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Edited by: Cheng Yong Tan, The University of Hong Kong, Hong Kong

Reviewed by: Ming Lui, Hong Kong Baptist University, Hong Kong; Angelica Moè, University of Padua, Italy

This article was submitted to Educational Psychology, a section of the journal Frontiers in Education

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Parents play an important role in children’s academic achievement. The purpose of the present study was to explore the internal structure of an established parent survey and to investigate the relationships among different aspects of parental involvement in predicting children’s mathematics achievement. The study involved secondary data from 139 parents and math achievement scores of 121 elementary school-aged children. Guided by Hoover-Dempsey and Sandler’s Revised Parent Involvement Process model, a Principal Component Analysis with direct oblimin rotation was conducted on the parent survey, followed by path analysis to predict children’s math achievement. Five principal components were retained. Standardized results of the path analysis indicated that parental self-efficacy had the largest direct effect on children’s math achievement. Moreover, parental self-efficacy was favored directly by parental perceptions of specific school invitations to become involved. These findings shed light on the interplay between parental involvement and children’s achievement and underscore the importance of school-family collaboration, which can potentially link to parental self-efficacy.

Mathematics achievement is an integral part of overall academic achievement. Children’s early math achievement can strongly predict later academic achievement, financial success, and future career choices (e.g.,

Since parents play an important role in their children’s growth and learning, the goal of this research was to investigate parental involvement in their children’s education, and specifically the effects of this involvement on children’s math achievement. Moreover, this research focused on examining the ways in which two valuable scholarly tools—a well-known research survey and a theoretical model–could be used in combination to further understanding of parental involvement in children’s achievement. Examining the ways in which survey tools and theoretical models work in tandem can contribute to the evidentiary support of both the tool and the model, and provide insights into our own “blind spots.”

The present study focused on math achievement for three reasons. First, math achievement can play a prominent role in facilitating children’s pursuit of a breadth of educational opportunities in science, technology, engineering and mathematical (STEM) fields. Second, compared to language arts achievement, math achievement can generally be more objectively graded and quantified since there are standard answers. Third, given the sample size requirements for the multivariate analysis conducted in the present study, focusing on a single academic outcome was a necessary constraint. For these three reasons, the study focused solely on math achievement; however, future research should investigate whether the work presented here applies to other academic disciplines. Two research questions guided the study: (1) What is the structure of the

There are many definitions of parent involvement in children’s schooling and ways to operationalize its practice (

One of the most comprehensive accounts of parental involvement is the

Hoover-Dempsey and Sandler Model of the parental involvement process (

Level 1 of the model includes three broad variables comprising parental motivational beliefs, perceptions of invitations for involvement, and perceptions of life context. Level 1 serves as the basis of the model. Each of these three broad variables involves finer-grained definitional variables. For example, parental motivation beliefs include (a) parental construction (beliefs) about their roles to become involved in their children’s education, and (b) parental self-efficacy for helping their child succeed in school. The variables at Level 1 are hypothesized to contribute to parental involvement behaviors at Level 2.

Level 2 parental involvement behaviors can include home-based or school-based involvement actions, which would involve mechanisms such as encouraging the child, modeling academic-related behaviors for the child, reinforcing the child’s activities, and instructional activities with the child. Level 2 behaviors in turn influence Level 3 variables such as children’s perceptions of parental involvement. Children’s perceptions of parental involvement include children’s perceptions of parental encouragement, modeling, reinforcement and instructional activities. Level 3 variables are hypothesized to influence children’s underlying attributes for achievement at Level 4; for example, children’s academic self-efficacy and intrinsic motivation for learning at school. Finally, Level 4 variables are hypothesized to influence children’s academic achievement at Level 5, reflecting one of the final outcomes of the parental involvement process.

The R-PIP model was used as a guiding framework for the present study. However, not all levels of the R-PIP model were able to be included in this research. In particular, only Levels 1, 2, and 5 were included given constraints in data collection. One constraint involved the use of

Overall, the R-PIP model (

Parental self-efficacy is a critical factor that determines the goals parents choose for themselves and how persistent they are in working toward those goals (

The second variable at Level 1 is parental perceptions of invitations for involvement from others. This second variable is defined by parents’ perceptions of general school invitations, specific child invitations, and specific teacher invitations. The term “invitation” in the R-PIP model is to refer to actions that make parents feel needed, valued and welcomed (

The third variable at Level 1 is parents’ perceived life context. This third variable is defined by parents’ self-perceived knowledge and skills and self-perceived time and energy (

The second level of the model includes one main variable—parental involvement behaviors. Parental involvement behaviors can occur in the home (e.g., helping a child with homework) or at school (e.g., volunteering to help with a class field trip). Parental involvement behaviors take different forms within the home or at school. For example, parents can involve themselves by verbally encouraging children, modeling interest and time-management strategies to their children, reinforcing children’s completion of school tasks, and directly instructing children during homework time. Although previous research has shown parental involvement to be positively associated with children’s academic achievement (

The main variable at Level 5 of the model is student achievement.

