Time spent on homework, mathematics anxiety and mathematics achievement: Evidence from a US sample
Jehanzeb R. Cheema
University of Illinois, Illinois
Kimberly Sheridan
George Mason University, Virginia
This study investigated the effect of time spent on homework and mathematics anxiety on mathematics achievement. Data from a nationally representative US sample consisting of 4,978 cases was used to predict mathematics achievement from time spent on homework and mathematics anxiety while controlling for demographic differences such as gender, grade, race, and socioeconomic status. Multiple regression results showed that both maths anxiety and time spent on homework had a significant effect on maths achievement. The implications are discussed.
Although a wealth of literature in the field of education exists on the link between time spent on homework and academic achievement, many of the prior studies based their findings on samples that do not readily generalise to national populations. Even in nationally representative studies, results are not always in agreement across subpopulations. For instance, using the American National Educational Longitudinal Study of 1988, comprising a sample of 18,352 eighth grade students from 1,052 schools, Mau and Lynn (2000) showed the existence of significant positive correlations between time spent on homework and achievement scores in maths, reading, and science. These correlations ranged between .17 and .36. Furthermore, they showed that such correlations differed significantly between males and females with the correlations for females exceeding those for males. These differences suggest that homework plays a more important role in the achievement scores of females than those of males. This positive association between homework and achievement is not unique to the US education system. Walberg (1991) looked at a survey of eighthgraders in eleven countries and observed that countries where students on average spent more time on homework had higher achievement scores. The US was located at the bottom of this list. The positive link between time spent on homework and achievement has been challenged by some studies. For instance, in a recent study, Kitsantas, Cheema, and Ware (2011) showed that more time spent on maths homework does not necessarily translate into higher test scores in maths. Using a sample of 5,200 fifteen year old high school US students from a national survey, they showed that a negative and weak but significant association exists between proportion of time spent on maths homework and maths achievement. They also showed that the gender gap in achievement ceased to exist once one controlled for important predictors of achievement such as selfefficacy, and demographic differences such as race and socioeconomic status. Unlike Mau and Lynn (2000), Kitsantas et al. (2011) did not find any significant difference between males and females in terms of the effect of time spent on homework on academic achievement.
The apparent contrast between the findings of Mau and Lynn (2000) and Kitsantas et al. (2011) presented as examples above should not be taken as absolute evidence of a lack of consensus in current literature regarding the relationship between time spent on homework and academic achievement. An extensive metaanalysis of literature spanning the 19872003 period by Cooper et al. (2006) established a convincing link between homework and achievement even though their review of variables that moderate the relationship between homework and achievement remained inconclusive. Examples of other studies that support the existence of a homeworkachievement link include Cooper, Lindsay, Nye and Greathouse (1998), Keith (1982), Mulhenbruck, Cooper, Nye and Lindsay (1999), and Pezdek, Berry and Reno (2002).
In context of schoolwork, anxiety is the feeling of helplessness, tension, and/or psychological distress that occurs when a student finds it difficult to cope with the said schoolwork. In general, such anxiety is expected to be negatively associated with achievement (Suinn, Taylor & Edwards, 1988). Unfortunately, studies investigating anxiety in the context of maths tend to look at either test anxiety or anxiety in general. Studies that investigate the component of anxiety which occurs specifically due to maths are scarce. A metaanalysis of 26 studies on the relationship between maths anxiety and maths achievement by Ma (1999) found an average correlation of .27, with the relationship being consistent across gender, grade level (grades 46, grades 79, grades 1012), and race/ethnicity. Using a sample of 324 Israeli students, ages 13, 14, and 16, Milgram and Toubiana (1999) administered an instrument of maths homework anxiety based on ten items which had a reliability of .93. They found that students tended to exhibit lower anxiety for homework as compared to other forms of assessment such as exams. They also reported that students who were more anxious about their homework tended to complete it faster than those who were less anxious. Although they did not include maths achievement in their analysis, the relationship between time spent on homework and anxiety suggests that the possibility of an interaction effect should be considered whenever these two variables occur together. Milgram and Toubiana's study (1999) was the only one we could find which used a homeworkspecific measure of anxiety. For a more involved discussion of nonhomeworkspecific maths anxiety we refer the reader to Ma (1999).
