Literature Search and Selection

To gather primary studies that linked parental homework involvement to academic achievement, we first searched the following databases: Taylor & Francis, Sage, Elsevier, John Wiley, Spinger, PsycINFO, Education Resources Information Center (ERIC), and JSTOR. Specifically, we used the following terms and their combinations to search the title, abstract, and keyword: “parental” (or “paternal”, “maternal”, “mother”, “father”) “involvement” (or “assistance”, “help”); “homework”; and “achievement”.

To minimize publication biases, we further searched other databases (e.g., google scholar and ProQuest Dissertations & Theses Global) for grey literature such as dissertations, preprints, government reports, or conference proceedings. Moreover, to order not to miss relevant studies on parental homework involvement and achievement, we searched primary studies in meta-analyses and reviews, including ^{Ariës et al. (2015)} , ^{Boonk et al. (2018)} , ^{Castro et al. (2015)} , ^{Fan and Chen (2001)} , ^{Henderson and Mapp (2002)} , ^{Kim (2022)} , ^{Patall et al. (2008)} , and ^{Vasquez et al. (2016)} .

Our search included documents available as of October 31, 2022, yielding 477 unique records. Through our reading of the titles, abstracts, and keywords, we identified 162 primary studies as possible candidates for inclusion into our study. Figure 1 visually depicts our search process. These studies were retrieved and set aside for further scrutiny.

Figure 1. Flowchart for Inclusion of Primary Studies in the Meta-analysis 

Inclusion and Exclusion Criteria

To be included in our study, a primary study must meet the following criteria:

When a study contained parental homework involvement and students' achievement more than one data point, we only included the relationship between parental homework involvement at data point one and subsequent students' achievement at data point two (or three). For example, ^{Silinskas et al. (2022)} linked maternal homework involvement to students' achievement across Grades 6, 7, and 9. We only included maternal homework involvement at data point one (Grade 6) and students' achievement at data point three (Grade 9).

Study Features Extracted from Primary Studies

To identify the study features that could serve as possible moderators to explain mixed results of primary studies, we implemented a systematic process to code pertinent features of primary studies included in our study. The final set of the study features is shown in Table 1. We described the process for coding these features below.

Coding Process and Reliability

The coding process included several steps. The first step was to make coding plan. According to the purpose and research question of the current study, the coding plan included variables listed in Table 1 and Table S1. Some variables such as research design (correlation vs. experiment), student gender, prior knowledge, reliability of measure of parental homework involvement, classroom type, and SES or educational level of parents were in the initial coding plan, but not presented here because the primary studies did not provide sufficient information.

The second step was to extract information the primary studies. Several graduate students in the author list received coding training from the first and the corresponding author which provided the basic information and requirement about the meta-analysis, and coding processing in particular. After coding five primary studies, they attended a conference to discuss about how to appropriately code relevant study features. Following that, they extracted information from the rest of the primary studies.

The third step was for cross checking and validation. It was conducted by two graduate assistants and the corresponding author. When encountering inconsistence, they discussed and re-extracted relevant information for corresponding primary studies. Following that, the corresponding author checked all the primary studies and cells of the coding table. Overall, the reliability (i.e., the coding consistency rate) was 96%, indicating a high degree of consistency between coders in meta-analyses.

Statistical Computation

Study Characteristics

Based on the coding of 162 primary studies considered as potentially relevant, 28 studies satisfied the inclusion criteria as discussed above, therefore eligible for our study. These 28 studies involved 32 independent samples. Two studies (^{Dumont et al., 2012}; ^{Harris, 1991}) involved two independent samples, one study (^{Schultz, 1999}) involved three independent samples. The primary studies were published between 1988 and 2022. The total accumulated sample size was 378222. The sample sizes ranged from 79 to 343900, with median of 449. Table 1 lists study characteristics and their frequency distribution. Basic information of each primary study are included in Table S1 (see https://osf.io/u3syb/?view_only=c8894b14dd28406da57257bd9930a010 ).

