Mathematics placement and the transition to middle school.

The transition to middle school has been a frequent research topic in recent years. The findings have highlighted both the significant risk and opportunity for school counselor intervention in the transition. One particularly important component of the multifaceted transition is course placement. The importance and influence of mathematics and mathematics placement and the role of the school counselor in this process are outlined. Specifically, pilot data that underscore the importance of school counselor collaboration with parents and mathematics faculty are presented.

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School counselors are in an excellent position to construct and enact programs that promote students' successful and equitable transition from elementary school to middle school (American School Counselor Association, 2005). In particular, the potential influence of school counselors with respect to students' placement in middle school mathematics is crucial. This article begins broadly with a presentation of the research on the transition to middle school, then examines more specifically research highlighting the critical importance of initial mathematics placement and the effects of inequitable patterns of placement on students' future learning trajectories. Finally, pilot data from a survey of fifth- and sixth-grade parents about their children's mathematics placement demonstrate the need for parent, teacher, and school counselor collaboration in this transition.

Prior research has identified significant declines in academic achievement following the elementary to middle school or junior high transition (e.g., Alspaugh, 1998; Anderman, Maeher, & Midgley, 1999; Chung, Elias, & Schneider, 1998; Crockett, Peterson, Graber, Schulenberg, & Ebata, 1989; Diemert, 1992; Gutman & Midgley, 2000; Seidman, Allen, Aber, Mitchell, & Feinman, 1994). Along with achievement declines, students' self-concept of ability and motivation also suffer (Mizelle & Irvin, 2000; Wigfield, Eccles, Mac Iver, Reuman, & Midgley, 1991). Significantly, these negative effects have been found to be most pronounced in students' achievement in and attitudes toward mathematics (Eccles et al., 1993).

The transition to middle school has a direct impact on a student's educational trajectory in mathematics due to the typically stratified nature of the courses to which students are assigned and the often strong performance focus of the teaching and learning that occurs. During the middle school years, students may be inequitably distributed among hierarchies of mathematics courses on the basis of race and economic background, becoming increasingly stratified within these tracks (Dauber, Alexander, & Entwisle, 1996). Emphasis on competition and individual success, which is particularly prevalent in mathematics courses, is not necessarily developmentally appropriate and has been shown to be a less than optimal approach to learning for many girls and students from diverse cultures (Eccles et al., 1993; Malloy & Malloy, 1998).

In addition, school procedures for placement decisions may not be uniformly applied, with students of low social economic status (SES) and minority students often inequitably kept from higher-level courses, in spite of assessed ability, and disproportionately recommended for lower-level courses (Dauber et al., 1996; Hallinan, 1994; Plata, Masten, & Trusty, 1999). The combined impact of this increase in differentiation by mathematics class, decrease in mathematics self-efficacy, use of developmentally inappropriate approaches to teaching, and beliefs regarding potential barriers and lack of support may lead to lower achievement levels and, therefore, lower grades among students, disproportionately impacting girls and minorities. This, then, impacts students' educational trajectories in mathematics for subsequent years and contributes to the underrepresentation of women and minorities in high-level mathematics coursework in high school and college.

Beginning in middle school, mathematics content and the mathematics course sequence become less fluid and less changeable. Once in a track, students' placement is not likely to change to a higher-ability placement unless there is parental intervention (Dauber et al., 1996; Hallinan, 1994; McGrath & Kuriloff, 1999a). This cumulative effect puts the transition to middle school and the mathematics sequence upon entry at a pivotal point for post-secondary schooling because of its effect on college opportunities, career development, and, ultimately, career possibilities. If, at any point in middle school, a student chooses or is forced to choose a lower-level mathematics course, it becomes significantly less likely the student will end up taking the upper-level high school mathematics courses required for admission to a 4-year college (Oakes, Gamoran, & Page, 1992). The importance of persistence in high school mathematics was demonstrated by Trusty and Niles (2003), whose analyses of NELS data from 1988 to 2000 showed a marked increase in the likelihood of college graduation with each mathematics course taken from advanced algebra and beyond.

