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Diving into Students' Transcripts: High School Course-Taking Sequences and Postsecondary Outcomes

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Title: Diving into Students' Transcripts: High School Course-Taking Sequences and Postsecondary Outcomes
Language: English
Authors: Burhan Ogut (ORCID 0000-0003-1729-1396), Ruhan Circi (ORCID 0000-0003-3854-1796)
Source: Grantee Submission. 2023.
Peer Reviewed: Y
Page Count: 29
Publication Date: 2023
Sponsoring Agency: Institute of Education Sciences (ED)
Contract Number: R305A190073
Document Type: Reports - Research
Education Level: High Schools
Secondary Education
Higher Education
Postsecondary Education
Descriptors: High School Students, Course Selection (Students), Correlation, College Attendance, Mathematics Education, English, Language Arts, Science Education, Student Records, Classification, Student Characteristics
DOI: 10.1111/emip.12554
Abstract: The purpose of this study was to explore high school course-taking sequences and their relationship to college enrollment. Specifically, we implemented sequence analysis to discover common course-taking trajectories in math, science, and English language arts using high school transcript data from a recent nationally representative survey. Through sequence clustering, we reduced the complexity of the sequences and examined representative course-taking sequences. Classification tree, random forests, and multinomial logistic regression analyses were used to explore the relationship between the course sequences students complete and their postsecondary outcomes. Results showed that distinct representative course-taking sequences can be identified for all students as well as student subgroups. More advanced and complex course-taking sequences were associated with postsecondary enrollment. [This paper was published in "Educational Measurement: Issues and Practice" v42 n2 2023.]
Abstractor: As Provided
IES Funded: Yes
Entry Date: 2024
Accession Number: ED653225
Database: ERIC
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  Value: <anid>AN0164231921;ems01jun.23;2023Jun13.07:39;v2.2.500</anid> <title id="AN0164231921-1">Diving Into Students' Transcripts: High School Course‐Taking Sequences and Postsecondary Enrollment </title> <p>The purpose of this study was to explore high school course‐taking sequences and their relationship to college enrollment. Specifically, we implemented sequence analysis to discover common course‐taking trajectories in math, science, and English language arts using high school transcript data from a recent nationally representative survey. Through sequence clustering, we reduced the complexity of the sequences and examined representative course‐taking sequences. Classification tree, random forests, and multinomial logistic regression analyses were used to explore the relationship between the course sequences students complete and their postsecondary outcomes. Results showed that distinct representative course‐taking sequences can be identified for all students as well as student subgroups. More advanced and complex course‐taking sequences were associated with postsecondary enrollment.</p> <p>Keywords: clustering; high school course‐taking; postsecondary enrollment; sequence analysis; transcript data</p> <p>A student's academic preparedness in high school has a profound impact on life after graduation. Students who have taken rigorous courses and completed a higher intensity of high school coursework are more likely to obtain high scores on tests, continue postsecondary education, and enroll in selective colleges than other students (Adelman, [<reflink idref="bib3" id="ref1">3</reflink>]; Attewell & Domina, [<reflink idref="bib4" id="ref2">4</reflink>]; Byun et al., 2015; Long et al., [<reflink idref="bib20" id="ref3">20</reflink>]). However, studies of student course‐taking sequences and how course‐taking sequences relate to postsecondary outcomes are relatively rare. Studies that have examined course‐taking sequences have suffered from several weaknesses, including a failure to classify the high number of course‐taking sequences into meaningful groups (Bozick & Ingels, [<reflink idref="bib8" id="ref4">8</reflink>]), a focus only on math course‐taking (Bastedo & Jaquette, [<reflink idref="bib5" id="ref5">5</reflink>]), and a reliance on outdated data.</p> <p>This study leverages developments in data mining and machine learning to uncover patterns in high school course‐taking. We built upon prior course‐taking sequence literature by focusing on three major academic subjects (math, science, and English language arts [ELA]), exploring the transitions between courses within‐subjects and clustering course‐taking sequences into smaller groups. For cluster interpretation, we considered the representative sequences within each cluster. With this approach, we find course‐taking patterns that are informative and easy to use in subsequent analyses. We employ these course‐taking patterns to explore how math, science, and ELA course‐taking relates to postsecondary success.