Heterogeneity Tests

As presented in Table 2, the Q test was statistically significant, indicating substantial heterogeneity across the effect sizes (Q (251) = 12924.145, p < 0.001). The total I² was 99%, indicating substantial heterogeneity among the included primary studies. Specifically, 1.0% of the total variance could be attributed to level 1 variation (at the sampling); 82.4% could be attributed to the level 2 variation (within-study); and 16.6% could be attributed to the level 3 variation (between-study). As commonly recommended (^{Borenstein et al., 2019}; ^{Hunter & Schmidt, 1990}), investigating the moderation effects of other variables on the overall effect size can be meaningful if less than 75% of the variance is accounted for by the sampling variance. In our study, only 1.0% variance was attributed to the samples. As a result, there is a critical need to examine and identify the potential moderators in our meta-analysis (see Table 3).

Publications Bias

First, funnel plot analysis indicated it was somewhat asymmetric where more effect sizes located in the left side, and the missed effect sizes located in the right (see Figure 2). Second, trim and fill method identified that the number of missed effect sizes is 49. After adding 49 effect sizes, we found that re-estimated overall effect size was r = −0.034 (95% CI [−0.060, −0.080], p < 0.001), which was almost identical to the previous pooled effect size r = −0.064 (95% CI [−0.105, −0.023], p < 0.001). Third, Rosenthal's Fail-safe N of our meta-analysis was 266869.7, which is much greater than the critical value that 5k + 10 = 5 × 32 + 10 = 170 (^{Card, 2015}). Overall, these assessment results suggest that the publication bias would be small and negligible.

Figure 2. Funnel Plot of Effect Sizes 

Quality Assessment

Of the total of 32 independent samples, 3 (9.38%) were in the medium-low quality level (quality score ranging from 7 to 12); and 24 (75.00%) were in the medium-high quality level (quality score ranging from 13 to 17); and 5 (15.63%) were in high quality level (quality score ranging from 18 to 24). Of the total of 252 effect sizes, 13 (5.16%) were in the medium-low quality level; 223 (88.49%) were in the medium-high quality level; and 16 (6.35%) were in high quality level.

Taking the quality score as independent variable, the values of effect sizes as dependent variables, a meta-regression was conducted. Results revealed that F _{(1, 250)} = 0.180; p = 0.671; intercept = −0.116; se = 0.127; beta coefficient = 0.003; se = 0.008; t = 0.425; p = 0.671. The variance between primary studies = 0.006, and the variance among effect sizes = 0.029. These results showed a non-significant correlation between quality score and effect size, suggesting that the quality of the primary studies did not systematically influence the effect sizes.

Main Effect

Table 2 presents results from the three-level meta-analysis. The overall relationship between parental homework involvement and students' achievement across all primary studies (k1 = 28) and effect sizes (k2 = 252) was r = −0.064 (p < 0.001), with 95% confidence interval varying from −0.105 to −0.023. This finding suggests that, in spite of inconsistent results across primary studies, overall, there was a negative, although weak, relationship between parental homework involvement and students' achievement.

About 82.4% of the total variance could be attributed to within-study differences in effect sizes (level 2) and about 16.6% could be attributed to between-study differences (level 3). Provided with the variability in effect sizes within and between studies (i.e., heterogeneity), it would be important to conduct follow up analysis for potential moderators that may contribute to the inconsistence among the effect sizes across primary studies.

Effects of Moderators

Results of all moderator analysis are displayed in Table 3. These moderators included dimension of parental involvement, achievement measure, grade level, parent gender, geographical region, subject matter, research design, publication type, and sampling method.

Involvement Dimension

One of the most important findings in our study is that students' achievement was positively related to autonomy support, yet unrelated to other dimensions of parental homework involvement (content support, parental control, frequency, and mixed). A growing body of research, involving students from elementary schools to post-graduate institutions, has reported that autonomy support from parents (and teachers) lead to greater engagement and better performance (^{Ryan & Deci, 2020}). Two previous meta-analyses on parental homework involvement (^{Fernández-Alonso et al., 2022}; ^{Patall et al., 2008}) have alluded to the potential promise of parental autonomy support in the homework process.

