 SD is about 34%) in the Results section. In our base-10 system, 10% is a common reference number. Note that scaling a 10% increase is


329

not warranted, as the percentage increase is not linearly related to the standard deviation. We also used an alpha level of 0.05 for all statistical tests. As many tests on the same data can yield false rejections of null hypotheses, we used the two-stage linear step-up procedure as computer simulations showed that it outperformed 13 other methods (Benjamini, Krieger, & Yekutieli, 2006). A multilevel mediation test was used (Krull & MacKinnon, 2001). 3. Results e discussion 3.1. Explanatory model Past achievement, country, family, and student variables all contributed to explaining differences in students’ mathematics scores (see Table 2). Nearly half of the variance in students’ mathematics scores occurred at the student level (44%), a quarter at the school level (25%), and the remainder at the country level (31%). All results discussed below describe first entry into the regression, controlling for the effects of all previously included variables. Ancillary regressions and statistical tests are available upon request from the authors. 3.1.1. Past achievement Students averaged 33 points higher in mathematics per extra grade level above their expected grade level (likely indicating that they skipped grades due to higher past achievement). Students who never attended remedial courses in school (a proxy for past achievement) averaged 27 points higher in mathematics than those attending remedial courses in school (Table 2, Model 1). These variables accounted for 12% of the variance in mathematics scores. 3.1.2. Countries’ economic conditions and cultural values Mathematics scores were associated with countries’ economic conditions, but not with their cultural values. Students in richer countries scored higher than students in poorer countries. When a country’s GDP per capita is 10% higher than the mean, its students averaged seven points higher in mathematics (7 ¼ ln(1 þ 10%) 74.26 [computing the effect of a log variable, ln(1 þ 10%) b]; see Table 2, Model 2). Students in countries with greater income inequality scored lower. When a country’s Gini is one point higher (more unequal) than the mean, its students averaged two points lower in mathematics (Table 2, Model 2). All cultural values showed no significant effects on students’ mathematics scores. Overall, country variables accounted for 52% of the country-level variance and 16% of the total variance in mathematics scores. 3.1.3. Family structure First and second generation immigrant students averaged 12 and 5 points lower in mathematics, respectively, than native-born students (Table 2, Model 3). Students whose spoken language at home differed from that at school averaged 11 points lower in mathematics than other students. Meanwhile, students averaged five points higher with an extra 10% increase in their family SES. Controlling for family SES, Gini was no longer significant (see Table 2, Models 2 and 3). Students in two-parent families outperformed students in all other kinds of families. Students with two parents averaged six points higher in mathematics than those with single parents; six points higher in mathematics than those with mixed parents; and 16 points higher in mathematics than those living without parents (Table 2, Model 3). These results support the view that two parents provide more resources and learning opportunities for their children, who are likely to achieve more. Likewise, these results support the view that children with separated parents perform lower than children with non-separated parents, possibly because they are exposed to less caring step-parents or from conflicts between their separated parents (Amato, 2001). Students living in families without grandparents averaged 12 points higher in mathematics than those living with grandparents. Sibling structure also affected student scores. Students with more siblings in the family scored lower, averaging four points lower in mathematics per extra sibling (Table 2, Model 3). Furthermore, students with older siblings in the family tended to score lower. Family structure accounted for an extra 5% of the variance in students’ mathematics scores.