MATHEMATICS SELF-EFFICACY, EXPECTATIONS, AND PERCEIVED SUPPORTS

The predictive power of mathematics self-efficacy in forecasting science- and mathematics-related interests is well supported by research. In their seminal work, Hackett and Betz (1981) suggested that girls' and women's beliefs regarding specific careers and activities, primarily those in mathematics, science, and technology, are influenced by low self-efficacy resulting from gender socialization experiences. This lower self-efficacy often limits their interest in and exploration of mathematics, including higher-level mathematics courses. For example, girls transitioning to middle school often experience a significant decline in their self-described ability in mathematics, or mathematics self-efficacy, along with a growing shift of focus toward more social and relational issues. While some research suggests that gifts do feel efficacious in regard to a few activities (e.g., computer use), involvement in scientific and mathematical careers and a lack of self-efficacy in mathematics remain problematic (American Association of University Women [AAUW], 2000).

The importance of self-efficacy and classroom ecology (e.g., whether learning is focused on relative performance or individual mastery) is not only limited to girls. Waxman, Huang, and Padron (1997) examined academically successful and less successful Latino middle school students in nontracked mathematics classes (i.e., schools with one mathematics course for all students in each grade). They found no effect for English language ability but found successful students to have significantly stronger perceptions of a positive classroom environment, more involvement in class, higher academic self-concept, and higher academic aspirations. Knowledge of the importance of high self-efficacy and classroom ecology takes on even greater importance considering that (a) tracking--the separation of students into different levels of coursework--in mathematics is common in middle schools; (b) students in higher-level classes hold significantly higher academic aspirations while students in lower-level classes have significantly less interest in their work; and (c) minority students tend to be overrepresented in lower-level mathematics classes and underrepresented in higher-level mathematics classes (Dauber et al., 1996; Educational Testing Service, 1991; Loveless, 1999; McGrath & Kuriloff, 1999b).

For girls, studies show dramatic changes in self-concept, self-efficacy, and achievement during the middle school years (AAUW, 1998). These factors have long-term academic and career effects because of screening out of critical mathematics during this time (Dawes, Horan, & Hackett, 2000). It is therefore essential that school counselors increase the possibility of students beginning higher-level mathematics sequencing so that students will have equitable access to higher-level mathematics in high school and, ultimately, readiness for college. When the mathematics sequence is differentiated in middle school, some students are limited in the quantity and quality of mathematics curricula to which they may have access in high school. Essentially, the tracking and placement in middle school mathematics may create or perpetuate "aspiration gaps" in which students begin to aspire to distinct career paths based on their school experiences (Akos, Lambie, Milsom, & Gilbert, in press). School counselors can be instrumental in guiding students toward appropriate mathematics courses and curricula so that their educational career options are not prematurely foreclosed (Shoffner & Vacc, 1999).

PARENTAL INVOLVEMENT AND MATHEMATICS PLACEMENT

The effect of parental involvement appears to have a significant role in the quality of transition as experienced by students. Parental involvement also affects mathematics placement and performance of middle school students. For example, Dauber et al. (1996) found that African American students were less likely to be placed in advanced mathematics courses and more likely to be placed in remedial courses despite prior achievement. They also found that positive parental expectations served to increase the likelihood of students' placement in advanced mathematics courses. The transition to sixth-grade mathematics presents itself as a time when parental involvement can have long-term consequences on children's educational outcomes.

It is important for school counselors to examine, therefore, patterns of parental influence to ensure equitable involvement in mathematics placement decisions. Useem (1992) found significant correlations between parents' education levels and their children's placement in mathematics ability groups. Parents with baccalaureate and graduate degrees were more likely to be involved in their children's education by being more aware of the importance of academic choices made in schools. Data from Useem's index of parental involvement showed that parents' involvement in the school affected their children's assignment to courses, a phenomenon corroborated by the more recent work of McGrath and Kuriloff (1999a). Research also has suggested that parents' lack of involvement, social isolation, and reluctance to intervene have a larger influence on their children's placement in a lower-level mathematics course than do the children's abilities (Useem). Clearly, this suggests that parental involvement is a salient factor in mathematics placement, mathematics efficacy, and, more broadly, a successful transition to middle school. The role of the school counselor in creating an awareness of and support for positive parental involvement in this process cannot be understated.

