Peer & Parent Encouragement of Early Algebra Enrollment & Mathematics Achievement

Algebra is perceived by many educators to be a “gateway course”. Many state graduation requirements include at least one year of algebra as a prerequisite for higher-level mathematics courses. In a study of the long-term effects of studying algebra in eighth grade using NELS:88, Atnada (1999) found eighth-graders studying algebra were more likely to take high-level mathematics courses and apply to college than those who did not take algebra. Controlling for socioeconomic background, Smith (1996) found students studying algebra earlier had more exposure to advanced mathematics curricula and showed higher mathematics achievement by the end of high school. Based on the findings, it is important for students to study algebra prior to high school.

Spielhagen (2006) supported these findings with a study of a school district in the southeast where students enrolled in algebra prior to high school showed higher mathematics scores and more advanced course taking in high school. This study went further, examining how students gained access to algebra in the eighth grade. Although the school system had a placement policy for eighth grade algebra based on prior mathematics performance and standardized test scores, some students (mostly in the high SES schools) gained access through parent or teacher “override” of the placement policy. Teachers reported students who were placed in the class by parent or teacher override still succeeded in algebra. Spielhagen’s findings call into question the role of social factors in determining students’ enrollment in eighth grade algebra and the effects of encouragement on the study of algebra prior to high school.

Numerous studies have addressed the benefits of algebra for all students. However, the social factors underlying a student’s choice to enroll in algebra early are not well understood. The present study examines the effects of peer and parent encouragement to take algebra and socio-economic level on algebra attendance prior to high school and the subsequent effects on eighth grade mathematics achievement.

In the famous study completed nearly forty years ago, Equality of Educational Opportunity,Coleman (1966) studied the features of a school environment that lead to student academic differences. Coleman reported the educational and social background of a student’s family was the most important variable in determining academic achievement. Poverty, and other health problems (poor nutrition, low birth weight, substandard housing, high violence, and substance abuse) associated with poverty, can depress achievement. Although a portion of the achievement gap can be explained by socioeconomic background, when these differences are factored out there is still an achievement gap that must be due to other factors (Kober, 2001).

Often students from low SES backgrounds are not afforded the same educational opportunities as students from wealthier families. In the “Equity 2000” program, the College Board encourages the participating school systems to introduce algebraic concepts in elementary and middle school to ensure students are prepared for algebra (College Board, 1994). The program reports success with increased enrollment in higher level mathematics courses with stable or improved pass rates (College Board, 1998). Although making algebra accessible for all students has been implemented in many school systems, it is not a universal practice and its impact on academic achievement has not been fully assessed (Gamoran & Hannigan, 2000).

In a 2000 study of algebra taking using the NELS data, Gamoran and Hannigan found students who take algebra gain in math achievement regardless of initial achievement when controlling for background variables such as SES. The study concluded with the recommendation that all students enroll in algebra to maximize achievement although students of diverse backgrounds “may need more diverse and thought-provoking instructional methods than are typically offered in high school algebra” (Gamoran & Hannigan, 2000, p.250).

Parents as well as teachers significantly contribute to a student’s attitudes and outcomes at school (Frome & Eccles, 1998). Singh, Bickley, Keith, Keith, Trivette, and Anderson (1995) explored the effect of different components of parental involvement on the achievement of eighth-graders. The study identified four components of parent involvement including: parental aspirations for the child’s education, parent-child communication about school, home-structure, and parental participation in school related activities. These four factors had little to no effect on achievement, except for parental aspirations. Parental aspiration had the greatest impact on pupil achievement after controlling for social class factors.

As children approach adolescence, they spend increasing amounts of time with their peers and less time with their parents. As peerinfluence becomes more important in a child’s life, it is important to study if student-peer relationships are an important predictor of student achievement. However, examining the effects of significant others in children’s achievement has primarily focused on parents and teachers, and often the role of peers has not proven nearly as influential as the role of parents in a student’s academic achievement.

Peer group research is complex and difficult to measure because children’s friendships are based, in part, on similarity. It is difficult to determine if friends have influenced each other because their friendships may be based on being similar (Cohen, 1983). Although peer influences are difficult to examine, they cannot be overlooked. A key finding of the Coleman report (1966) was student achievement is linked to the educational backgrounds and goals of other students. Horn and Chen (1998) supported this finding in a study of high school students at-risk of dropping out. The study found students at moderate or high risk levels were nearly four times more likely to enroll in college if most of their friends were planning to attend a four-year college. Peers’ college goals play a role in at-risk student college enrollment.

Peer influence on academics has only been examined by a few studies although students spend large amounts of time with friends. There is evidence children may spend 25-40% of their nonclass time with friends (Larson & Richards, 1991). In a 2003 study, Altermatt and Pomerantz found friends to be the most influential with regard to report card grades. Friends also influenced achievement-related beliefs such as: to what they attributed their academic successes; the importance of meeting academic standards; as well as preference for challenging coursework. The study also concluded close friendships (i.e. personal and long-lasting) had more influence on academics than other friendships or peer group associations.