The primary motivation for this study came from a metaanalysis by Cooper, et al. (2006) where they encouraged future research on the homeworkachievement link to use, preferably within a single analytical model, different grade levels, control for demographic factors such as socioeconomic status and gender, and look at other subject areas in addition to maths and reading. In order to obtain a clearer picture of the homeworkachievement relationship, we have tried to follow as many of those recommendations as were feasible within the constraints imposed by our dataset.
The main objective of this study is to look at the effect of maths anxiety and time spent on homework, on maths achievement. The contribution of our study is that we use a measure of maths anxiety which includes an item that measures anxiety specifically due to maths homework, and amount of time spent on homework simultaneously as predictors of maths achievement. In addition, in order to improve the reliability of our analytical results and conclusions derived from those results, unlike most other studies investigating the homeworkachievement relationship, we employ multivariate tools that simultaneously look at the effects of anxiety and homework on achievement while allowing us to control for important demographic differences such as gender, race, grade, and socioeconomic status. Most past studies investigating the homeworkachievement link employed samples that did not allow generalisation of statistical results (Cooper et al., 2006). We intend to use a nationally representative sample that allows our findings to be projected to the entire population of 15year old high school students in the US.
Our hypothesis is that both maths anxiety and time spent on homework are significant predictors of maths achievement after we control for demographic differences such as gender, race, socioeconomic status and grade. More specifically, we expect anxiety to have a negative effect and time spent on homework to have a positive effect on achievement. In the next section of this paper we describe our sample, variables, and analytical method. This is followed by a presentation of empirical results in section three, and a discussion of those results in section four. Section four also describes the limitations of our study and provides guidance for future research.
In the US the PISA 2012 survey was administered by the National Center for Education Statistics (NCES, 2014). The sample consisted of 4,978 students sampled from 166 schools across the US and are representative of 3,538,783 students in 31,091 schools. This sample comprised 2,440 girls and 2,538 boys from five grade levels, 8 (n = 13), 9 (n = 585), 10 (n = 3545), 11 (n = 825), and 12 (n = 10). Of these 4,978 students, 2,537 identified themselves as White, 639 as Black, 1237 as Hispanic, 236 as Asian, 230 as Multiracial, and the rest as belonging to Other races.
Maths anxiety
This scale is based on five items (see Table 1) that measured a student's anxiety related to performing mathematicsrelated tasks. A sample item included, "How much do you agree or disagree with the following statement about how you feel when studying mathematics? I get very tense when I have to do mathematics homework." The response choice for all items were 1 (strongly agree), 2 (agree), 3 (strongly disagree), and 4 (disagree). The scale scores were derived by applying a partial credit item response theorybased model that estimated an anxiety score for each student based on her responses to the five underlying items (Masters, 1982; OECD, 2006). The scale was constructed in such a way that higher scale scores indicate greater maths anxiety. The reliability of this scale was .88 in our sample, and its standardised values ranged from a minimum of 2.21 to a maximum of 2.53 (M = 0, SD = 1).
Time spent on homework
This variable measured the average number of hours spent by a student per week including the weekend on homework or other material assigned by teachers. In our sample the values of this variable ranged between 0 and 30 hours (M = 6.61, SD = 5.49).
Mathematics anxiety

Demographic controls
The following variables were used as controls for individual differences.
where Y_{i} is the maths achievement score of student i; β 's, γ 's, and λ 's are regression coefficients; X's are k = 10 dummy variables that represent grade, gender, and race (four for grade, one for gender, and five for race); SES = socioeconomic status; Time = time spent on homework; and ε, ν, and π are studentspecific error terms.