PARENTS' PERCEPTIONS OF MATHEMATICS PLACEMENT

As part of a school-university partnership focused on school transitions, the first author conducted a pilot study in which fifth- and sixth-grade parents' perceptions of the mathematics placement process in their children's transition to middle school were examined. The investigation was multipurpose and focused on the local context. Nonetheless, this pilot study generated compelling information related to the need for school counselor collaboration with parents in mathematics placement during the transition to middle school.

Participants and Setting

Forty-seven parents of fifth-grade students at one public elementary school and 60 parents of sixth graders at the receiving middle school in the Southeastern United States participated in the study (approximately 50% of all parents). While no demographic data were collected on the participants, the middle school demographic profile includes 57% Caucasian, 20% African American, 9% Asian, 8% Hispanic, and approximately 6% multiracial. Both the elementary school and the middle school are part of a medium-sized Southeastern school district that includes eight elementary schools, four middle schools, and two high schools. The middle school primarily serves students from two of the elementary schools, one of which is included in the study. The schools are located in a university community. Overall, the school district can be characterized as high performing, with over 90% of the students annually attending postsecondary education.

Procedure and Data Collection

Parent questionnaires were distributed in fifth-grade classrooms at the elementary school and in sixth-grade classrooms in middle school during the fourth academic quarter (April). Classroom teachers distributed questionnaires about mathematics placement to students for parents to complete at home. The students returned completed questionnaires to the classroom teachers. The questionnaires were collected by research personnel for analysis.

The fifth-grade parents completed a 12-item questionnaire. Questions were designed to ascertain the parent's knowledge and opinions about the mathematics placement process in the transition from elementary to middle school. For example, questions asked about parental knowledge of placement criteria, parents' roles in the placement process, opportunities for parents to communicate with school staff, and appropriate placement for their children in sixth-grade mathematics. Similar questions were asked retrospectively of sixth-grade parents. The sixth-grade parent questionnaire consisted of 17 items, with 5 additional questions to determine satisfaction with their child's current mathematics experience (sixth grade). Questions were either open-ended or multiple choice with additional space for written-in answers. A copy of each of these questionnaires can be obtained from the first author upon request.

DATA ANALYSIS AND RESULTS

Frequencies and percentages were calculated for responses to each question. Because some questions were used for school-specific purposes (e.g., feedback on specific teachers), only results that illustrated parent perceptions of the mathematics placement process are presented.

Four questions in particular demonstrated interesting findings: (a) "Do you know how your child's sixth-grade mathematics placement is determined?"; (b) "What is your role in your child's sixth-grade mathematics placement?"; (c) "Should students in the sixth grade be separated into mathematics classes based on their abilities?"; and (d) "How important is your child's sixth-grade mathematics placement in relation to future academic courses in college?" Table 1 displays these findings.

Additional findings from the fifth-grade parent questionnaire included indications of a high level of parent comfort in talking to school personnel, yet limited knowledge about the factors involved in mathematics placement or about the available mathematics curriculum for sixth grade. For example, parents chose the factors they perceived to determine mathematics placement as teacher recommendation (89%), state exams/standardized test placement (64%), administrative decision (26%), or parent preference (21%). Fewer than 5% listed other factors (e.g., grades, other tests) as affecting their children's mathematics placement. The district policy for the corresponding academic year indicates that test scores (e.g., state exams scores, Iowa Algebra Aptitude Test) and at least three qualifying components (recommendation by fifth-grade mathematics teachers, demonstrated mathematics achievement, mathematics class grades, work and organizational habits, motivation levels) determined mathematics placement in sixth grade. Additionally, 40% of the parents indicated a lack of knowledge regarding mathematics courses available to sixth graders, and 19% listed courses not currently offered in sixth grade. These results were found even though 94% of the parents reported feeling either comfortable or very comfortable talking to elementary school teachers and 81% reported feeling comfortable or very comfortable talking to middle school teachers.