No prior meta-analyses on this topic to the best of our knowledge, however, have incorporated parental autonomy support along with other dimensions of involvement (e.g., content support, parental control, and frequency or amount). Thus, it can be argued that our meta-analysis extends and expands extant literature, thereby providing empirical support to the proposition that autonomy support as one dimension of parent homework involvement that is distinctive from other dimensions of involvement. This is particularly revealing and has important implications for homework practice and research, as homework involvement is often viewed as the most common yet controversial aspect of parental involvement (^{Dumont et al., 2014}; ^{Hill & Tyson, 2009}; ^{Moroni et al., 2015}).

Grade Level

Our meta-analysis revealed that the association between parental homework involvement and students' achievement was negative for elementary school students and not significant from zero for middle and high school students. These findings are not consistent with the meta-analysis by ^{Patall et al. (2008)} , in which the relationship was negative for middle school students, not significant from zero for elementary school students, and positive for high school students. One likely explanation for this discrepancy is that Patal et al.'s meta-analysis was based on a very small number of studies (i.e., 2-5) involving middle and high school students, whereas our meta-analysis was based on a very small number of studies (i.e., 3) involving high school students. Another plausible explanation is that, during the elementary school years, parents are more likely to react to poor mathematics and reading performance of their children (^{Silinskas et al., 2013}). A related explanation is that, because of limited self-regulation skills (e.g., time management), elementary school students tend to receive more parental monitoring and control than autonomy support (^{Bronson, 2000}; ^{Núñez et al., 2015}).

Still another possible explanation is that perceived parental homework involvement is associated with students' productive homework behaviors (e.g., homework time management) at the middle and high school level, yet not at the elementary school level (^{Núñez et al., 2015}). These productive homework behaviors, in turn, influences students' achievement. Thus, it is likely that the lack of linkage between perceived parental homework involvement and productive homework behaviors may further contribute to the parental homework involvement - students' achievement relationship at the elementary school level.

Subject Matter

Our meta-analysis did not find significant differences across different subjects (mathematics, language arts, reading, social sciences, and mixed). Our result is consistent with the meta-analysis by ^{Fernández-Alonso et al. (2022)} that showed the general relationship between parental homework involvement and students' achievement varied little across subjects (mathematics, reading, and science). On the other hand, our result is somewhat not in line with the meta-analysis by ^{Patall et al. (2008)} that reported that “involvement had a positive relationship with achievement in verbal subject matter but a negative relationship with achievement in mathematics” (p. 1091). Patall et al. posited that “involvement in mathematics homework may be more difficult for parents” (p. 1091). One likely explanation for this difference (i.e., Patall et al's meta-anallysis on the one hand, and Fernández-Alonso et al.'s and our meth-analyses on the other hand) is that involvement in mathematics homework may become relatively less challenging for parents over the last fifteen years since the meta-analysis by ^{Patall et al. (2008)}. This explanation is, to some degree, substantiated by a recent literature review on parent involvement and mathematic outcome over the last decade (i.e., 2010 to 2019; ^{Fiskerstrand, 2022}), which showed the positive influence of parental involvement on children's mathematics activities. Have recently been exposed to new materials and strategies for learning mathematics, a new generation of parents may become less overwhelmed by the demands of helping their children's mathematics homework.

Geographical Region

Our meta-analysis did not find significant difference across primary studies carried out in different geographical regions (American, Europe, and Asia) on the relationship between parental homework involvement and students' achievement. This result is not in line with a previous meta-analysis that showed the effects were greater in Europe than in Asia (^{Fernández-Alonso et al., 2022}). Given that the meta-analysis by Fernández-Alonso et al. focused on one dimension of parental involvement (i.e., frequency), whereas our meta-analysis included multiple dimensions of involvement (e.g., autonomy support, content support, parental control, and frequency), it is necessary to include geographical region as a possible moderator in future meta-analyses on the relationship between parental homework involvement and students' achievement.