</p> <hd id="AN0164231921-2">Literature Review</hd> <p>Course‐taking has received much attention at the policy level and among researchers. Prior literature on course‐taking has focused on the highest course taken in math, examined advanced course‐taking (e.g., Advanced Placement [AP] courses), and used indices to capture the rigor of high school coursework (Adelman, [<reflink idref="bib3" id="ref6">3</reflink>]). Only a few studies have examined course‐taking sequences, and, in general, they resulted in a high number of sequences. Schiller and Hunt ([<reflink idref="bib24" id="ref7">24</reflink>]) examined math course‐taking sequences for a nationally representative sample of students who started eighth grade in 1988 and participated in the National Education Longitudinal Study of 1988 (NELS:88). They found 1,278 combinations of math courses from students' high school transcripts, with the most frequent pattern (Algebra I‐geometry‐Algebra II‐no mathematics) representing only 5.8% of the sample. Using data from a later cohort of nationally representative students who started 10th grade in 2002 and took part in the Education Longitudinal Study of 2002–2006 (ELS:2002), Bozick and Ingels ([<reflink idref="bib8" id="ref8">8</reflink>]) identified 180 different math course‐taking sequences. Among those, the Algebra II‐no mathematics combination (i.e., no math course after Algebra II) was the most popular course‐taking sequence, representing 13% of the students in the ELS:2002 sample, followed by geometry‐geometry/no mathematics (combination of two sequences; geometry‐geometry and geometry‐no math where geometry is not followed by any course) (8%), Algebra II‐precalculus (7%), Algebra II‐Algebra II/trigonometry (6%), and precalculus‐AP/International Baccalaureate (IB) calculus (6%).</p> <p>Studies using data from individual states also resulted in a large number of sequences. Using data from California, Finkelstein et al. ([<reflink idref="bib11" id="ref9">11</reflink>]) investigated mathematics course‐taking sequences of students who were in Grade 7 in the 2004–2005 school year and followed them until they were in Grade 12. There were, again, many course‐taking sequences, and the 20 most common patterns represented 31% of the overall sample. The most common sequence was taking Algebra I in eighth grade, followed by geometry, Intermediate Algebra/Algebra II, precalculus, and calculus, yet it represented only 3.3% of the sample. The large number of sequences identified in these studies points to the need to apply reduction techniques to represent the sequences in a more consolidated way and examination of representative sequences by student groups.</p> <p>A few studies attempted to classify course‐taking sequences. For example, Stevenson et al. ([<reflink idref="bib25" id="ref10">25</reflink>]) classified math and science course‐taking sequences of NELS:88 students using observed patterns in the data along with patterns identified by national experts and came up with three sequences. In math, sequences are classified into (<reflink idref="bib1" id="ref11">1</reflink>) Algebra I and geometry or other mathematics, including trigonometry and calculus; (<reflink idref="bib2" id="ref12">2</reflink>) Algebra II or geometry, but not both nor any other higher mathematics; and (<reflink idref="bib3" id="ref13">3</reflink>) neither Algebra II nor geometry. In science, sequences are grouped into three: (<reflink idref="bib1" id="ref14">1</reflink>) chemistry or physics; (<reflink idref="bib2" id="ref15">2</reflink>) biology and additional sciences, but not chemistry or physics; and (<reflink idref="bib3" id="ref16">3</reflink>) only biology or no other science courses.</p> <p>In addition to identifying course‐taking sequences, some studies also examined the relationship between course sequences and academic performance. For example, Lee et al. ([<reflink idref="bib19" id="ref17">19</reflink>]) used eight mathematics course‐taking patterns they identified in the NELS:88 and showed that increasing levels in the difficulty of the courses taken were correlated with academic achievement in mathematics. Similarly, Bozick and Ingels ([<reflink idref="bib8" id="ref18">8</reflink>]) found that the largest overall gains in Grade 12 mathematics achievement from Grade 10 were observed in students who took precalculus paired with another course during the last 2 years of high school.</p> <hd id="AN0164231921-3">Current Study</hd> <p>This study uses nationally representative data collected by the High School Longitudinal Study of 2009 (HSLS:09) and applies data‐mining and machine‐learning approaches to examine course‐taking sequences, identify patterns, and explore how course‐taking patterns relate to postsecondary enrollment. We make four contributions to the literature on course‐taking sequences. First, we use the most recent national survey that collected transcript data. Second, we examine course‐taking in three core academic subjects; math, science, and ELA. Third, we identify representative sequences through dimension reduction and cluster analyses to create clusters of students with similar coursework sequences. Finally, we explore the relationship between course‐taking clusters and postsecondary outcomes using decision trees and multinomial logistic regression analyses. Specifically, this study addresses the following research questions:</p> <p></p> <ulist> <item> What are the course‐taking sequences over Grades 9–12 and their characteristics in math, science, and ELA?</item> <p></p> <item> What are the representative course‐taking sequences? Do they differ across student groups? What are the characteristics of students within course‐taking cluster?</item> <p></p> <item> Are course‐taking sequence clusters in high school associated with postsecondary enrollment?</item> </ulist> <hd id="AN0164231921-4">Methods</hd> <p></p> <hd id="AN0164231921-5">Data</hd> <p>The data for this study were drawn from HSLS:09, a nationally representative, longitudinal study of students who were in the ninth grade in 2009. The HSLS:09 collects information on students' trajectories from the beginning of high school into postsecondary education and beyond. It surveyed students, their parents, mathematics and science teachers, school administrators, and school counselors. Baseline data were collected in the fall of Grade 9. The transcript data were collected from the schools in 2013 after most students had completed high school. The students were surveyed again in 2016, 2 years after high school graduation, to learn about their educational and occupational experiences postgraduation (Ingels et al., [<reflink idref="bib18" id="ref19">18</reflink>]).