The sixth-grade parent surveys revealed a positive experience in sixth-grade mathematics, although a lower percentage of students in this cohort were placed in advanced mathematics (as compared to the fifth-grade cohort's expectations). These parents were also less comfortable in talking to school personnel, and there was little or no mention of school counselors. When asked about their perception of the sixth-grade mathematics teachers, 90% of the comments were positive (e.g., good teachers, challenge students at all levels) rather than negative (e.g., not communicative with parents). Further, whereas 51% of the fifth-grade parents indicated that accelerated mathematics was most appropriate for their child, only 20% of the parents in the sixth grade had children in pre-algebra (the accelerated option). Sixth-grade parents reported feeling less comfortable talking to elementary school staff (68% comfortable or very comfortable) and middle school staff (57% comfortable or very comfortable) as compared to the fifth-grade parents. Finally, in several questions regarding communication with school staff about placement, the school counselor was only mentioned twice (3% of all respondents) in the sixth-grade parent survey (not mentioned at all in the fifth-grade results).

DISCUSSION

Results of our study shed some light on parental knowledge about engagement in the mathematics placement process in children's transition to middle school. For example, it is problematic that 60% of fifth-grade parents and 42% of sixth-grade parents were unaware of mathematics placement criteria. This is especially disheartening in sixth grade where 55% of the responses for the parent role in mathematics placement were "I have no role" or "I don't know." Research clearly indicates that parents need to have knowledge of placement procedures and a clear articulation of their role in the placement process. This is particularly true when students are segregated by ability levels in sixth grade. These findings were from a high-SES, well-educated, and often active (e.g., school governance) parent community. Because these data suggest low levels of engagement and uninformed parents in a school district composed of well-educated parents, one must ask if parental awareness and level of engagement may be even less in less affluent or academically lower-performing contexts.

It is also compelling to note the suggested shifts in perceptions of parents from fifth and sixth grade relative to tracking and their understanding of the importance of sixth-grade mathematics placement. While many fifth-grade parents appear to feel strongly about tracking, parents of sixth-grade students seem to be less positive about the use of ability grouping (94% of fifth-grade parents agreed with grouping as compared to 77% of sixth-grade parents). Although this is not a longitudinal design, the students' experiences in sixth-grade mathematics may have stimulated equity concerns for some parents. Although this pilot study has obvious limitations (e.g., limited generalizability), these data in combination with current research on the importance of mathematics placement have critical implications for school counselors.

IMPLICATIONS FOR SCHOOL COUNSELORS

Information from this study and prior research on mathematics and school transition suggests that preventive or proactive programming is needed to assist parents and students with the transition to middle school. While school counselors rarely teach mathematics, and infrequently make final placement decisions, they have a responsibility to advocate for all students and have a unique opportunity to play a critical role in individualized educational planning.

One approach would be for school counselors to provide parent consultation and parent meetings on the transition to middle school (Arowosafe & Irvin, 1992). In fact, students look to parents as their primary source of advice during the fifth-grade year (Akos, 2002). Clearly, parents' involvement during students' transition to middle school, both direct (e.g., advocating for higher placement for their child) and indirect (e.g., expressing high expectations to their child), is important. School counselors, as leaders and advocates for transition programming, must inform all parents of the ways they can support their children and of the ways that they can become actively engaged in ensuring equitable placement decisions. School counselors also can work with parents and other members of the community to increase collaboration and communication between the family and school.

Making parents partners in the placement process can lead to empowerment for children and parents (Yonezawa & Oakes, 1999). This can be done by helping parents to recognize prejudice, privilege, and entitlement and how these arc exercised, by removing barriers to knowledge, by providing alternative sources of information, and by engaging students and parents in advocating for all. Many, if not most, middle school counselors actively explain curriculum choices to fifth-grade students and parents as part of the scheduling process. This opportunity to talk with parents provides an ideal arena for counselor advocacy and leadership. When parents are knowledgeable about the process and encourage their child, and when middle schoolers feel confident in their abilities, students are more likely to pursue and be successful in advanced mathematics courses. Schools must especially advocate for and monitor students typically underrepresented in mathematics/science fields, and they should find equitable means to place students in appropriate mathematics courses.

Placement challenges and advocacy are only a part of the solution, however. In addition, school counselors can be instrumental in increasing the self-efficacy beliefs of youth regarding their ability to succeed with higher-level mathematics courses. Similar to working with parents on placement procedures and empowerment, parents' beliefs about mathematics influence children's beliefs about mathematics. Parents with mathematics-related anxiety who are working with their children on mathematics homework will indirectly influence the beliefs and expectations their children will have about mathematics and future careers, and other more proximal activities involving mathematics or science.