Parent Gender

Our meta-analysis further examined whether parent gender moderated the association between parental homework involvement and students' achievement. Results revealed that the relationship was negative for mothers, and not significant from zero for fathers and parents. One possible explanation is that mothers, compared with fathers, are frequently more involved in all aspects of their children's schooling (e.g., homework; ^{Kim & Hill, 2015}; ^{Lamb, 2010}). Homework involvement in particular tends to be viewed as being the responsibility of mothers, and they more likely to react to poor academic performance of their children “by providing more help than is typical of fathers” (^{Silinskas et al., 2013, p. 53} ). This explanation is to some degree further illustrated by interview data from the study by ^{Kim and Fong (2014)} in that mothers' homework involvement tends to be more remedial by focusing on what their children are struggling at school. For example, one student stated:

My Ma helped me in subjects I wasn't so good at. So for instance, Chinese, English . . . she would test me on homework given by the teacher. My Ma would also later help me with areas I didn't understand well… When my grades were not stable, then she would get involved. (p.626)

By contrast, fathers get involved in homework when they feel competent and not necessarily because their children are struggling at school. Another student commented, ‘‘[My Pa] basically tutored me in math. He was better at math, so he tutored me in math. I was on my own studying Chinese” (p. 626).

Other Moderate Variables

Aside from involvement dimension, grade level, subject matter, geographical region, and parent gender, our meta-analysis examined other study features that may moderate the association between parental homework involvement and students' achievement. These moderators include publication type, achievement measure, sampling method, and research design.

Our finding regarding publication type is in concordance with the corresponding finding from the metal-analysis by ^{Patall et al. (2008)} in that publication type was not significant when applying a random-effects model. As for achievement measure, our meta-analysis found that it moderated the relationship between parental homework involvement and students' achievement, whereas the meta-analysis by ^{Patall et al. (2008)} did not find significant difference between standardized and unstandardized measures. Hence, it would be important to include achievement measure as a possible moderator in future meta-analyses.

Concerning sampling method and research design, our analysis revealed no significant differences between studies using random and nonrandom sampling, and between studies based on cross-sectional and longitudinal design. As sampling method and research design were not examined as moderators in previous meta-analyses on parental homework involvement (^{Fernández-Alonso et al., 2022}; ^{Patall et al., 2008}), these results extend previous work, by suggesting that the relationship between parental homework involvement and students' achievement would be comparable with what the general literature would suggest based on both correlational and longitudinal designs.

Limitations and Future Directions

Our meta-analysis extends and expands extant literature on the relationship between parental homework involvement and students' achievement, by providing an up-to-date synthesis of recent findings (e.g., autonomy support), by applying the three-level meta-analytic approach, and by incorporating potential moderators that have not been explored in prior meta-analyses (e.g., parent gender and research design). Yet, certain limitations ought to be acknowledged. Even though our meta-analysis included studies carried out in different geographical regions, it was limited to primary studies written in English. The exclusion of primary studies in other languages may to some extent limit the generalizability of our results. Second, regarding student gender, we found too few studies that contained parental homework involvement - achievement correlations separately for boys and girls. Therefore, it is not clear whether the relationship between parental homework involvement and students' achievement is moderated by student gender. Third, a small number of primary studies were identified at the senior high school level or in subjects other than mathematics, language arts, and reading.

Consequently, it would be desirable to conduct a line of research concerning the relationship between parental homework involvement and students' achievement at the high school level and in other subject matters (e.g., science). Furthermore, the effect of parental homework involvement can be influenced by individual characteristics of children (e.g., prior knowledge; ^{Núñez et al., 2017}; ^{Silinskas et al., 2013}) and parents (e.g., educational level and pedagogical knowledge; ^{Fernández-Alonso et al., 2022}; ^{Patall et al., 2008}). Because of the lack of such information in primary studies included in our meta-analysis, we were not able to examine their potential influences on the effect of parental homework involvement in our meta-analysis. It would be informative to examine the interaction of parental homework involvement and individual characteristics of children and parents in further investigation.

In addition, given our finding that parental autonomy support was the only dimension that was positively related to students' achievement, it would be highly desirable to pursue a line of studies that randomly assign parents into different experimental conditions (e.g., autonomy support vs. content support) and then assesse their respective effects on students' achievement. Finally, consistent with the recommendation by ^{Patall et al. (2008)} , it would be informative to conduct qualitative research that provide thick longitudinal descriptions of what occurs surrounding the parent-child interactions over homework tasks, as children make their transition from elementary to middle and high school.