</p> <p>Transcripts included detailed information on the courses taken, credits received, and grades. Courses were classified using school codes for the exchange of data (SCED), a common classification system for prior‐to‐secondary and secondary courses. For each subject, using the SCED courses we further classified courses into meaningful categories that preserve the students' course‐taking experiences and prevent sparse data for further analyses (see supplemental materials for more information on the processing of transcript data and recoding of the course codes). For mathematics, we created 12 Math Course categories using 67 unique SCED codes—ranging from Basic Math to AP/IB Calculus following the classification created by HSLS:09. Science courses were classified based on the subject and level of the course. Seventy‐four unique SCED values in science were sorted into 12‐course categories. The 55 distinct ELA codes were narrowed down to 15 categories. We defined course‐taking as enrolling in a class and receiving any credits toward graduation. The analysis sample included students who have complete transcript information from Grades 9 to 12 and participated in the base and second data collections (<emph>N</emph> ≈ 15,140).</p> <p>For predictive analyses, we used the first postsecondary institution enrolled after high school as the outcome. Selectivity of colleges enrolled was included in HSLS:09 data and measured by the Integrated Postsecondary Education Data System (less than 2 years; 2 years; 4 years, selectivity not classified; 4 years, inclusive; 4 years, moderately selective; and 4 years, highly selective). We combine less than 2 years and 2‐year college enrollment into a single category and differentiate between moderately and highly selective colleges versus the others for 4‐year colleges. This resulted in an enrollment outcome with four ordinal categories: no college; 2 years or less; 4 years, not selective; and 4 years, selective.</p> <hd id="AN0164231921-6">Analysis</hd> <p></p> <hd id="AN0164231921-7">Course‐taking sequences</hd> <p>Sequence analysis has two main steps: (<reflink idref="bib1" id="ref20">1</reflink>) extracting the sequences from the data, and (<reflink idref="bib2" id="ref21">2</reflink>) computing similarities between the sequences and analyzing sequences via clustering. Two types of sequence analysis exist in the literature: state sequences and event sequences. State sequences represent activities that happen within a specific period, such as going to school for a particular time and a student stays in this state until they graduate. Event sequences, conversely, link an activity with a certain time point and represent transitions from one event to another, such as graduating from high school at a specific time and transition to workforce (Abbot & Tsay, [<reflink idref="bib2" id="ref22">2</reflink>]; Gabadinho et al., [<reflink idref="bib13" id="ref23">13</reflink>]). Shortly, states last while events happen at a specific time, event can define entry and exit points for states (e.g., entering school at a specific time and graduating at a specific time forms a state of being at school). For our purposes, we treat coursework in high school as state sequences that are characterized by the courses taken in a school year in order. We create course‐taking sequences within each subject (math, science, and ELA) using all the courses students have taken in those subjects in high school.</p> <p>Transcript data include information from different academic‐year divisions (e.g., trimester, semester). To standardize course‐taking across these divisions, we aggregated course‐taking at the school‐year level by combining the courses in the same subject matter (e.g., math) within a given school year. For example, if a student was in a school using trimesters and took Algebra I in all three trimesters in Grade 9, then that student's sequence would start with Algebra I instead of Algebra I‐Algebra I‐Algebra I. If the student took Algebra I in two trimesters, the student would also have Algebra I as the first course in their sequence, and not Algebra I‐Algebra I. The order of sequences was created based on when the course information appears on the student's transcript (i.e., Grade 9 fall semester).</p> <p>We used the TraMineR R package (Gabadinho et al., [<reflink idref="bib14" id="ref24">14</reflink>]) to create the course‐taking sequences, the characteristics of the sequences, and measures of sequence diversity. Given that many sequences exist within each subject, we used multiple measures to fully describe the sequences. Basic measures include the length of the sequence and the number of distinct courses. More advanced measures of course‐taking diversity (i.e., the variety of courses taken within a subject) include within‐sequence entropy, turbulence, and complexity (Ritschard, [<reflink idref="bib22" id="ref25">22</reflink>]).</p> <p>Within‐sequence entropy and turbulence reflect sequence diversity, with higher values indicating more diverse course‐taking sequence. The proportion of time allocated to each course state throughout high school and the number of distinct course states that a student took drive the value of entropy. The entropy is zero when the sequence includes only one course and one when sequence includes all possible courses. The turbulence index is defined as the number of distinct partial sequences (i.e., geometry‐Algebra II in Algebra I‐geometry‐Algebra II). Turbulence is a measure of variability in relation to distinct courses, the order of these courses, and the variance of the durations of these courses throughout the high school. A high turbulence value indicates that the number of courses and transitions across courses varies within a sequence. The complexity index is a composite measure that depends on the number of transitions within a sequence and entropy of the sequence. A value of 0 on the complexity index indicates a complete similarity of courses and that no transitions occurred between courses, while a value of 1 indicates a high number of transitions between courses. The formulas for these indices are provided in the supplemental materials.