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3.1.4. Family investment and involvement Family investment and involvement also affected students’ mathematics scores. Students with more books at home tended to score higher (Table 2, Model 4). Students averaged one point higher in mathematics with an extra 10% of cultural possessions in their homes. Furthermore, students averaged one point higher in mathematics with an extra 10% of cultural communication with their parents. Family investment and involvement accounted for an extra 3% of the variance in students’ mathematics scores. Controlling for number of books at home reduced the first generation immigrant regression coefficient by 34%; reduced that of second generation immigrant by 26%; reduced that of SES by 32%; reduced that of single parent by 29%; and reduced that of mixed parents by 26% (see Table 2, Models 3 and 4). 3.1.5. Student variables Boys outperformed girls by 18 points in mathematics (Table 2, Model 5). Controlling for gender also reduced the regression coefficient of mixed parents further by 25% (see Table 2, Models 3 and 5). Students averaged two more points in mathematics with an extra 10% increase in their interest in mathematics (Table 2, Model 6). The effect of mixed parents on mathematics scores was reduced further by 21% after controlling for interest in mathematics (see Table 2, Models 3 and 6). Students averaged one point higher in mathematics with an extra 10% increase in their perseverance and effort. Also, students averaged one and three points higher in mathematics per extra 10% increase in selfefficacy and self-concept, respectively (Table 2, Model 7). Controlling for self-concept, the effect of interest in mathematics was reduced by 31% and the effect of mixed parents was no longer significant (see Table 2, Models 6 and 7). 3.1.6. Interactions Some of these regression coefficients differed across countries. In more individualistic countries, the negative association between single parents and mathematics score was stronger (Table 2, Model 8). This result supports the view that unlike students in individualistic countries, students benefit more from extended family members in collectivist countries (collective dilution hypothesis). In richer countries, the negative regression coefficients of mixed parents and of living with no parents were larger. Likewise, the positive regression coefficient of cultural communication was larger in richer countries. Together, these results support the view that parents are more important to student achievement in richer countries because parents provide valuable intangible resources that complement plentiful tangible resources in richer countries (complementary intangibles hypothesis). 3.2. Difference in effects across countries Past achievement, family, and student variables showed similar effects in most countries and schools (see Tables 3 and 4). Students scored higher if they were in higher grades for their age (significantly higher in 88% of the countries) or never attended any remedial courses in school (88%). Students scored lower in some countries if they were first generation immigrants (32%), were second generation immigrants (32%), spoke a foreign language at home (44%), had single parents (32%), had mixed parents (15%), lived without parents (46%), or lived with grandparents (68%). In many countries, students scored higher if they had higher family SES (95%), had fewer siblings (54%), were born earlier (49%), had more cultural possessions (34%), had more cultural communication with their parents (44%), were boys (85%), were more interested in mathematics (78%), had more perseverance and effort (32%), had higher self-efficacy (68%), or had higher self-concept (73%). However, there were a few exceptions in which the regression coefficients were small but significant, in the opposite direction (first generation immigrant: Hong Kong and Ireland [þ]; second generation immigrant: Israel [þ]; foreign language at home: Spain [þ]; cultural possessions: Indonesia []; interest in mathematics: Indonesia []; perseverance and effort: Belgium and the Netherlands []; self-efficacy: Albania []; and self-concept: Thailand []). Within each country, the effects did not vary much across schools, and no school showed a significant effect in the opposite direction of the country effect. 4. General discussion Researchers have shown that students’ families and personal motivation are associated with their academic achievement in the USA and Western European countries (e.g., Deci & Ryan, 2002; Hampden-Thompson &


331

Table 3 Summary of two-level parameter estimates predicting students’ mathematics scores for each country (upon first entry) Predictor

Relative grade Any remedial 1st generation immigrant 2nd generation immigrant Foreign language at home Family SES Single parent Mixed parentsa Living with no parents Grandparents Number of siblings Birth order Number of books at home Cultural possessions Cultural communication Girl Interest in mathematics Effort and perseverance Self-efficacy Self-concept a

Predictor effect on mathematics

% of Countries

M

SD

Min

Median

Max

Significance

Significance þ

34.47 28.63 12.14 17.53 15.18 16.40 5.00 4.72 18.98 16.20 3.08 3.39 9.05 2.38 3.38 19.43 8.02 3.13 6.65 9.30

22.14 22.27 30.82 24.13 15.47 9.69 8.42 9.77 19.75 13.42 2.61 2.17 3.42 3.86 3.55 9.12 5.74 5.47 5.81 8.99

28.56 89.14 60.59 88.74 45.49 1.13 23.29 24.63 91.13 47.48 10.87 0.90 1.58 8.72 2.01 31.39 7.64 4.99 4.87 11.90

30.04 22.17 15.72 18.59 15.94 14.84 4.71 3.24 13.63 14.02 2.81 3.20 8.82 1.51 2.99 21.82 8.39 2.34 6.03 8.85

91.57 3.64 84.20 20.77 12.94 38.34 10.99 17.95 30.09 4.29 0.41 7.15 15.74 10.17 11.42 5.95 16.30 19.45 19.81 26.39

0 88 32 32 44 0 32 15 46 68 54 0 0 2 0 85 2 5 2 2

88 0 5 2 5 95 0 0 0 0 0 49 93 34 44 0 78 32 66 73

Mixed parents refer to living with one parent and one step-parent.