In order to retain sample representativeness without inflating sample size, we employed normalised sampling weights in all of our computations. We evaluated underlying theoretical assumptions for each estimated regression model, evaluated tests of hypotheses at .05 level of significance, employed single random imputation as missing data handling method, and used Cohen's (1992) cutoffs for interpretation of effect sizes.
The pattern of correlations presented in Table 3 suggests that maths achievement had moderate correlations with maths anxiety, time spent on maths homework, socioeconomic status, and grade. Although many of the reported interpredictor correlations were significant, none of them were larger than .2 suggesting small or trivial effect sizes.
Factor  n  Maths achievement  Maths anxiety  Time spent on homework  Socioeconomic status  
M  SD  M  SD  M  SD  M  SD  
Gender  Female  2440  0.04  0.98  0.08  1.02  7.40  5.74  0.01  1.01 
Male  2538  0.03  1.04  0.09  0.97  5.85  5.12  0.02  0.99  
Grade  8  13  1.44  0.81  0.10  0.57  3.65  2.92  1.65  0.52 
9  585  0.81  0.84  0.20  0.94  4.53  4.28  0.42  0.96  
10  3545  0.06  0.96  0.01  0.99  6.70  5.34  0.05  0.99  
11  825  0.30  1.02  0.09  1.02  7.75  6.39  0.00  0.98  
12  10  1.01  1.71  1.25  0.96  7.77  8.44  0.46  1.03  
Race  White  2537  0.26  0.94  0.03  1.01  6.57  5.07  0.29  0.87 
Black  639  0.72  0.89  0.02  0.98  5.61  5.35  0.11  0.86  
Hispanic  1237  0.30  0.92  0.06  0.96  6.42  5.36  0.65  1.02  
Asian  236  0.76  1.01  0.01  1.03  10.60  7.30  0.17  1.10  
Multiracial  230  0.10  0.94  0.16  1.00  6.95  6.43  0.13  0.89  
Other  99  0.54  0.83  0.06  0.84  6.12  6.68  0.04  0.94  
Notes: N = 4978. Math achievement, math anxiety, and socioeconomic status are standardised variables with M = 0, SD = 1. Time spent on homework is measured as number of hours per week. 
Variable  Correlation, r  
1  2  3  4  5  6  
1. Math achievement    
2. Math anxiety  .39***    
3. Time spent on homework  .34***  .11***    
4. Socioeconomic status  .39***  .15***  .20***    
5. Grade  .26***  .08***  .14***  .10***    
6. Gender  .03*  .09***  .14***  ~0  .08***   
Notes: N = 4978. Reported r is rank biserial correlation between grade and gender; Spearman's rank correlation between grade and continuous variables (achievement, anxiety, time spent on homework and socioeconomic status); point biserial correlation between gender and continuous variables; and Pearson correlation between continuous variables. Cohen's (1992) cutoffs for r : small effect, .1; medium effect, .3; large effect, .5. *p < .05. **p < .01. ***p < .001 
We note that number of students sampled from grades 8 and 12 (see Table 2) is somewhat small. However, we carefully examined the distribution of maths achievement scores in our sample and found it to be approximately normally distributed (see Figure 1). This observed distribution makes it very unlikely that maths achievement is not normally distributed in our target population. It is well known that for a normally distributed variable samples as small as 3 are sufficient to ensure normality in the sampling distribution of sample means (McClave, Benson & Sincich, 2005). For this reason we decided not to discard cases belonging to grades 8 and 12. Excluding these cases entailed the risk of our sample not remaining representative of its target population.