</p> <hd id="AN0164231921-8">Patterns of course‐taking sequences</hd> <p>When we work with the data from a large number of students, many sequences are not easy to interpret. To address this problem, we used sequence clustering techniques to identify groups of students with similar course‐taking sequences within each subject. Two sequences are alike when parts of the sequences overlap (e.g., Algebra I‐geometry‐Algebra II versus Algebra I‐geometry‐Algebra II‐trigonometry). Different measures can be used to quantify the similarity and dissimilarity among sequences. In general, dissimilarity measures for sequences can be classified into three categories based on (a) the course‐taking distribution; (b) the frequency of common courses; and (c) the edit distance, which is the minimum cost of transforming one sequence to the other sequence with substitution, insertion, or deletion of courses. If there is an "ideal" course‐taking sequence, then distances between sequences can be calculated from students' observed sequence to the ideal sequence. However, because no ideal course‐taking sequence exists, we use optimal matching as the distance matrix for clustering analyses (Bergner et al., [<reflink idref="bib6" id="ref26">6</reflink>]; Ritschard et al., [<reflink idref="bib23" id="ref27">23</reflink>]).</p> <p>One way of describing course‐taking patterns is to identify a "representative" sequence within a given set of sequences (Aassve et al., [<reflink idref="bib1" id="ref28">1</reflink>]; Gabadinho & Ritschard, [<reflink idref="bib12" id="ref29">12</reflink>]). Specifically, Aassve et al. ([<reflink idref="bib1" id="ref30">1</reflink>]) proposed to take the medoid of the cluster (i.e., the sequence that is the nearest to the virtual center of the cluster) as the representative sequence, while Gabadinho and Ritschard ([<reflink idref="bib12" id="ref31">12</reflink>]) used a data‐driven method to find a subset of sequence(s) in the cluster that can represent the whole set with a certain accuracy level. To identify the representative course‐taking sequences for a subject and student groups within a subject, we used the optimal matching (OM) edit distance matrix, which measures dissimilarities between all pairs of sequences. OM is designed for discrete sequences and allows for the comparison of sequences that are partly similar but might have slight shifts in order (e.g., Algebra II‐geometry‐trigonometry versus Algebra I‐Algebra II‐geometry‐trigonometry). The medoid of all the sequences within a subject (i.e., the sequence that is the nearest to the virtual center of the cluster) and within a cluster of a specific subject is treated as the sequence that represents the typical course‐taking for that subject.</p> <p>Although identifying representative sequences for each subject helps interpretation, one representative sequence for all available sequences may not be sufficient. To capture the variation in course‐taking sequences across students, we applied clustering techniques within each subject. Specifically, we employ Ward's algorithm that forms clusters by maximizing within‐cluster homogeneity and choose the number of clusters by examining the length of the vertical lines on the dendrogram (a longer vertical line indicates a greater difference between groups) as well as the number of participants within each cluster (to avoid having clusters with a small number of students) and the interpretability of the clusters based on representative sequences. Specifically, we examined the cluster medoids with the number of clusters ranging from 2 to 4 and choose the number of clusters that results in the most interpretable clusters from a practical perspective. Student characteristics were compared across the sequence clusters identified. Multinomial logistic regression was conducted to test the statistical significance of the relationship covariates (i.e., gender, ethnicity, language at home status, disability status, parental education) and the probability of cluster membership.</p> <hd id="AN0164231921-9">Predictive analyses</hd> <p>To examine the relationship between course‐taking sequences and postsecondary enrollment, we used a classification tree to examine visual results, random forests (RF), and multinomial logistic regression (MLR) models.</p> <p>A decision tree is a nonparametric method used for classification. It splits the predictors in such a way that the resulting groups are as different from each other as possible. The final result is a tree that shows the decision splits (i.e., nodes) that are associated with a student outcome. RF is a modeling approach in machine learning for classification based on generating a large number of decision trees on random subsets of predictors and then averaging out their predictions (Breiman, [<reflink idref="bib9" id="ref32">9</reflink>]; Hastie et al., [<reflink idref="bib16" id="ref33">16</reflink>]). We also used a logistic regression model of the form <ephtml> <math display="inline" altimg="urn:x-wiley:07311745:media:emip12554:emip12554-math-0001" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>o</mi><mi>g</mi><mi>i</mi><mi>t</mi><mrow><mo>(</mo><msub><mi>Y</mi><mi>i</mi></msub><mo>)</mo></mrow><mspace width="0.28em" /><mo>=</mo><msup><mi>β</mi><mo>′</mo></msup><mspace width="0.28em" /><msub><mi mathvariant="bold">X</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">$Logit({{Y_i}})\; = {\bf{\beta ^{\prime}}}\;{{\bf{X}}_i}$</annotation></semantics></math> </ephtml> , where <ephtml> <math display="inline" altimg="urn:x-wiley:07311745:media:emip12554:emip12554-math-0002" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><msub><mi mathvariant="bold">X</mi><mi>i</mi></msub><annotation encoding="application/x-tex">${{\bf{X}}_i}$</annotation></semantics></math> </ephtml> is a vector of cluster membership and sequence characteristics, including complexity, turbulence, and entropy, and <emph>Y</emph> is the postsecondary enrollment outcome.