The present study focused on Levels 1, 2, and 5 of the R-PIP model. The aim was to measure select variables at these levels using a previously developed survey called the ^{1}. The

The data used in the present study originated from a previous project designed to investigate the relationship between a specific pedagogical approach employed in a public elementary school and students’ learning outcomes (

Of the 25 teachers participating in the original study, two teachers from each of Grades 1, 2, 4, 5, and 6 participated in the original study. Four teachers from Grade 3 participated as well, and 2 Educational Assistants. The original participating students (

Among the participating parents, close to 90% were female primary caregivers (

Procedures of the original data collection are outlined by

The present study included two global measures. First, the

The complete

For purposes of the present research, only 5 sections (55 items) of

Descriptive analysis of all survey items.

Item | n | ||

[SECTION 1- Perceptions of teacher-parent contact] 16 Items My child’s teacher or someone at the school… Response Scale: 1-Well, 2-OK, 3-Poorly, and 4-Never | |||

1a. Helps me understand my child’s stage of development. * | 137 | 2.01 | 0.89 |

1b. Tells me how my child is doing in school. * | 138 | 1.64 | 0.80 |

1c. Ask me to volunteer at the school. * | 138 | 1.55 | 0.80 |

1d. Explains how to check my child’s homework. | 139 | 2.06 | 1.05 |

1e. Sends home news about things happening at school. | 139 | 1.18 | 0.49 |

1f1. Tells me what skills my child needs to learn in: math. * | 139 | 1.89 | 0.91 |

1f2. Tells me what skills my child needs to learn in: reading/language arts. * | 138 | 1.83 | 0.86 |

1f3. Tells me what skills my child needs to learn in: science. * | 138 | 1.99 | 0.93 |

1g. Provides information on community services that I may want to use with my family. * | 138 | 2.16 | 1.04 |

1h. Invites me to School Council meetings. * | 139 | 1.46 | 0.79 |

1i. Assigns homework that requires my child to talk with me about things learned in class. | 137 | 1.58 | 0.76 |

1j. Invites me to a program at the school. | 139 | 1.42 | 0.77 |

1k. Asks me to help with fund raising. | 139 | 1.48 | 0.78 |

1l. Has a parent-teacher conference with me. | 135 | 1.84 | 1.09 |

1m. Includes parents on school committees, such as curriculum, budget, or improvement committees. * | 138 | 1.53 | 0.74 |

1n. Provides information on community events that I may want to attend with my child. | 138 | 1.70 | 0.84 |

[SECTION 2–Parents’ attitudes about the school and teachers in general] 4 Items How much do you agree or disagree with the following statements about your child’s school and teachers? Response Scale: 1-Strongly Agree, 2-Agree, 3-Disagree, 4-Strongly Disagree | |||

2a. This is a very good school. * | 138 | 1.14 | 0.41 |

2b. I feel welcome at the school. * | 138 | 1.19 | 0.48 |

2c. I get along well with my child’s teacher(s). * | 138 | 1.30 | 0.56 |

2d. The teachers at this school care about my child. * | 138 | 1.25 | 0.50 |

[SECTION 3–Parents’ involvement behaviors] 17 Items How often do you… Response Scale: 1-Everyday/Most Days, 2-Once a Week, 3-Once in a While, 4-Never | |||

3a. Read with your child? * | 139 | 1.60 | 0.90 |

3b. Volunteer in the classroom or at the school? | 139 | 2.96 | 0.64 |

3c. Work with your child on science homework? * | 138 | 2.65 | 0.89 |

3d. Review and discuss the schoolwork your child brings home? * | 139 | 1.31 | 0.60 |

3e. Help your child with math? * | 139 | 1.68 | 0.77 |

3f. Visit your child’s school? * | 138 | 1.45 | 0.76 |

3g. Go over spelling or vocabulary with your child? * | 139 | 1.57 | 0.75 |

3h. Ask your child about what he/she is learning in science? * | 138 | 2.12 | 1.00 |

3i. Talk to your child’s teacher? * | 138 | 2.23 | 0.91 |

3j. Ask your child about what he/she is learning in math? * | 139 | 1.74 | 0.83 |