Figure 1: Distribution of math achievement scores in the sample, n = 4978
Parameter  B  t  p  95% CI  
LL  UL  
a. Model 1  Intercept  0.38  1.46  .145  0.13  0.90  
Grade  8  1.83  5.31  < .001  2.50  1.15  
9  1.37  5.36  < .001  1.87  0.87  
10  0.73  2.89  .004  1.23  0.24  
11  0.46  1.82  .068  0.96  0.04  
Gender  0.13  5.47  < .001  0.17  0.08  
Race  White  0.60  7.40  < .001  0.44  0.76  
Black  0.20  2.38  .018  0.37  0.04  
Hispanic  0.34  4.07  < .001  0.18  0.50  
Asian  1.08  11.36  < .001  0.90  1.27  
Multiracial  0.49  5.08  < .001  0.30  0.68  
Socioeconomic status  0.30  23.50  <.001  0.27  0.32  
b. Model 2  Intercept  0.18  0.76  .447  0.64  0.28  
Grade  8  1.45  4.73  < .001  2.06  0.85  
9  0.92  4.02  < .001  1.37  0.47  
10  0.39  1.72  .085  0.83  0.05  
11  0.19  0.82  .412  0.63  0.26  
Gender  0.12  5.83  < .001  0.16  0.08  
Race  White  0.59  8.12  < .001  0.45  0.73  
Black  0.20  2.66  .008  0.35  0.05  
Hispanic  0.28  3.77  < .001  0.13  0.43  
Asian  0.94  10.97  < .001  0.77  1.11  
Multiracial  0.41  4.72  < .001  0.24  0.58  
Socioeconomic status  0.21  18.17  < .001  0.19  0.23  
Maths anxiety  0.31  29.66  < .001  0.33  0.29  
Time spent on homework  0.04  18.93  < .001  0.03  0.04  
Notes: N = 4978. CI = confidence interval. LL = lower limit. UL = upper limit. R ^{2} is 30.3% for model 1 and 44.5% for model 2. Math achievement, math anxiety, and socioeconomic status are standardised variables with M = 0, SD = 1. Time spent on homework is measured as number of hours per week. Reference category is Grade 12 for grade, Male for gender, and Other for race. Cohen's (1992) cutoffs for d: small effect (S), .2; medium effect (M), .5; large effect (L), .8. 
Regression model 3 augmented model 2 by adding all possible two way interactions that included either maths anxiety or time spent on maths homework. A clean version of this model obtained after discarding interactions that were entirely insignificant (i.e. insignificant for all levels of a categorical variable) is presented in Table 5. The results presented in this model suggest that although some interactions were significant, the magnitudes of their partial slope coefficients were small, and inclusion of these interactions added only .3% to the percentage of explained variation in maths achievement. For these reasons these interactions were not examined any further.
Parameter  B  t  p  95% CI  
LL  UL  
Intercept  0.11  0.45  .650  0.59  0.37  
Grade  8  1.42  4.61  < .001  2.03  0.82 
9  0.91  3.95  < .001  1.35  0.46  
10  0.37  1.64  .102  0.82  0.07  
11  0.17  0.74  .458  0.62  0.28  
Gender  0.12  5.85  < .001  0.16  0.08  
Race  White  0.51  5.16  < .001  0.32  0.71 
Black  0.28  2.67  .008  0.49  0.08  
Hispanic  0.20  1.92  .055  0.00  0.40  
Asian  0.76  5.99  < .001  0.51  1.01  
Multiracial  0.15  1.21  .225  0.09  0.38  
Socioeconomic status  0.21  18.15  < .001  0.19  0.23  
Math anxiety  0.34  22.21  < .001  0.37  0.31  
Time spent on homework  0.02  2.03  .042  0.00  0.04  
Interactions  Time spent on homework x White  0.01  1.17  .242  0.01  0.04 
Time spent on homework x Black  0.01  1.15  .252  0.01  0.04  
Time spent on homework x Hispanic  0.01  1.24  .214  0.01  0.04  
Time spent on homework x Asian  0.02  1.85  .065  0.00  0.05  
Time spent on homework x Multiracial  0.04  2.91  .004  0.01  0.06  
Math anxiety x Gender  0.04  2.11  .035  0.00  0.08  
Math anxiety x Socioeconomic status  0.03  2.75  .006  0.05  0.01  
Notes: N = 4978. CI = confidence interval. LL = lower limit. UL = upper limit. R ^{2} = 44.8%. Math achievement, math anxiety, and socioeconomic status are standardised variables with M = 0, SD = 1. Time spent on homework is measured as number of hours per week. Reference category is Grade 12 for grade, Male for gender, and Other for race. Cohen's (1992) cutoffs for d: small effect (S), .2; medium effect (M), .5; large effect (L), .8. 