</p> <p>We used all the data for classification tree analyses since the purpose is to explore the relationship between course‐taking sequences and postsecondary enrollment. However, we divided our dataset into training and test data (70% and 30%, respectively) for RF and MLR analyses to compare the predictive power of the models on an unseen test data. We used fivefold cross‐validation with hyperparameter tuning (i.e., number of trees and number of variables randomly selected for each split within a tree) for training using RandomForest R package. For predictive analysis, we also fit the MLR model on the training data and assess predictive performance in the test data using course‐taking sequence information as the only predictor. To test whether the predictive power increases with the addition of variables and the relationship between course‐taking sequences and postsecondary enrollment still holds, we also run models with additional variables, including gender, race/ethnicity, high school grade point average, parental education, and family income.</p> <hd id="AN0164231921-10">Results</hd> <p></p> <hd id="AN0164231921-11">Sample</hd> <p>Table 1 displays the characteristics of the sample. It was evenly split between males and females. A little over half of the students were White, followed by Hispanic, Black, and Asian students comprising 22, 13, and 4% of the sample correspondingly. Majority of the students had a parent that has at least high school diploma. In terms of postsecondary enrollment, about 41% of the students enrolled in a nonselective or selective 4‐year college.</p> <p>1 Table Characteristics of the Sample</p> <p> <ephtml> <table><thead><tr><th /><th align="left">Percent</th><th align="left">SE</th></tr></thead><tbody><tr><td>Gender</td><td /><td /></tr><tr><td>Female</td><td>49.6</td><td>.6</td></tr><tr><td>Male</td><td>50.3</td><td>.6</td></tr><tr><td>Ethnicity</td><td /><td /></tr><tr><td>White</td><td>48.8</td><td>.6</td></tr><tr><td>Black</td><td>13.2</td><td>.5</td></tr><tr><td>Hispanic</td><td>21.5</td><td>.6</td></tr><tr><td>Asian</td><td>3.6</td><td>.2</td></tr><tr><td>Indian American</td><td>.6</td><td>.1</td></tr><tr><td>More than one race</td><td>7.4</td><td>.3</td></tr><tr><td>Parent education</td><td /><td /></tr><tr><td>No response</td><td>28.1</td><td>.6</td></tr><tr><td>Less than HS</td><td>7.3</td><td>.4</td></tr><tr><td>HS</td><td>30.6</td><td>.6</td></tr><tr><td>Associate</td><td>11.6</td><td>.4</td></tr><tr><td>Bachelors</td><td>14.7</td><td>.4</td></tr><tr><td>Higher</td><td>7.5</td><td>.3</td></tr><tr><td>College enrollment</td><td /><td /></tr><tr><td>Selective 4 years</td><td>12.1</td><td>.4</td></tr><tr><td>Nonselective 4 years</td><td>29.1</td><td>.5</td></tr><tr><td>Two years</td><td>26.8</td><td>.6</td></tr><tr><td>Less than 2 years</td><td>2.5</td><td>.2</td></tr><tr><td>No college</td><td>28.8</td><td>.6</td></tr></tbody></table> </ephtml> </p> <p>1 <emph>Note</emph>. Sample size is about 15,140. HS refers to high school.</p> <p>2 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <hd id="AN0164231921-12">Course‐Taking Sequences</hd> <p>We find that more than 5,000 unique course‐taking sequences in math exist, and 96.4% of them consist of one to six courses (maximum length is 12). In science, more than 5,000 unique sequences exist, and 97.5 % of them consist of one to six courses (maximum length is 12). In ELA, almost 6,000 distinct sequences exist, and 96.7% of them consist of one to seven courses (maximum length is 14).</p> <p>Figure 1 shows the 10 most frequent sequences and associated frequencies for mathematics, science, and ELA, respectively. Across subjects, the 10 most common sequences account for 22.9%, 18.5%, and 29.7% of all sequences for each subject. The most common sequence in math is Algebra I, geometry, Algebra II, and precalculus (Figure 1, the sequence at the very bottom) a change from Bozick and Ingels's ([<reflink idref="bib8" id="ref34">8</reflink>]) finding of the Algebra II‐no mathematics combination as the most frequent. The second most common sequence is Algebra I, geometry, and Algebra II. For science, the most common sequence is general biology, general chemistry, and general physics, with a similar percentage to the second most common sequence consisting of physical science, general biology, and general chemistry. For ELA, the most common sequence consists of ELA I, ELA II, ELA III, and ELA IV (The distribution of courses by the order the courses taken within each subject are shown in supplemental materials in Figures A1–A3).</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EMS/01jun23/emip12554-fig-0001.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="emip12554-fig-0001.jpg" title="1 Sequence Frequency Plots. Data source: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009 [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <hd id="AN0164231921-14">Characteristics of Course‐Taking Sequences</hd> <p>Table 2 lists the summary statistics of four sequence measures; the number of course transitions, within‐sequence entropy, turbulence, and complexity across courses. A "course transition" refers to switching from one course to another (e.g., Algebra I to geometry). The number of transitions is zero for students who took only one course. The average number of course transitions is 3.1, 2.6, and 3.4 for mathematics, science, and ELA, respectively.