Organizational Decision Making

https://doi.org/10.1177/0192636517709368

NASSP Bulletin 2017, Vol. 101(2) 77 –89

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Article

Longitudinal Analysis Technique to Assist School Leaders in Making Critical Curriculum and Instruction Decisions for School Improvement

Gary D. Bigham1 and Mark R. Riney1

Abstract To meet the constantly changing needs of schools and diverse learners, educators must frequently monitor student learning, revise curricula, and improve instruction. Consequently, it is critical that careful analyses of student performance data are ongoing components of curriculum decision-making processes. The primary purpose of this study is to demonstrate the application of panel study longitudinal analysis techniques to inform curricula and instructional improvement efforts using actual data retrieved from state accountability reports of a Texas school district.

Keywords longitudinal panel analysis, school leadership, curriculum and instruction, summative student assessment, data-driven decision making

The 1983 publication of A Nation at Risk report by the National Commission on Excellence in Education became a catalyst for closer public scrutiny of American schools, standards-based testing, and increased accountabilities for education in gen- eral. Nineteen years later, the No Child Left Behind Act increased accountability mea- sures and federal control of K-12 education. For instance, the No Child Left Behind Act resulted in substantial changes nationally on school accountability systems by

1West Texas A&M University, Texas, USA.

Corresponding Author: Gary D. Bigham, P.O. Box 60208, Canyon, TX 79016-0001, USA. Email: [email protected]

709368 BULXXX10.1177/0192636517709368NASSP BulletinBigham and Riney research-article2017

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mandating student performance assessments and accountability measures at individ- ual school levels (Groen, 2012; Hunt, 2008).

Similarly, the recent Every Student Succeeds Act requires states to assess stu- dents annually to continue accountability measures. Consequently, school dis- tricts are under considerable pressure to increase student learning as measured on state-mandated standardized tests, and school administrators must assiduously analyze longitudinal and current student performance data to inform collabora- tive decision making processes about how to improve curricula and classroom instruction to foster student learning and to meet changing needs of diverse stu- dent populations (Darling-Hammond, Ramos-Beban, Altamirano, & Hyler, 2016; Fullan, 2016).

Background

To enhance the reality and applicability of the longitudinal analysis technique demon- strated, data were collected from publicly accessible state reports for a small, rural, early childhood through 12th-grade Texas public school district. The school district’s total student enrolment ranged from 370 to 431 with an average enrolment of 393.6 over the 10-year period from which data were collected. Although the data in Table 1 were restricted to state-assessed reading scores, they provide a sense of the high levels of success the school district had experienced with its student population over the decade covered by this study. However, the aggregate longitudinal performance of four graduating classes grouped as panels and tracked by class from Grades 3 through 9, resulted in an unfavorable trend line in overall reading performance as measured by the state-mandated standardized reading assessment.

Table 1. Percentage of Students Meeting Minimum State-Standardized Reading Performance Standard From Year 1 to Year 10.

Year

Elementary grades Middle school grades High school

3 4 5 6 7 8 9

1 93 100 90 100 100 100 96 2 91 97 96 88 100 100 100 3 94 92 100 100 93 100 100 4 100 97 88 100 100 100 100 5 96 100 100 96 100 100 100 6 100 82 95 94 86 100 95 7 100 95 89 100 96 100 100 8 90 81 95 100 100 96 95 9 100 76 78 86 100 91 93 10 80 96 84 89 81 96 83

Note. The brackets group the four graduating classes as each progressed from grade 3 to grade 9. Bold face and lighter bold face are used only to facilitate ease of comparison of the individual classes for the reader as they progressed from grade to grade.