First, our results suggest that maths anxiety and time spent on homework are both important predictors of maths achievement. A one standard deviation increase in maths anxiety was associated with a decrease of almost a third of a standard deviation in maths achievement. A similar increase in time spent on homework on the other hand was associated with an increase in maths achievement of more than a fifth of a standard deviation. Of the total variation in maths achievement that we were able to explain, a third came from these two variables. This is a considerable effect size, and suggests that any serious study of maths achievement should not ignore these two variables. Excluding these variables can results in a model specification bias that can negatively affect parameter estimates and their standard errors.
Second, we observe that time spent on maths homework and anxiety have opposite effects on maths achievement. Thus, for maths achievement the negative effect of increase in anxiety can be (at least partially) countered by increasing the number of hours spent on homework. This can be an important tool for teachers who feel that anxiety is affecting their students' achievement scores in maths. For example, a half a standard deviation increase in maths anxiety can be countered by increasing number of hours of homework by four hours per week. Given that we did not find evidence of a significant interaction between maths anxiety and time spent on homework, we expect more time spent on homework to equally benefit less anxious and more anxious students.
Third, although control variables appeared in our models of maths achievement in order to account for individual differences and did not motivate the purpose of this study, we note that the gender gap in achievement always favoured boys and that this gap expanded when we controlled for other individual differences such as grade, race, and socioeconomic status. Although small in magnitude this observed gender gap did not disappear with the introduction of maths anxiety and time spent on homework in our models of maths achievement. Our results thus support the position that on average boys tend to have higher scores as compared to girls in mathematics. This finding is in line with recent findings based on similar large scale assessments of 13 and 17 year old US students (NCES, 2013). We also note that like gender, socioeconomic status and race also had significant effects on maths achievement. These results are also in line with findings reported by past research based on US PISA samples (e.g. Cheema & Galluzzo, 2013; Kitsantas, Cheema & Ware, 2011).
Although our study revealed several significant results, caution should be exercised when generalising our findings to (1) nonUS populations, (2) subjects other than mathematics, and (3) populations of students that are very different from the one represented by our sample. For example, since our sample was based on high school students, our findings may not be generalisable to students enrolled in colleges or universities. Furthermore, some of our measures such as maths anxiety, socioeconomic status, and race were selfreported by students. Although it is unlikely that there was large scale misreporting in a data set of the size used in our study, any findings based on selfreported data are accurate only to the extent that such data were accurately reported. Future research in this area can proceed in several directions such as (1) replicating our study with samples from other countries, (2) looking at the relationship of anxiety and homework with achievement in subjects other than mathematics, and (3) examining this relationship in populations other than 15year old students.
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Authors: Jehanzeb Cheema is Clinical Assistant Professor at the College of Education, University of Illinois at UrbanaChampaign. He received his doctorate in Education in May 2012 from George Mason University and a doctorate in Economics in December 2006 from University of WisconsinMilwaukee. Email: jrcheema@illinois.edu Kimberly Sheridan is an Associate Professor of Educational Psychology at George Mason University. She received her doctorate in Human Development and Psychology in June 2006 from Harvard University's Graduate School of Education and holds a joint appointment in the College of Visual and Performing Arts at GMU. Email: ksherida@gmu.edu Web: http://cehd.gmu.edu/people/faculty/ksherida Please cite as: Cheema, J. R. & Sheridan, K. (2015). Time spent on homework, mathematics anxiety and mathematics achievement: Evidence from a US sample. Issues in Educational Research, 25(3), 246259. http://www.iier.org.au/iier25/cheema.html 