</p> <p>2 Table Characteristics of Course‐Taking Sequences by Subject</p> <p> <ephtml> <table><thead><tr><th>Measure</th><th>Subject</th><th align="left">Median</th><th align="left">Mean</th><th align="left">Max</th></tr></thead><tbody><tr><td>Transitions</td><td>Mathematics</td><td>3.0</td><td>3.1</td><td>18.0</td></tr><tr><td /><td>Science</td><td>3.0</td><td>2.6</td><td>11.0</td></tr><tr><td /><td>English</td><td>3.0</td><td>3.4</td><td>12.0</td></tr><tr><td>Entropy</td><td>Mathematics</td><td>.5</td><td>.5</td><td>.8</td></tr><tr><td /><td>Science</td><td>.4</td><td>.4</td><td>.8</td></tr><tr><td /><td>English</td><td>.5</td><td>.5</td><td>.8</td></tr><tr><td>Turbulence</td><td>Mathematics</td><td>4.9</td><td>4.8</td><td>17.5</td></tr><tr><td /><td>Science</td><td>3.9</td><td>3.6</td><td>11.5</td></tr><tr><td /><td>English</td><td>4.0</td><td>4.3</td><td>12.8</td></tr><tr><td>Complexity</td><td>Mathematics</td><td>.5</td><td>.5</td><td>.9</td></tr><tr><td /><td>Science</td><td>.6</td><td>.6</td><td>.9</td></tr><tr><td /><td>English</td><td>.6</td><td>.6</td><td>.9</td></tr></tbody></table> </ephtml> </p> <p>3 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <p>On average, the measures of complexity and diversity are similar across subjects with a few differences. Science sequences have lower entropy, indicating that students' course‐taking in science is more similar; in contrast, mathematics sequences have high turbulence, indicating higher numbers of subsequences. ELA has the highest complexity, with the most variation of sequences across students' course‐taking sequences.</p> <p>We also examined the sequence characteristics of the courses across several student groups. We found that the average sequence length (number of courses) in mathematics is higher for Asian students, students with higher parental education, and students with a higher interest in mathematics and science. Sequence transition and complexity are lower for Black students and students with lower parental education, indicating that these students likely take only the mandatory courses. Not many differences exist between male and female students. In science, Hispanic students have lower complexity. For ELA, smaller variations exist in terms of the characteristics of the course‐taking sequences.</p> <p>Concerning college enrollment, the complexity of course‐taking in mathematics and science increased with the level of postsecondary enrollment, from no college to 4‐year selective college. (Results for these analyses are provided in supplemental materials in Tables A6–A8.)</p> <hd id="AN0164231921-15">Representative Course‐Taking Sequences</hd> <p>A large number of unique course‐taking sequences within each subject reflects the diversity of individual paths but makes it difficult to draw inferences and identify course‐taking sequences that students typically go through. To remedy that, we identified representative sequence(s) that represent all the sequences within each subject and refer to these sequences as typical sequences. To be representative of all sequences, a typical sequence needs to cover a predefined percentage of sequences within a given subject. Using 30% as the criteria, we found that the typical course‐taking for mathematics is Algebra I, geometry, and Algebra II. For science, two typical sequences exist: (a) general biology and general chemistry, and (b) physical science, general biology, general chemistry, and general physics. For ELA, the typical sequence is represented by two sequences as well: (a) ELA I, ELA II, ELA III, and ELA IV and (b) ELA I, ELA II, and American Literature.</p> <p>In addition to identifying the representative course‐taking sequences for all students, we also examined representative sequences by student subgroups. Results in Table 3 show the subgroups of students whose typical sequences are different from the overall representative sequences described previously. In mathematics, students whose parents have higher degrees of education, students from higher socioeconomic status (SES), and Asian students had typical sequences that include more advanced courses. Similarly, White students, Asian students, and students from higher SES in science, and Asian students and students from higher SES in ELA had typical sequences with more advanced courses.</p> <p>3 Table Typical Course‐Taking Sequences Across Groups</p> <p> <ephtml> <table><thead><tr><th>Subject</th><th>Subgroup</th><th>Typical Sequence</th></tr></thead><tbody><tr><td>Math</td><td>AsianParent education—Graduate degree</td><td>Algebra I‐geometry‐Algebra II‐precalculusGeometry‐Algebra II‐precalculus‐calculus</td></tr><tr><td>SES (higher than 80th percentile)</td><td>Algebra I‐geometry‐Algebra II‐precalculus</td></tr><tr><td>Science</td><td>AsianWhiteSES (higher than 80th percentile)</td><td>General biology‐general chemistry‐general physics</td></tr><tr><td>ELA</td><td>AsianSES (higher than 80th percentile)</td><td>ELA I‐ELA II‐ELA III‐ELA IV‐AP literature</td></tr></tbody></table> </ephtml> </p> <p>4 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <p>To reduce the number of course‐taking sequences without much loss of information, we grouped similar course sequences into clusters. We chose clusters that are most interpretable and parsimonious based on the examination of dendrograms from the hierarchical clustering analysis as described earlier and identify three clusters for math, science, and ELA (Table 4).</p> <p>4 Table Representative Course‐Taking Sequences by Subject</p> <p> <ephtml> <table><thead><tr><th align="left">Subject</th><th>Cluster Name</th><th>Sequence</th><th align="left">Coverage (%)</th></tr></thead><tbody><tr><td align="left">Math</td><td>Conventional</td><td>Algebra I‐geometry‐Algebra II</td><td>32.3</td></tr><tr><td /><td>Advanced</td><td>Algebra I‐geometry‐Algebra II‐precalculus</td><td>33.6</td></tr><tr><td /><td>Alternative</td><td>Other advanced math</td><td>36.3</td></tr><tr><td align="left">Science</td><td>Conventional</td><td>Physical science‐general biology‐general chemistryEarth science‐general biology‐general chemistry</td><td>33.4</td></tr><tr><td /><td>Conventional‐integrated science</td><td>Integrated science‐general biology‐general chemistry</td><td>44.9</td></tr><tr><td /><td>Physics added</td><td>General biology‐general chemistry‐general physics</td><td>57.2</td></tr><tr><td align="left">ELA</td><td>Conventional</td><td>ELA I‐ELA II‐ELA III‐ELA