Bigham and Riney 79

Problem

Public schools are data-rich institutions; yet thorough analysis of available data may be lacking in many cases. This is not to suggest that school leaders do not analyze student achievement data in making curricula and instruction decisions, but full sched- ules with endless task lists and limited time may prevent many school leaders from engaging in data analysis extending beyond previous- and current-year information that is listed on most state and federal accountability reports. In this era of high-stakes accountability, school effectiveness is mostly measured by the aggregate student per- formance on state-mandated standardized exams by class at the campus level and by both class and campus at the district level. In the school from which the data for this study were obtained, reading achievement measured via state-wide assessments increased slightly as students transitioned from elementary to middle school and then dropped noticeably as students transitioned from middle school to high school.

Purpose

The purpose of this study was to demonstrate a panel study longitudinal data analysis technique as applied to student test scores aggregated by class and campus as obtained from state accountability reports. Since the stated purpose was to demonstrate a data analysis technique, we opted to use data reported on accountability reports accessible by the public on the state education agency’s website with whom the school district was associated. To avoid potential violations of institutional review board policies and procedures, no attempt was made to contact the school district. A fictitious data set could have been used to fulfil this article’s purpose; however, because the focus was on the demonstration of a technique, the use of data from an actual school was employed to add practical reality to the method demonstrated. The technique reported is applicable to any school district with historical student achievement data and should facilitate campus- or district-level decision making with respect to curricula and instruction. The information yielded by this type of analysis is valuable to school lead- ers in making mission-critical decisions and the technique demonstrated can be con- ducted by most practitioners with minimal data analysis expertise.

Research Hypotheses

Through trend analyses of 10-year reading performance data obtained from the school district’s state accountability reports, mean student passing percentage scores were computed for four graduating classes by grade level and by campus. The calculated data were analyzed to answer the following question: Is the drop in aggregate test scores from middle school to high school significant enough to constitute examination of cur- ricula and methods of instruction employed in the high school and if so, what possible factors should be taken into consideration before implementing changes? Considering the case study parameters, (i.e., a single school district and the ex post facto nature of the data collected), the answer to the question was sought through hypothesis testing by comparing student reading achievement, aggregated by campus, among the three

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campuses within the same school district. While acknowledging obvious extraneous variables, the single distinguishing variable isolated among the three campuses was the transition of students from elementary to middle school and from middle school to high school. The research question was therefore addressed through the testing of the null hypotheses, from 10-year data compilations that read as follows:

Hypothesis 1: The transition of four graduating classes from elementary to middle school demonstrates no significant relationship to student performance on the state- mandated standardized reading assessment, tracked by class and aggregated by campus. Hypothesis 2: The transition of four graduating classes from middle school to high school demonstrates no significant relationship to student performance on the state- mandated standardized reading assessment, tracked by class and aggregated by campus.

Review of Literature

In many respects, reading is the foundation of school learning, and students’ levels of academic success are significantly determined by their reading abilities. Consequently, it is not surprising that most elementary schools devote substantial instructional time to reading in early elementary grades to address complexities of reading processes and key components of reading such as phonemic awareness, phonics, vocabulary, flu- ency, and comprehension (National Reading Panel, 2000). Also, many school districts allocate considerable resources for intervention programs to ensure that struggling readers are provided opportunities in the early elementary grades to improve their reading (Roskos & Neuman, 2014).

However, reading instruction is not only part of school curricula in early elemen- tary grades but also is a key component of language development for students through- out their years of schooling. For instance, in elementary, middle school, and secondary grades, teachers should instruct students on comprehension strategies, such as making inferences (Hansen & Hubbard, 1984; Pearson, Raphael, Benson & Madda, 2007), identifying salient information (Pressley, 2000), and summarizing and mapping (Graves, 2006; Graves, August, & Mancilla-Martinez, 2013), to develop students’ abilities to become strategic readers. Furthermore, it is important that content area teachers teach students content-specific reading strategies to improve their reading comprehension and to foster critical thinking and development of higher levels of lit- eracy (Hapgood & Palincsar, 2006; McKeown, Beck, & Blake, 2009; Ness, 2007; Shanahan & Shanahan, 2017). Equally important, instruction in academic vocabulary development and word-learning strategies improve students’ reading comprehension and increase literacy development at all grade levels (Graves et al., 2013; Neuman & Wright, 2013).