Johnston, 2006). This study extends this research by examining these associations across 41 countries and across schools within each country. The results supported some parts of our model, but not others (see Fig. 1 and Table 2). Economic resources in a country, family characteristics, and four types of student motivation were associated with student achievement in most countries. However, neither cultural values nor extrinsic motivation was associated with mathematics achievement. Family effects varied across countries’ economic and cultural dimensions, supporting our complementary intangibles and collective dilution hypotheses. In contrast, motivation effects were fairly consistent across countries and not correlated with either country or family variables. 4.1. Family characteristics and motivation The family results supported the resource provider and resource dilution hypotheses. Students living with two parents often scored higher in mathematics than those living with one parent, mixed parents (parent and step-parent), or no parents. Students also scored higher in families with greater SES, more investment in educational resources (books, cultural possessions), or more family involvement (cultural communication). All of the above results support the resource provider hypothesis that students with more resources have more learning opportunities and often achieve more. Students, on the other hand, scored lower if they lived with grandparents or more siblings, especially older siblings. These results support the resource dilution hypothesis that a child often competes with resident grandparents and siblings, especially older ones, for family resources, resulting in fewer learning opportunities and lower achievement (Downey, 2001; Patillo-McCoy et al., 2003). Note that these results might differ for more independent, nonfamily-resident grandparents who might be richer and healthier than family-resident grandparents (Patillo-McCoy et al., 2003). Together, these results show the importance of family characteristics to student achievement and the need for greater support for students from less privileged families to reduce the richepoor achievement gap. Student achievement was associated with intrinsic motivation, but not extrinsic motivation. Hence, students learn more if educators focus their efforts on raising students’ academic interests rather than emphasizing extrinsic motivation. Consistent with past research, students with higher self-efficacy and self-concept also had higher mathematics achievement (Bandura, 1997). Student motivation was not associated with any family characteristics.


332

Table 4 Signs of significant coefficients into two-level regressions predicting students’ mathematics scores for each country, controlling for all within country variables included in the three-level regression Country

AL AR AUS AUT BE BR BU CHL CZ DK FI FR GE GR HK HU IC IDO IR IS IT KO LV LIE LU ME HO NZ NO PE PL PT RO RU SP SE SZ THA FY UK USA

Predictors 1

2

3

4

þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ

þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ

þ

5

þ þ

þ

7

8

þ

9

þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ

11

12

13

14

þ þ þ þ þ

þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ

þ þ þ

þ þ

þ þ þ þ þ þ þ þ

10

6 þ þ þ þ þ þ þ þ þ þ þ þ þ þ

þ þ

þ þ þ þ þ

þ þ þ þ þ þ

þ þ þ þ þ þ þ þ þ þ þ þ þ þ þ

þ þ

15 þ þ

þ þ

þ þ

þ þ

þ þ

16

17

18

19

20

þ

þ

þ

þ þ þ þ þ þ þ þ þ

þ

þ þ þ þ

þ þ

þ

þ

þ

þ

þ þ þ

þ

þ

þ þ þ

þ þ þ þ þ

þ þ

þ þ

þ

þ þ þ þ

þ þ þ þ þ

þ

þ

þ

þ


þ þ þ þ þ

þ þ þ þ þ

þ

þ

þ

þ

þ þ

þ þ þ þ þ

þ þ þ þ þ þ þ þ þ þ þ þ þ þ

þ þ þ þ þ þ

þ


þ þ

þ þ þ

1, Relative grade; 2, Any remedial; 3, 1st generation immigrant; 4, 2nd generation immigrant; 5, Foreign language at home; 6, Family SES; 7, Single parent; 8, Mixed parents (living with one parent and one step-parent); 9, Living with no parents; 10, Grandparents; 11, Number of siblings; 12, Birth order; 13, Number of books at home; 14, Cultural possessions; 15, Cultural communication; 16, Girl; 17, Interest in mathematics; 18, Effort and perseverance; 19, Self-efficacy; 20, Self-concept. AL, Albania; AR, Argentina; AUS, Austria; AUT, Australia; BE, Belgium; BR, Brazil; BU, Bulgaria; CHL, Chile; CZ, Czech Republic; DK, Denmark; FI, Finland; FR, France; GE, Germany; GR, Greece; HO, Holland; HK, Hong Kong; HU, Hungary; IC, Iceland; IDO, Indonesia; IR, Ireland; IS, Israel; IT, Italy; KO, Korea; LV, Latvia; LIE, Liechtenstein; LU, Luxembourg; FY, FYROM; ME, Mexico; NO, Norway; NZ, New Zealand; PE, Peru; PL, Poland; PT, Portugal; RO, Romania; RU, Russian Federation; SP, Spain; SE, Sweden; SZ, Switzerland; THA, Thailand; UK, United Kingdom; USA, United States of America. The symbols indicate a significant positive effect (þ), a significant negative effect (), or no significant effect (a blank).