School counselors also have a key responsibility to engage girls and minority students in meaningful learning and to work with all students who have a lowered mathematics self-efficacy due to developmental or environmental influences. For example, a common myth is that mathematics is only for those who are already quite good at it. Another myth is that gender, race/ethnicity, and physical ability are critical and insurmountable barriers to doing well in mathematics. These myths can be critiqued and confronted in classroom, group, or individual interventions. Issues of self-efficacy, outcome expectations, and perceived supports and barriers can be directly addressed through classroom guidance and small group activities. School counselors also can address issues of confidence, self-efficacy, and attitudes regarding mathematics success. Moreover, school counselors can provide students with individualized success experiences and role models beginning as early as kindergarten (e.g., bringing in adults who use mathematics in their careers to talk about their work and the courses they took in middle school that were instrumental in their educational and vocational trajectories).

Part of the systemic effort to increase equitable mathematics placement and success must involve the school system and teachers. Teachers and their interaction with students are critical in providing equitable opportunity, access, and unbiased feedback for all students in their courses (Davenport, 1994). School counselors can provide direct service to teachers in helping them examine their interactions with students. In addition, counselors can support the infusion of exploratory activities in mathematics for all K-12 courses. School counselors can help students, teachers, and the larger school system to examine their inadvertent and perhaps even unrecognized biases by facilitating a balance between higher mathematics expectations for all students and a limited focus on providing the highest level of mathematics courses for only the brightest (Peterson, 1993). This may include an examination of the validity of mathematics placement criteria or the quality of advising. School counselors also must develop support systems (e.g., tutoring, mentoring, field visits) in order that all students can achieve success. advocating for higher placement and engaging parents in the process is incomplete if school counselors do not also systematically support mathematics teachers and promote student success in the higher-level placements.

CONCLUSION

These types of systemic interventions for mathematics course placement and mathematics success in sixth grade are but a subset of the programmatic efforts to promote an optimal transition to middle school. The transition from elementary school to middle school is more than a single event through which students pass. Rather, it is an ongoing process through which students navigate academic, organizational, and social processes toward high school and beyond. Therefore, it becomes important for school counselors to consider all aspects of this transition, in particular, its impact on students' educational trajectories. The authors of this article examined parent perceptions of students' sixth-grade mathematics placement within the larger context of the middle school transition, and its potential effect on the mathematics trajectory. Because these decisions have long-lasting and instrumental consequences, the role of the school counselor in this process is critical in ensuring the positive and productive participation of parents/guardians and teachers.

References

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Dr. Patrick Akos is an assistant professor at the University of North Carolina at Chapel Hill. E-mail: [e-mail]

Dr. Marie Shoffner is an associate professor at the University of Virginia, Charlottesville.

Dr. Mark Ellis is an assistant professor at California State University, Fullerton.

Table 1. Fifth- and Sixth-Grade Parents' Perceptions of Mathematics
Placement Criteria

Question                   Fifth-Grade Parents     Sixth-Grade Parents

(a) Do you know how        Yes, 40%                Yes, 58%
your child's sixth-grade   No, 60%                 No, 42%
mathematics placement
is determined?

(b) What is your role in   Don't know/             Don't know/
your child's sixth-grade   no role, 38%            no role, 55%
mathematics placement? *   Support child, 21%      Support child, 23%
                           Discuss with            Discuss with
                           school staff, 28%       school staff, 25%
                           Advocate for            Advocate for
                           placement, 19%          placement, 15%

(c) Should students in     Strongly agree, 47%     Strongly agree, 45%
the sixth grade be         Agree, 47%              Agree, 32%
separated into mathe-      No opinion, 4%          No opinion, 3%
matics classes based       Disagree, 0%            Disagree, 15%
on their abilities?        Strongly disagree, 2%   Strongly
                                                   disagree, 5%

(d) How important is       Very important, 2%      Very important, 33%
your child's sixth-grade   Important, 6%           Important, 25%
mathematics placement      Somewhat important,     Somewhat important,
in relation to fixture     39%                     27%
academic courses in        Not important, 51%      Not important, 10%
college?                   No opinion, 2%          No opinion, 5%

* Percentages equal over 100% due to multiple responses from parents.