Another way to improve students’ reading abilities is through writing instruction. Reading and writing have reciprocal functions in that students’ understanding of texts increases when they write analytically about what they read (Gomez & Gomez,

Bigham and Riney 81

2007). Conversely, close analytical readings of essays provide students with exam- ples of types of compositions they are expected to produce in addition to critical reading and logical writing activities in content areas help students develop concep- tual knowledge of academic disciplines they study (Adams, 2011; McConachie et al., 2006).

Method

Research Design

The descriptive research design was employed in this study and is appropriate for school leaders to use in their data analysis procedures when the objective is limited to describing educational phenomena (Gall, Gall, & Borg, 2003, p. 290), such as tracking aggregate class performance on state-mandated standardized exams. Moreover, the descriptive research design is instrumental in providing answers to questions about relationships among variables (Best & Kahn, 2006, p. 133). Since this study endeavored to determine the relationship between student classes transi- tioning from campus to campus (the independent variable) and aggregated student class performance on the state-mandated standardized reading assessment (the dependent variable), longitudinal tracking was conducted by class and aggregated by campus.

Because the collected data consisted of historical student performance on state- mandated standardized reading assessments as reported on state accountability reports over a 10-year period of time, the longitudinal study methodology—a deri- vation of the descriptive research design—was designated as the most appropriate method for this study. Pursuant to the direction of Gall et al. (2003), aggregate class- level student achievement data were collected from publicly accessible annual accountability reports.

Longitudinal research designs from which to choose include trend, cohort, panel, and cross-sectional approaches. Considering the data collected, the panel methodol- ogy was most appropriate for this study. Whereas a panel study in its truest form is designed to focus on individuals within the preselected samples, due to the impor- tance placed on class- and campus-level performance by state and federal account- ability systems, the individual classes selected for analysis were operationally defined as the “individuals.” Thus, no effort was made to actually track individual students within the selected graduating classes. In taking this approach, it must be acknowl- edged that individual students within the tracked graduating classes change as each class gains or loses students across time. While a change of students within the classes will alter outcomes, in most cases, the “base” of each class remains constant. Consequently, this approach remedied concerns of loss of subjects and biased sam- ples addressed by Gall et al. (2003). Furthermore, since standardized examinations were administered annually to all students in designated grade levels as required by state law, the concern of unintended side effects from repeated measures (Gall et al., 2003) ceased to be problematic as well.

82 NASSP Bulletin 101(2)

Population and Sample

The population was defined as aggregate student classes in Grades 3 through 9 on three campuses in the selected school district over a 10-year period. The samples were defined as the four graduating classes of students tracked (diagonally in Table 1) as they progressed from the third to the ninth grade. Thus, with data collection occurring annually at the designated grade levels, the samples remained constant each year (moving down one row and one column to the right in Table 1).

Data Collection

Ten years of state-mandated standardized reading assessment data were extrapolated from the selected school district’s state accountability reports accessible from its state education agency’s Website. The data were reported as the percentage of students meeting the state standard, hereinafter referred to throughout this study as the passing rate. It should be noted that as with any state testing system, state-level changes to the exam over time are common. Although these changes are beyond the control of school leaders, those who wish to employ any longitudinal data analysis techniques do so acknowledging that a change in the exam will alter the results that would have been obtained in the absence of the change. However, all state-mandated reading assess- ments in Texas focused primarily on reading comprehension. Reading performance data, reported as the percentage of students in each class meeting the passing rate, were collected and organized on a spreadsheet in columns by grade level and in rows by year as displayed in Table 1.