Previous academic achievement is often used by school systems to determine which students to enroll in eighth grade algebra (Spielhagen, 2006). However social factors such as socio-economic background, parent aspirations, and peer influence may also play a roll in student goal-setting, course selection, and academic achievement. In an effort to better understand the relationships between socio-economic background, parent and peer social factors, enrollment in algebra prior to high school, and mathematics achievement, a theoretical model was proposed.

Using the National Education Longitudinal Study: 1988/2000 (NELS) dataset, the present study tested a theoretical model of relationships between parent and peer influence, SES, algebra course taking prior to high school, and mathematics achievement. Specifically, the following research questions were addressed:

• Does encouragement to take algebra by parents and peers have direct effects on algebra course taking prior to high school?

• Does student socioeconomic status have a direct effect on algebra course taking prior to high school?

• Does algebra instruction prior to high school have a direct effect on mathematics achievement?

• What are the total effects of parent and peer encouragement and SES on eighth grade mathematics achievement?

The theoretical model proposed in this study suggests a direct benefit in taking algebra in eighth grade on mathematics achievement. Achievement is also a direct result of the social factors of peer and parent encouragement and SES. The model also hypothesizes these social factors are correlated with one another and can predict early algebra taking. Path analysis was used to test the theoretical relationships proposed in the model. An extension of multiple regression models, path analysis involves the analysis of several multiple regression equations using observed variables (Schumacker & Lomax, 2004). The theoretical model was estimated using LISREL 8.80 (Jöreskog & Sörbom, 2006).

This study uses four measures from the base year of the NELS survey (1988). Schools and students were selected for the nationally representative survey using a two-stage stratified probability design. The schools were selected at the first stage of the sampling using probabilities proportional to the estimated 8th grade enrollment, and approximately 26 students were randomly selected from each school in the second stage. The NELS contained four waves of data beginning with 1988 eighth graders, following a substantial subsample of these students in 1990 and 1992 in thetenth and twelfth grades. The data collection ended in 2000 with a postsecondary transcript study. The base year sampled 1,032 schools (815 public and 237 private) from a national frame of about 39,000 schools containing the 8th grade and 24, 599 students randomly selected from participating sampled schools. In the current study, students with missing transcript data were excluded and a sample size of 3,288 was used.

NELS oversampled private schools and Hispanics and Asian/Pacific Islanders in the base year; therefore, correlations, means, and standard deviations were weighted with the Base Year Questionnaire Weight (BYQWT) using AM Statistical Software Beta Version 0.06.03 (American Institutes for Research & Cohen, 2005). The weighted results were then used in model specification using LISREL 8.80 (Jöreskog & Sörbom, 2006).

The dependent variable is the eighth grade math IRT scale score as measured by a 40-item multiple choice test. The mediating variable was measured by the student survey question: “Did you attend algebra at least once per week?” Answers were recoded 0-did not attend and 1-attend. The independent variable, peer influences, was measured by a student survey item asking if peers encouraged algebra enrollment. The peer encouragement categories were recoded 0-discouraged me and 1-encouraged me. The second independent variable used was to determine the role of parent influence. Parent influence was measured with a student survey question asking if parents wanted the student to take algebra. The survey results were coded 0-no and 1-yes. The SES composite was used as the measure of socio-economic status. The SES composite is derived using responses from the parent survey and is the mean of the non-missing standardized values of parents’ occupation, parents’ education, and family income. The SES composite is a standardized value with a mean of zero.

Correlations, mean scores, and standard deviations for all study variables are displayed in Table 1. The relatively high correlation between parent encouragement and peer encouragement (r = .404) reflects the relationship between parents and friends who encouraged higher level course taking in middle school. Students with parents who encouraged algebra taking also had peers who encouraged them to take algebra. However, the correlations between parent encouragement and SES (r = .171) and peer encouragement and SES (r = .112) showed weak associations, the encouragement of early algebra course taking by significant others not strongly tied to economic background.

SES and the encouragement variables showed relatively strong associations with attendance in algebra in eighth grade. Algebra attendance correlated with parent encouragement (r = .359) more strongly than peer encouragement (r = .257) and SES (r = .244) All variables showed relatively large correlations with eighth grade achievement scores, with SES (r = .478) and attending algebra (r = .444) indicating stronger achievement associations than parent (r = .311) and peer (r = .245) encouragement.