333

4.2. Country differences Students in richer countries or countries with more equal distributions of income scored higher in mathematics, while cultural values were not associated with mathematics achievement. Students in richer countries are likely to have access to more resources and to achieve more (Baker et al., 2002). Furthermore, students in countries with more equal household incomes had higher mathematics scores, and log GDP per capita showed a better fit than linear GDP per capita, both of which are evidence of diminishing marginal returns. The association of motivation to achievement was similar across countries, while family effects on mathematics achievement differed across countries. Intrinsic motivation, self-efficacy, and self-concept generally showed consistent positive associations with mathematics achievement across countries, with few exceptions. In contrast, family structure and family communication differed substantially across countries. While the results confirm the negative effects of single and mixed parents in the USA, Canada, and a handful of Western European countries (Pong, Dronkers, & Hampden-Thompson, 2003), they are the exception, not the rule. Living with single parents, mixed parents, or no parents showed no significant effects in most countries. In more collectivist countries, the weaker negative association between living with a single parent and mathematics achievement supports the collective dilution hypothesis (greater reliance on extended families in collectivistic countries dilutes the impact of immediate family characteristics). Meanwhile, most family characteristics had similar effects to student achievement across countries, supporting the social reproduction hypothesis that privileged families find academic advantages for their children despite greater public educational resources. Furthermore, several family characteristics were more strongly associated with student achievement in richer countries, consistent with results from the 1970s and 1990s (Baker et al., 2002; Heyneman & Loxley, 1982). Specifically, the stronger associations between mathematics achievement and mixed parents, living with no parents, and cultural communication support the complementary intangibles hypothesis that relatively scarce intangible family attributes complement abundant physical resources in richer countries. Together, these results suggest that family characteristics are becoming more important to student achievement over time as countries develop economically and culturally to become richer and less collectivist (Inglehart & Baker, 2000). The present study had some limitations. First, the students sampled might not be fully representative of all 15-yearolds as students with very low achievement levels or very poor children might not attend school (UNICEF, 2001). Second, this correlational study does not warrant causal interpretations. Third, the cross-sectional data on 15-yearold students in this study does not address developmental effects. Fourth, this study only examined mathematics achievement, and the results might differ for other subjects, such as history or literature. Fifth, PISA did not measure the quality of family processes and, thus, cannot address how the quality of family processes is associated with mathematics achievement. 5. Conclusion Nevertheless, this study has expanded our understanding of family characteristics, motivation, and student achievement in five ways. First, students in families with more resources and fewer competing family members scored higher in mathematics in most countries (supporting the resource provider and resource dilution hypotheses, respectively). Second, students’ interest in mathematics (intrinsic motivation) was associated with higher mathematics achievement in most countries, while extrinsic motivation was not. Third, students’ with single parents did not show lower student achievement in collectivist countries, supporting the collective dilution hypothesis (extended families dilute the impact of immediate family characteristics). Fourth, similar associations between most family variables and student achievement regardless of country income support the social reproduction hypothesis. Fifth, the strong associations between achievement and several family characteristics (mixed parents, living with no parents, cultural communication) in richer countries support the complementary intangibles hypothesis (relatively scarce intangible family attributes complement abundant physical resources). Acknowledgement This study was partially supported by a direct grant from the Chinese University of Hong Kong and a grant from the Spencer Foundation. We appreciate the research assistance of Yik Ting Choi.

334


Appendix A. Summary statistics of significant variables Variable

Mean

SD

Description

Mathematics score Past achievement (R) Relative grade

469

116

Mathematics test scores. Min ¼ 09, Max ¼ 864.

Remediation

0.184

0.720

Students’ reported grade level e expected grade level. Expected grade level is the grade level of a student who never skipped a grade and had no grade retention. Min ¼ 5, Max ¼ 3. 1 ¼ Reading remedial courses in school.