3k. Help your child with reading/language arts homework? * | 139 | 1.68 | 0.88 |

3l. Help your child understand what he/she is learning in science? * | 137 | 2.41 | 1.00 |

3m. Help your child prepare for math tests? * | 136 | 2.46 | 1.15 |

3n. Ask your child how well he/she is doing in school? | 139 | 1.30 | 0.61 |

3o. Ask your child to read something he/she wrote? | 138 | 1.78 | 0.87 |

3p. Go to a school event (e.g., sports, music, drama) or meeting? | 139 | 2.25 | 0.82 |

3q. Check to see if your child finished his/her homework? * | 139 | 1.23 | 0.58 |

[SECTION 4–Parents’ beliefs about their responsibility in children’s education] 10 Items It is a parent’s responsibility to… Response Scale: 1-Strongly Agree, 2-Agree, 3-Disagree, 4-Strongly Disagree | |||

4a. Make sure that their child learns at school. * | 137 | 1.53 | 0.71 |

4b. Teach their child to value schoolwork. * | 138 | 1.27 | 0.52 |

4c. Show their child how to use things like a dictionary or encyclopedia. | 137 | 1.60 | 0.68 |

4d. Contact the teacher as soon as academic problems arise. * | 139 | 1.32 | 0.55 |

4e. Test their child on subjects taught in school. | 138 | 2.06 | 0.92 |

4f. Keep track of their child’s progress in school. * | 139 | 1.30 | 0.55 |

4g. Contact the teacher if they think their child is struggling in school. | 139 | 1.11 | 0.33 |

4h. Show an interest in their child’s schoolwork. | 139 | 1.12 | 0.33 |

4i. Help their child understand homework. | 139 | 1.30 | 0.56 |

4j. Know if their child is having trouble in school. * | 138 | 1.14 | 0.37 |

[SECTION 5–Parents’ beliefs about their capability in helping with children’s education] 8 Items How much do you agree or disagree with the following statements? Response Scale: 1-Strongly Agree, 2-Agree, 3-Disagree, 4-Strongly Disagree | |||

5a. I know how to help my child do well in school. * | 138 | 1.76 | 0.60 |

5b. I never know if I’m getting through to my child. * | 138 | 3.06 | 0.72 |

5c. I know how to help my child make good grades in school. * | 137 | 1.80 | 0.67 |

5d. I can motivate my child to do well in school. * | 138 | 1.77 | 0.66 |

5e. I feel good about my efforts to help my child learn. * | 138 | 1.59 | 0.62 |

5f. I don’t know how to help my child on schoolwork. * | 138 | 3.32 | 0.70 |

5g. My efforts to help my child learn are successful. * | 138 | 1.70 | 0.59 |

5h. I make a difference in my child’s school performance. * | 138 | 1.60 | 0.61 |

Mapping of

Although the parent survey sections could be mapped to R-PIP model, it is important to note that the survey

With permission from the publisher, slight changes to the wording of some items and probes were made to maximize the clarity of the items for the parents in this study. For example, a question was altered to reflect the proper name of meetings at the school instead of using the American term “PTA.” A final section requesting demographic information about the family was also included in the survey.

The parent survey was administered and completed in November, 2012. In December 2012, children’s mid-term report-card grades were collected from the school principal. According to school assessment practices, children’s academic achievement was operationalized by teachers’ classroom-based assessments in Mathematics. Teachers’ classroom-based assessments included in-class assignments, homework, quizzes, and end-of-unit tests. Student assessment outcomes were formalized using the school’s five-point system (

Since no previous studies had examined the internal structure of the

After conducting the PCA, scale scores for each component were calculated. Scale scores were calculated by taking the average of item ratings that loaded on a particular component. Path analysis using Mplus v. 7.11 (

Path analysis required data from parents and children to be cross-linked. Complete data were available from only 121 parent-child dyads. A few parents did not consent to reveal their children’s achievement data, but they consented to have their own data included in the path analysis; thus, their children’s data were coded as missing. The normality assumption of scale scores and children’s math achievement scores was verified using the Kolmogorov-Smirnov test and the Shapiro-Wilk’s test in SPSS. All components were found to be negatively skewed and revealed a departure from normality in distribution (

In the process of conducting PCA, missing data were addressed in SPSS 21.0 using the listwise deletion method. Listwise deletion method was used instead of pairwise deletion because the latter approach can lead to non-positive definite correlation matrices, causing estimation problems for subsequent multivariate analyses (

To verify the adequacy of the data for PCA, the KMO test (

Sixteen items with cross-loadings were removed. Items with cross-loading are typically removed to facilitate component interpretation. However, an exception was made to temporarily retain one item that would have otherwise been removed due to cross-loadings. This decision was made to see how it might be interpreted in the rotated solution. Item 3j, shown in ^{∗}) indicate those 39 that were retained.