The main findings from the path analysis are summarized in Table 2. To aid in interpretations, the parameter estimates for the causal relationships in the path model are plotted in Figure 1. The model was saturated with all paths significant. Examining the maximum likelihood equation for eighth grade mathematics achievement, approximately 37% of the variance in achievement was explained by the model. The direct effects were significant with attending algebra in eighth grade contributing positively to achievement scores (β = .291, p < .05). Increased achievement on the eighth grade mathematics test was also predicted by higher SES (β = .379, p < .05). Parent encouragement (β = .108, p < .05, η² = .01) had a significant direct effect on mathematics achievement with those students encouraged by their parents to take algebra in eighth grade scoring higher on the mathematics achievement test although it showed a small effect size. Peer encouragement (β = .084, p < .05, η² < .01) was also a significant predictor of achievement with eighth graders encouraged by their friends to take algebra scoring higher on the eighth grade mathematics test with a small effect size.

Attending algebra in eighth grade served as the mediating variable between the social factors and mathematics achievement with approximately 18% of the variance in algebra attendance explained by the social factors of parent encouragement, peer encouragement and SES. Increased participation in eighth grade algebra was predicted by parent encouragement to take algebra (β = .278, p < .01, η²= .10) with students more likely to attend algebra if their parents encouraged them. Peer encouragement (β = .152, p < .01, η²= .06) was also a significant predictor of algebra taking, those students encouraged by their friends to take algebra in eighth grade attended at a higher rate than those discouraged. SES (β = .118, p < .01) was also a factor in student early algebra taking with higher SES students more likely to attend than low SES students.

When examining the total effects of the social variables on mathematics achievement, high SES was a significant predictor of increased achievement scores (β = .432, p < .05). Parent encouragement (β = .188, p < .05) and peer encouragement (β = .120, p < .05) to take algebra significantly predicated increased mathematics achievement in eighth grade.

The purpose of the current study was to propose and test a model of social factors contributing to algebra attendance prior to high school and the effects of the social factors and early algebra taking on middle school mathematics achievement. Consistent with previous research, our findings showed attending an algebra class at least once per week leads to increased mathematics achievement for eighth grade students.

The social factors of SES and peer and parent encouragement had significant effects on a student’s participation in an algebra class. Parent encouragement to take algebra in eighth grade was a strong predictor of attending an algebra course prior to high school with students encouraged by their parents more likely to attend. Additionally peer encouragement to take algebra predicted algebra attendance with students discouraged from taking algebra by their friends less likely to attend. Parent and peer encouragement was highly related with students encouraged by their parents to take algebra more likely to have friends who encouraged algebra taking. SES was also a significant predictor of algebra attendance with low SES students less likely to attend algebra at least once a week than high SES students. Although SES was a factor in algebra taking, it was not highly correlated to peer and parent encouragement, so parents and peers encourage algebra taking regardless of SES, but fewer low SES students were taking algebra.

Higher mathematics achievement was also found to be significantly related to SES, parent encouragement and peer encouragement to take algebra. Supporting Coleman’s report (1966), the current findings showed a significant total effect of SES on math achievement with students from more advantaged socio-economic backgrounds more likely to score higher on the math test. Overall parent encouragement to take algebra had a significant impact on mathematics achievement with students who are encouraged by their parents to take algebra showing increased math scores in middle school. From a policy perspective, family background and parental encouragement are important to achievement; therefore, making algebra available to students in all middle schools and communicating the importance of algebra prior to high school may help parents and students recognize its impact on mathematics achievement.

Peer encouragement to take algebra also had a significant impact on overall mathematics achievement with students encouraged by their friends more likely to post higher math scores. If peers actively discouraged enrollment in algebra, mathematics achievement was negatively affected. This study, however, showed a small effect size with the other variables contributing to math achievement variance more than peer encouragement. Additional research needs to be conducted to better understand the nature of friendship and if similar academic achievement is a product of friendships or one of the reasons students become friends. Also, research needs to examine the social structures of students at school to understand how friendships may foster or undermine student academic achievement.

In reporting these findings, it is important to acknowledge some limitations of the study. The NELS:88 study did not include many questions assessing algebra taking; therefore, the best representations of peer and parent encouragement and algebra attendance were chosen with single observed variables used. Also, when predicting algebra taking, the error variance was large (SE = .635, p < .01) and the effects sizes were small, indicating other variables were contributing to a student’s enrollment in algebra in eighth grade. Previous academic achievement can be a strong predictor of participation in algebra prior to high school as many school systems have minimum academic requirements for a student to be considered for eighth grade algebra as Spielhagen (2006) indicated. Using the base year for the data set, a measure of past performance was not available to use as a control, but past performance should be considered when testing this model in future research.

In conclusion, the findings from the present study suggest students’ mathematics achievement is influenced by the social factors of family background and the encouragement of peers as well as parents. Students with parents with high academic aspirations participate in higher level mathematics and perform better on achievement tests in middle school. This study showed peer influences also affect academic achievement and algebra attendance, although the effects are not as great as the parent-child relationship. Future research in this area needs to specifically examine the long-term impact of peer and parent encouragement to take algebra on student enrollment in higher-level mathematics courses throughout high school and the resulting effects on mathematics achievement.