0.200

0.400

Country-level variables (S) Log GDP per capita GDP Gini Individualism

9.090 35.194 51.736

0.601 8.420 23.381

Family variables (T) 1st generation immigrant

0.038

0.190

0.113 0.049

0.317 1.038

Single parent Mixed parents Living with no parents Grandparent Number of siblings Birth order

0.142 0.062 0.037 0.189 1.944 1.800

0.349 0.240 0.189 0.391 1.449 0.980

Family process variables (U) Number of books at home

4.175

1.576

0.008

0.979

0.061

1.016

Girl (V)

0.507

0.500

1 ¼ girl.

Students’ motivation variables (W) Interest in mathematics

0.118

0.878

Extrinsic motivation

0.072

0.864

Self-efficacy (SE)

0.028

0.949

Index of ‘‘When I do mathematics, I sometimes get totally absorbed’’, ‘‘Mathematics is important to me personally’’, and ‘‘Because doing mathematics is fun, I wouldn’t want to give it up’’. Choices: strongly disagree, disagree, agree, and strongly agree. Reliability ¼ 0.75 (ranged from 0.51 [Mexico] to 0.83 [Denmark and Korea]). Min ¼ 1.93, Max ¼ 2.27. Index of studying to ‘‘Increase my job opportunities’’, ‘‘Ensure that my future will be financially secure’’, and ‘‘Get a good job’’. Choices were almost never, sometimes, often, and almost always Reliability ¼ 0.82 (ranged from 0.69 [Mexico and Latvia] to 0.85 [Hungary, Ireland, New Zealand, and Sweden]). Min ¼ 2.44, Max ¼ 1.48. Index of ‘‘I am certain I can understand the most difficult material presented in readings’’, ‘‘I am confident I can do an excellent job on assignments and tests’’, and ‘‘I am certain I can master the skills being taught’’. Choices: almost never, sometimes, often, and almost always. Reliability ¼ 0.70 (ranged from 0.61 [Switzerland] to 0.79 [Iceland]). Min ¼ 2.900, Max ¼ 2.280.

Foreign language SES

Cultural possessions

Cultural communication

Min ¼ 7.625, Max ¼ 9.881 (World Bank, 2004). Min ¼ 24.4, Max ¼ 59.1 (World Bank, 2004). Min ¼ 14, Max ¼ 91 (Hofstede, 2003). 1 ¼ First generation immigrant (Student, mother, and father were all born outside the country). 1 ¼ Foreign language spoken at home. Standardized index created from mother’s years of schooling, father’s years of schooling, and highest parent job status. Min ¼ 3.591, Max ¼ 2.372. 1 ¼ single parent (baseline ¼ two parents). 1 ¼ living with one parent and one step-parent. 1 ¼ living with no parents. 1 ¼ living with at least one grandparent. Min ¼ 0, Max ¼ 12. An ordered variable of birth order: (0) the youngest child (8%); (1) a middle child (35%); (2) the oldest child (25%); and (3) the only child (32%). An ordered variable of ‘‘How many books are there in your home?’’ The choices were: none (2%); 1e10 (13%); 11e50 (23%); 51e100 (21%); 101e250 (18%); 251e500 (13%); more than 500 (10%). Index of availability of ‘‘Classical literature’’, ‘‘Books of poetry’’, and ‘‘Works of art’’. Choices were: yes or no. Reliability ¼ 0.59 (ranged from 0.47 [Russian Federation] to 0.69 [Norway]) (OECD, 2002). Min ¼ 2.11, Max ¼ 1.22. Index of ‘‘Discussing political or social issues’’, ‘‘Discussing books, films or television programs’’, and ‘‘Listening to music’’. Choices: never or hardly ever, a few times a year, about once a month, several times a month, and several times a week. Reliability ¼ 0.55 (ranged from 0.44 [Greece] to 0.63 [Korea and United States]). Min ¼ 2.20, Max ¼ 2.72.


335

Appendix (continued) Variable Self-concept (SC)

Mean 0.022

SD 0.948

Description Self-concept index of ‘‘I learn things quickly in most school subjects’’, ‘‘I am good at most school subjects’’, and ‘‘I can do well in most school subjects’’. Choices: disagree, disagree somewhat, agree somewhat, and agree. Reliability ¼ 0.79 (ranged from 0.66 [Latvia] to 0.85 [Norway]). Min ¼ 2.510, Max ¼ 1.850.

Note: PISA data, unless otherwise noted. OECD (2002) created Warm (1989) indices standardized for OECD countries (M ¼ 0; SD ¼ 1). Negative means indicate lower values for non-OECD countries that were added later. Bold letters (e.g., R) are vectors in the regression.

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