Data Analysis

The data analyzed from Table 1 were restricted to the percentage of passing and failing test scores generated by students in the four graduating classes, contained within the brackets and displayed diagonally downward, from Grades 3 through 9. Since these data were obtained from a small school district with small classes ( X equals 31.7 in grade levels and years analyzed as reported in Table 2), the four graduating class data sets were aggregated by grade level and campus to enhance statistical power analysis. This aggregation process is not necessary in large school districts where student enrol- ments are sizable, but in small school settings, aggregation is recommended to enhance statistical findings (Gall et al., 2003). The data aggregated over the 10-year period for the four graduating classes resulted in 887 total state-mandated standardized reading exams completed by students in the classes selected for analysis in this school district as reported in Table 2.

Mean scores were calculated for each grade level reported in Table 1, reflective of percentages of students passing the reading assessments over the measured time periods. Then, campus-level mean scores for the elementary and middle school were calculated by averaging grade-level mean scores for Grades 3 through 5 and Grades 6 through 8, respectively. The high school mean score was computed by simply averaging ninth

Bigham and Riney 83

grade passing percentage scores. These grade- and campus-level mean scores were reported in graphical format in Figure 1 to facilitate the visual identification of evolving trends. The data were combined into a single graph whereby the grade-level scores were plotted linearly and campus-level data were plotted by histogram.

To methodically analyze the findings in a nonbiased fashion, the application of a quantitative data analysis technique was employed. Individual students’ state-man- dated standardized reading assessment results were not available to the researchers; thus, data collection was limited to the combined percentages of students passing the reading assessments as displayed on the school’s state accountability reports and reported in Table 1. This effectively reduced the analysis to two categories of stu- dents—those who passed and those who failed the state-mandated standardized read- ing assessment. Since only passing percentages were reported on the state accountability reports, the need for enrolment data came into play to calculate an estimated number of students tested. These data, also collected from the state accountability reports, are displayed in Table 2.

However, it should be noted that student enrolment per grade level, as indicated on the state accountability reports, did not necessarily represent the exact number of stu- dents who were actually tested in all cases. For example, an enrolled student could have been absent on the day of an assessment. Although this is problematic from a strict academic research perspective, the purpose of this study is to demonstrate these methods to school leaders and not to make generalizations. Therefore, it ceases to be a problem because school leaders have access to their exact enrolment and test partici- pation counts, which should be used in place of the more general and publicly acces- sible enrolment data reported on public documents as used by the authors of this study. Consequently, for demonstration in accordance with the stated purpose of this study,

Table 2. Aggregated Student Enrollment Counts by Year and Grade Level for the Graduating Classes Involved in the Study.

Year

Elementary grades Middle school grades High school

3 4 5 6 7 8 9

1 35 2 28 38 3 39 31 29 4 27 38 29 28 5 31 41 30 36 6 30 39 26 38 7 28 31 24 34 8 28 32 26 9 28 34 10 29 Total 129 138 129 125 121 122 123 Mean 32 35 32 31 30 31 31

84 NASSP Bulletin 101(2)

these calculations included all enrolled students in the frequency counts as test takers. Simple mathematical procedures were used to calculate passing and failing frequency counts by campus. Passing percentage rates were multiplied by the respective student enrolments in the tested grade levels on each campus to determine a total number of students passing the assessments. Then, by subtracting these products from the total enrolment counts, the total number of students failing the assessment per campus was derived.

Based on the categorical assessment results (i.e., passing or failing rates per cam- pus), the chi-square test was used to quantitatively analyze the data. The chi-square was the most appropriate statistical test, because the data being analyzed consisted of fre- quency counts (calculated from percentages) of students passing and failing (catego- ries) the state-mandated reading assessment. As noted by Gravetter and Wallnau (1996),

The chi-square test for goodness of fit uses sample data to test hypotheses about the shape or proportions of a population distribution. The test determines how well the obtained sample proportions fit the population proportions specified by the null hypothesis. (p. 548)

The null hypotheses stated that no relationship would exist between the indepen- dent and dependent variables for the population. For the purposes of these analyses, the independent variables were operationally defined as the classes of students transi- tioning from one campus to another and the dependent variable was student perfor- mance on the state-mandated standardized reading assessment, tracked by class and aggregated by campus.