Direct oblimin rotation was applied to the seven components resulting in sums of squares loadings ranging from 2.71 to 5.44.

Direct oblimin rotation loadings of parental involvement survey items (all seven components shown).

Item | Loadings |

Component 1: Parental Self-Efficacy (α = 0.86) * 5a. I know how to help my child do well in school. | 0.77 |

5b. I never know if I’m getting through to my child. | −0.50 |

5c. I know how to help my child make good grades in school. | 0.77 |

5d. I can motivate my child to do well in school. | 0.63 |

5e. I feel good about my efforts to help my child learn. | 0.68 |

5f. I don’t know how to help my child on schoolwork. | −0.72 |

5g. My efforts to help my child learn are successful. | 0.76 |

5h. I make a difference in my child’s school performance. | 0.59 |

Component 2: Parental Perceptions of General School Invitations (α = 0.88) * | |

2a. This is a very good school. | 0.87 |

2b. I feel welcome at the school. | 0.91 |

2c. I get along well with my child’s teacher(s). | 0.70 |

2d. The teachers at this school care about my child. | 0.84 |

Component 3: Parental Involvement Behaviors (α = 0.83) | |

How often do you… | |

3a. Read with your child? | 0.69 |

3d. Review and discuss the schoolwork your child brings home? | 0.62 |

3e. Help your child with math? | 0.66 |

3f. Visit your child’s school? | 0.57 |

3g. Go over spelling or vocabulary with your child? | 0.69 |

3i. Talk to your child’s teacher? | 0.59 |

3k. Help your child with reading/language arts homework? | 0.79 |

3q. Check to see if your child finished his/her homework? | 0.62 |

Component 4: Parental Perceptions of Specific Teacher Invitations (α = 0.89) * | |

My child’s teacher or someone at the school… | |

1a. Helps me understand my child’s stage of development. | 0.64 |

1b. Tells me how my child is doing at school. | 0.76 |

1f1. Tells me what skills my child needs to learn in: math. | 0.87 |

1f2. Tells me what skills my child needs to learn in: reading/language arts | 0.83 |

1f3. Tells me what skills my child needs to learn in: science | 0.76 |

Component 5: Parents’ Involvement Behaviors (α = 0.84) * | |

How often do you… | |

3c. Work with your child on science homework? | 0.76 |

3h. |
0.84 |

3j. |
0.52 |

3l. Help your child understand what he/she is learning in science? | 0.83 |

3m. Help your child prepare for math tests? | 0.67 |

Component 6: Parental role construction (α = 0.76) * | |

It is a parent’s responsibility to… | |

4a. Make sure that their child learns at school. | 0.76 |

4b. Teach their child to value schoolwork. | 0.66 |

4d. Contact the teacher as soon as academic problems arise. | 0.61 |

4f. Keep track of their child’s progress in school. | 0.60 |

4j. Know if their child is having trouble in school. | 0.75 |

Component 7: Parental Perceptions about Specific Teacher Invitations (α = 0.68) | |

1c. Asks me to volunteer at the school. | 0.52 |

1g. Provides information on community services that I may want to use with my family. | 0.66 |

1h. Invites me to School Council meetings. | 0.73 |

1m. Includes parents on school committees, such as curriculum, budget, or improvement committees. | 0.65 |

A review of

Mapping of

As shown in

A review of components 3 and 5 revealed a subtle difference in the nature of parental involvement items (section 3). For example, component 3 items reflected more active parental involvement (e.g.,

Three path models were tested in order of plausibility. The first model is shown in ^{2} = 10.08, df = 8, ^{2} to the df was 1.26. A ratio value of three or less reflects reasonably good indicator of model fit (

Path model for statistically significant effects of parental involvement factors on children’s mathematics achievement. The direct effects between Role Construction and Involvement Behaviors was tested but not significant. Likewise, the effect between Role Construction and Children’s Math Achievement. *

A second and third model were also tested for comparison. The second model was very similar to the first except that the variable of ^{2} = 14.89, df = 8, ^{2} = 14.73, df = 8,

Only statistically significant effects are shown in

As can be seen in

Raw (R) and standardized (S) coefficients of indirect effect estimates of parents’ perceptions of general school invitations on children’s math achievement.