Figure 1. Ten-year cumulative mean scores by grade level of all students tested in Grades 3 through 10 who met the passing standard established by the state of Texas for reading.

Bigham and Riney 85

Two methods of setting up the chi-square test for goodness of fit are (a) no prefer- ence, where nothing is known about the potential outcome, and all categories are weighted equally; and (b) no difference from a comparison population where informa- tion is known about the probable outcome based on prior knowledge (Gravetter & Wallnau, 1996). Since the null hypotheses stated that the transition of the four graduat- ing classes from one campus to another would demonstrate no significant relationship to student performance on the state-mandated standardized reading assessment, “No Difference From a Comparison Population” was deemed most appropriate for these analyses.

For this panel study, the chi-square calculation requires obtained and expected fre- quencies of students passing and failing from campus to campus. The obtained passing frequencies were calculated by multiplying the mean passing rates per campus (obtained from data displayed in Table 1) by the campus enrolments (obtained from data displayed in Table 2). Next, the products were subtracted from the total campus enrollments to determine failing frequencies. Expected frequencies were calculated by multiplying the passing/failing percentages of the previous campus by the enrollments in the current campus. On deriving obtained and expected frequencies, comparison groups for the “No Difference From a Comparison Population” chi-square tests were established. The elementary served as the comparison population against which the middle school was compared, and the middle school was used as the comparison pop- ulation against which the high school was compared. Hypothesis testing was con- ducted and results are displayed in Table 3.

The obtained passing/failing frequencies ( fo ) for the elementary, middle, and high schools were fo equals 378.50/17.50 for 396 exams; fo equals 355.41/12.59 for 368 exams; and fo equals 114.08/8.92 for 123 exams, respectively. The expected passing/ failing frequencies ( fe ) were fe equals 351.73/16.27 for the middle school and fe equals 118.79/4.21 for the high school. The .05 alpha was used for the level of signifi- cance, and with only two categories—passing and failing—the degrees of freedom (df) was 1. For df equals 1 and α equals .05, the critical chi-square χ2

crit is 3.84 (Gravetter & Wallnau, 1996).

Results

The findings were organized, as described in the methodology section, by presenting raw test score data presented graphically to facilitate the visual identification of evolv- ing trends. The data were combined into a single graph, whereby the grade-level scores were plotted linearly, and campus-level data were plotted by histogram.

A grade-level examination of the data, depicted in the linear graph in Figure 1, revealed a “seesaw” effect beginning in Grade 3 and ending in Grade 9. The linear graph peaked at the sixth grade and plummeted going into high school. The campus- level examination of the data, depicted by the histogram bars also in Figure 1, revealed a 1% student performance increase from elementary (95.58 for Grades 3 through 5), to middle school (96.58 for Grades 6 through 8). Later, student performance decreased 3.83 percentage points as students moved from middle school to high school (Grade 9).

86 NASSP Bulletin 101(2)

As described in the Method section, the chi-square test for goodness of fit was used to determine the significance of the differences observed in the campus mean scores. Setting up the chi-square test in accordance with the “No Difference From a Comparison Population” method, resulted in the testing of two hypotheses. The first null hypothesis indicated no significant difference from the elementary score to the middle school score where the elementary score served as the comparison population for determining the probable outcome of the middle school score. Similarly, the sec- ond null hypothesis indicated no significant difference from the middle school score to the high school score with the middle school score being employed as the comparison population for determining the probable outcome of the high school score. With only two categories of analysis—passing and failing—the df equaled 1 and with the alpha level set at .05, the critical chi-square was 3.84. The chi-square test results are reported in Table 3.

Where the calculated chi-square was 0.871, pursuant to standard hypothesis-testing practices, the decision was to fail to reject the first null hypothesis, indicating no sig- nificant difference from the elementary score to the middle school score. However, where the calculated chi-square was 5.455 in testing the second null hypothesis, the decision was to reject it, indicating a significant difference from the middle school score to the high school score.

Discussion

The primary purpose of longitudinal trend analysis is to provide school leaders with a viable tool of analysis of standardized test results over an extended period of time. The research question posed at the outset of this study read: Is the drop in aggregate test scores from middle school to high school significant enough to constitute examination of curricula and methods of instruction employed in the high school and if so, what possible factors should be taken into consideration before implementing changes? In

Table 3. Chi-Square Results in Testing the Goodness-of-Fit Using the “No Difference From a Comparison Population” Methodology Applied to 10 Years of Compiled Panel Data for Four Graduating Classes.

Campus No. of exams

fo fe

χ2Passing Failing Passing Failing

Elementary 396 .9558 (396) .0442 (396) N/A N/A N/A 378.50 17.50 378.50 17.50

Middle school 368 .9658 (368) .0342 (368) .9558 (368) .0442 (368) 0.871 355.41 12.59 351.73 16.27

High school 123 .9275 (123) .0725 (123) .9658 (123) .0342 (123) 5.455* 114.08 8.92 118.79 4.21

Total 887 847.99 39.01 849.02 37.98

*p < .05.

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lieu of the statistically significant drop in reading achievement found in the transition from middle school to high school, school leaders should target high school literacy– related curricula for reexamination as part of ongoing school improvement as advo- cated by Fullan (2016).

For instance, school leaders may want to determine whether teachers are taking time to teach students academic vocabulary/word-learning strategies, general read- ing strategies (e.g., prereading strategies), and content-specific reading strategies to increase students’ reading comprehension and conceptual understanding of con- tent-related themes (Graves, 2006; Hapgood & Palincsar, 2006; McKeown et al., 2009; Shanahan & Shanahan, 2008). Equally important, school leaders may decide to study how much and what types of writing are actually taught across school cur- ricula because focused writing instruction, such as teaching students how to sum- marize and to write analytically about key concepts, not only fosters literacy development but also increases students’ conceptual understanding of content area themes (Graves et al., 2013; Unrau, 2008). In addition, school leaders may need to determine if high school teachers require more staff development about efficacious content area–reading and writing- strategies and learning activities. Some high school content area teachers may be reluctant to emphasize reading and writing instruction in lessons if they do not believe they have adequate knowledge and skills to do so.

In brief, longitudinal panel analysis provides school leaders with a valuable and viable method of identifying key trends in student performance on state-mandated standardized exams, and in the case of this longitudinal panel analysis, school leaders may want to use data about the decline in state-mandated standardized test scores in reading comprehension in the transition from middle to high school initially to reex- amine emphases on literacy development at the high school level to determine possi- ble reasons for the decrease of student performance and to improve curricula and instruction to foster students’ language development. Because we live in an era of increased federal and state-mandated accountabilities as initiated by the No Child Left Behind Act and more recently continued by the Every Child Succeeds Act (Groen, 2012), school leaders are under substantial pressure to improve students’ levels of achievement on state-mandated tests, and the employment of longitudinal trend analy- sis is one way school leaders can monitor students’ academic progress to identify areas of strengths and weaknesses in school curricula and instruction for ongoing school renewal.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

88 NASSP Bulletin 101(2)

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Author Biographies

Gary D. Bigham is the program chair of educational leadership at West Texas A&M University. During his career in education, he has served in the positions of secondary teacher, principal, and superintendent in Texas public schools and adjunct, assistant, and associate professor in higher education.

Mark R. Riney is the program chair of curriculum and instruction at West Texas A&M University. He is a former English/language arts teacher, who currently teaches courses in cur- riculum theory and analysis, curriculum history, and multicultural education.