Predictor | Mediating variables (s) | Criterion | Coefficient estimate (95% CI) |

Perception of General School Invitations → | Perception of Specific Teacher Invitation → Parental Self-efficacy → | Math achievement | 0.039 (0.006, 0.122)* (R) |

0.020 (−0.010,0.049) (S) | |||

Perception of General School Invitations → | Perception of Specific Teacher Invitation → Parental Self-efficacy → Parental Involvement Behaviors → | Math achievement | −0.007 (−0.035, −0.001)* (R) |

−0.004 (−0.011,0.004) (S) | |||

Perception of General School Invitations → | Perception of Specific Teacher Invitation → Parental Self-efficacy → Role Construction → Parental Involvement Behaviors → | Math achievement | −0.003 (−0.018, −0.001)* (R) |

−0.001 (−0.004,0.001) (S) |

^{∗}95% confidence interval excludes zero and therefore is significant at p < 0.05.

Overall, the R-Square index showed that the best-fitting model shown in

Guided by

Based on a PCA with direct oblimin rotation, seven components were extracted from the

Congruent with the R-PIP model (

The present study also extended support of the R-PIP model with evidence that parental self-efficacy mediates the relationship between parental perceptions of general school invitations, specific teacher invitations and parental involvement behaviors, which sits as a Level 2 variable in the R-PIP model. Parental self-efficacy, more so than parental role construction beliefs, was shown to be predictive of parental involvement in children’s schooling (

Another directional influence found between Level 1 variables was from parental self-efficacy to help children succeed toward parental role construction beliefs. This directional influence suggests that parents who are confident in their ability to help children succeed may cultivate stronger beliefs about their role and responsibility in children’s math achievement. Interestingly, however, the relationship between role construction (beliefs) and involvement behaviors (action) was not statistically significant. The lack of statistical significance is not wholly unexpected as investigators have found that conscious thought or beliefs are not necessarily a good predictor of action (

Although parental self-efficacy was found to be a positive predictor of children’s math achievement, the effect was direct and not indirect as indicated in the R-PIP model. This discrepancy, however, may be attributed to the constraints of the present research as Level 3 and 4 variables were not measured in the sample of parents. Thus, they could not be included in the path model. In fact, one would expect an indirect effect of parental self-efficacy on children’s achievement. Previous research has shown that parents who have high self-efficacy may be more likely to engage in interactions that facilitate children’s math achievement

The negative association between parental involvement behaviors and children’s math achievement is also consistent with previous research (

Before concluding this section, it is important to note that although path model raw coefficients were statistically significant, the observed correlations among components were generally weaker. This incongruence may be explained by the use of listwise deletion in PCA to handle missing data. When listwise deletion is used, the data from a participant with even one missing item response are removed fully from consideration. This leads to the loss of information (and variation) in the calculation of individual correlations among components. However, in path analysis, scale score means can be computed with part information, allowing additional power in detecting significant relationships.

The present study has both theoretical and practical implications. Theoretically, this study was able to evaluate the interplay of variables in the R-PIP model (

The results of this study need to be considered in light of the following limitations. First, the present study involved a relatively small sample of convenience. Participants came from one elementary school in a moderately large city in Western Canada. Therefore, generalization of results must be limited to the specific attributes of the sample. In addition, the size of sample is likely to have contributed to the discrepancy in statistical significance between raw and standardized coefficients for the indirect effects found in the path model. Second, the use of a survey (

Future studies regarding parental involvement and children’s academic achievement should continue to explore the Levels of the R-PIP model, and attempt to include Levels 3 and 4. For example, collecting data about children’s perceptions of parents’ involvement behaviors to examine how well these data correlate with parental reports. Another important area for future research is examining the connection between aspects of self-efficacy for informing parental beliefs about getting involved in their children’s academic life. What makes this area fascinating is that low-confidence parents are likely modeling low-confidence to their children, and this lack of confidence is likely to discourage children’s academic attainment. The negative association between parental involvement behaviors and math achievement also deserves study. Investigating the quality of and mechanisms underlying the verbal and behavioral strategies parents use to help children with schoolwork may illuminate detrimental effects. For example, if homework conversations are contentious, this may be harmful to both children and parents. Additionally, different subject areas need to be considered as outcome variables (e.g., math, science, language arts) in future studies with larger sample sizes, thus providing more comprehensive understanding of the influence of parental involvement behaviors on children’s academic achievement.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by the Human Ethics Research Office (HERO) Pro00032355. Written informed consent to participate in this study was provided by the participants or participants’ legal guardian/next of kin where necessary.

YL wrote the first draft and conducted the analyses. JL revised all subsequent drafts and all parts of the manuscript, and reviewed appropriateness of analyses, and reworked all figures. Both authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.