IV</td><td>51</td></tr><tr><td /><td>Variational</td><td>ELA I‐ELA II‐ELA IIIELA I‐ELA II‐American LitELA I‐ELA II‐American Lit‐British LitELA I‐ELA II, ELA IV‐American Lit‐British LitELA I‐ELA II‐ELA III‐ELA IV‐British Lit</td><td>27</td></tr><tr><td /><td>Advanced</td><td>ELA I‐ELA II‐AP Language‐AP literature</td><td>48.1</td></tr></tbody></table> </ephtml> </p> <p>5 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <p>In terms of the number of students in each mathematics cluster, 55.8% of the students belonged to Cluster 1, 39.7% to Cluster 2, and 4.5% to Cluster 3. We named the clusters, examining the courses included in the sequences. In math, 32.2% of the students in the <emph>conventional</emph> cluster had Algebra I, geometry, and Algebra II. The <emph>advanced</emph> cluster (Cluster 2) includes Algebra I, geometry, Algebra II, and precalculus, which portrayed 33.6% of the cluster. The <emph>alternative</emph> cluster (Cluster 3) was characterized by other advanced math courses (e.g., Algebra III, statistics, advanced math, integrated math 3), presumably in addition to other lower level mandatory math courses, that represent 36.3% of the sequences in that cluster.</p> <p>In science, 33.4% of the students in Cluster 1 had taken either physical science‐general biology‐general chemistry or earth science‐general biology‐general chemistry; we referred to this cluster as <emph>conventional</emph>. The representative sequence in Cluster 2 (<emph>conventional‐integrated science</emph>) was integrated science‐general biology‐general chemistry and represented 44.9% of sequences. Students in Cluster 3 (<emph>physics</emph> added) took general biology‐general chemistry‐general physics, and this sequence covers 57.2% of students in that cluster. The percentages of students within each cluster were 68.1% (<emph>conventional</emph>), 15.4% (<emph>conventional‐integrated science</emph>), and 16.5% (<emph>physics added</emph>).</p> <p>The first cluster in ELA had several sequences that cover 27% of students in that sequence, so we referred to it as <emph>variational</emph>. Cluster 2, referred to as <emph>conventional</emph>, includes ELA I‐ELA II‐ELA III‐ELA IV as the representative sequence covering 51% of the students in that sequence. Students in the <emph>advanced</emph> cluster, Cluster 3, were represented by ELA I‐ELA II‐AP Language‐AP literature; this sequence had coverage of 48.1%. The rates of students in these clusters were 35.9%, 53.7%, and 10.4%, respectively.</p> <p>We also examined cluster characteristics in terms of average entropy, turbulence, and complexity (Table 5). In mathematics, the <emph>advanced</emph> cluster had more variation and complexity than the <emph>alternative</emph> cluster, and the <emph>conventional</emph> cluster included moderately complex course‐taking sequences. The <emph>conventional</emph> and <emph>conventional‐integrated science</emph> clusters in science had similar sequence characteristics while <emph>physics added</emph> had slightly more variation and complexity in course‐taking. In ELA, sequences across clusters were similar in entropy and turbulence but <emph>conventional</emph> and <emph>advanced</emph> clusters had slightly more complex sequences.</p> <p>5 Table Characteristics of Representative Clusters by Subject</p> <p> <ephtml> <table><thead><tr><th>Subject</th><th>Variable</th><th>Cluster 1</th><th>Cluster 2</th><th>Cluster 3</th></tr></thead><tbody><tr><td>Math</td><td>Entropy</td><td>.4</td><td>.5</td><td>.2</td></tr><tr><td /><td>Turbulence</td><td>.2</td><td>.3</td><td>.2</td></tr><tr><td /><td>Complexity</td><td>.6</td><td>.7</td><td>.3</td></tr><tr><td>Science</td><td>Entropy</td><td>.4</td><td>.4</td><td>.5</td></tr><tr><td /><td>Turbulence</td><td>.2</td><td>.2</td><td>.3</td></tr><tr><td /><td>Complexity</td><td>.6</td><td>.6</td><td>.7</td></tr><tr><td>ELA</td><td>Entropy</td><td>.5</td><td>.5</td><td>.5</td></tr><tr><td /><td>Turbulence</td><td>.4</td><td>.4</td><td>.4</td></tr><tr><td /><td>Complexity</td><td>.6</td><td>.7</td><td>.7</td></tr></tbody></table> </ephtml> </p> <p>6 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <p>In terms of the overlap between the course‐taking clusters across subjects (Table 6), results showed that more than 70% of students in the mathematics <emph>conventional</emph> and <emph>alternative</emph> clusters and more than half of the students in the mathematics <emph>advanced</emph> cluster were in the <emph>conventional‐integrated science</emph> cluster. About 31% of the students in the mathematics <emph>advanced</emph> cluster were in the <emph>physics added</emph> cluster. More than half of students in the mathematics <emph>alternative</emph> cluster were in the <emph>variational</emph> ELA cluster, and 42% of students in the mathematics <emph>conventional</emph> cluster were in the <emph>conventional‐integrated science</emph> and <emph>conventional</emph> ELA clusters.</p> <p>6 Table Overlap between Course Sequence Clusters</p> <p> <ephtml> <table><thead><tr><th align="left" /><th /><th align="center">Literature Cluster</th></tr><tr><th align="left">Math Cluster</th><th>Science Cluster</th><th align="left">Advanced</th><th align="left">Conventional</th><th align="left">Variational</th></tr></thead><tbody><tr><td align="left">Advanced</td><td>Conventional</td><td>1.0</td><td>4.2</td><td>4.2</td></tr><tr><td /><td>Conventional‐integrated science</td><td>8.2</td><td>27.9</td><td>24.4</td></tr><tr><td /><td>Physics added</td><td>7.8</td><td>11.3</td><td>11.1</td></tr><tr><td align="left">Alternative</td><td>Conventional</td><td>.6</td><td>4.6</td><td>3.3</td></tr><tr><td /><td>Conventional‐integrated science</td><td>3.1</td><td>22.2</td><td>54.4</td></tr><tr><td /><td>Physics added</td><td>2.9</td><td>2.3</td><td>6.7</td></tr><tr><td align="left">Conventional</td><td>Conventional</td><td>.6</td><td>10.7</td><td>6.5</td></tr><tr><td /><td>Conventional‐integrated science</td><td>2.5</td><td>41.6</td><td>30.2</td></tr><tr><td /><td>Physics added</td><td>1.2</td><td>3.5</td><td>3.2</td></tr></tbody></table> </ephtml> </p> <p>7 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <hd id="AN0164231921-16">Student Profiles by Representative Course‐Taking Sequence Clusters</hd> <p>After finding the clusters for course‐taking sequences, we examined the profiles of students within each cluster (see Tables A9–A11 in supplemental materials). The results showed that, for math, Cluster 1 (<emph>conventional</emph>) was characterized by a lower percentage of female students, lower SES, high percentage of Hispanic students, higher percentages of parental education with high school or less, and low college enrollment rates. Cluster 2 (<emph>advanced</emph>) had higher percentages of female students, Asian students, students with higher SES, students with parental education higher than a bachelor's degree, and higher college enrollment rates. Students in Cluster 2 (<emph>advanced</emph>) had taken precalculus and other advanced courses in addition to those courses that students in Cluster 1 took. Students in Cluster 3 (<emph>alternative</emph>) had a higher percentage of Black students and less complex sequences as well as moderate percentages of college enrollment.</p> <p>In science, <emph>conventional</emph> and <emph>conventional‐integrated science</emph> clusters were similar in terms of gender, SES, and college enrollment but the <emph>conventional‐earth science</emph> cluster had a higher percentage of Hispanic students. In course‐taking, the <emph>conventional‐integrated science</emph> cluster differed from the <emph>conventional</emph> cluster by integrated science. The <emph>physics added</emph> cluster had higher SES levels and college enrollment rates. Students in the <emph>physics added</emph> cluster were differentiated from other clusters by taking general physics, pointing to a potential relationship between general physics and college enrollment and with more complex course sequences.</p> <p>In ELA, the <emph>variational</emph> cluster had the highest percentage of White students, including students at the median SES, and less than half of the students in this cluster were enrolled in 2‐ or 4‐year colleges. More students of color were in the <emph>conventional</emph> cluster, with the lowest SES and lower percentage of enrollment in 4‐year colleges and a higher percentage of enrollment 2‐year colleges. Students in the <emph>advanced</emph> cluster had the highest SES, lower percentages of students of color, and had the highest levels of 4‐year college enrollment at about 70%. Students in the <emph>advanced</emph> cluster had taken advanced courses like AP literature.</p> <hd id="AN0164231921-17">Relationship between Course‐Taking Sequences and Postsecondary Enrollment</hd> <p>To examine the relationship between course‐taking sequences and postsecondary enrollment, we used multinomial logistic regression and classification analysis. Figure 2 displays the decision tree results from the trimmed tree for the relationship between course‐taking clusters in each subject and college enrollment. Each box in the figure is called a "node," and the four decimals in each box are the predicted proportions of students in one of the four categories (the first number is for no college, second is for not‐selective 4‐year college, third is for selective 4‐year college, and fourth is for 2‐year or less college). The name and color of the node are determined by the college enrollment category that has the highest proportion among the four categories. At each node, the outcome on the left is observed when the condition at the node is satisfied (i.e., answering "yes"), and the outcome on the right is observed if the condition is not satisfied.</p> <p> <img src="https://imageserver.ebscohost.com/img/embimages/rdk/EMS/01jun23/emip12554-fig-0002.jpg?ephost1=dGJyMNHX8kSepq84v%2bvlOLCmsE6epq5Srqa4SK6WxWXS" alt="emip12554-fig-0002.jpg" title="2 Classification Tree Results Using Clustering of Course‐Taking Sequences. Data source: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009 [Colour figure can be viewed at wileyonlinelibrary.com]" /> </p> <p></p> <p>Results showed that students who were not in the <emph>advanced</emph> math cluster had a 37% chance of not enrolling in college. If these students also did not have a complex science course‐taking sequence (science complexity <.61), the percentage of students who did not enroll went up to 53. Conversely, if the student was in the <emph>advanced</emph> math cluster and <emph>advanced/physics added</emph> science cluster with high variation in science course‐taking (i.e., entropy >.47), the student had a 52% chance of enrolling in a selective 4‐year college. A student could also get into a selective 4‐year college if they were in <emph>advanced</emph> math and not in <emph>physics added</emph> science but rather in the <emph>advanced</emph> ELA cluster.</p> <p>Students in the <emph>alternative</emph> or <emph>conventional</emph> math cluster had a 31% chance of attending a 2‐year or less college. Those who had high complexity in science course‐taking (complexity ≥.61) had a 33% chance of enrolling in a 4‐year not selective college. If those students were also in <emph>advanced</emph> cluster in literature, then the chances of enrolling in 4‐year selective college increased to more than 50%.</p> <p>Classification trees are easy to interpret and visually appealing because they represent only one tree; however, they might not have high predictive accuracy. To increase the predictive performance, we used RFs. We also conducted MLR analyses to gauge results from RFs.</p> <p>Table 7 shows that the classification performances of both models were similar (overall accuracy is.44 and.45 for RF and MLR, respectively) and can be characterized as moderate. For both models, the accuracy was over.54 for each college enrollment level. We also used the recall metric, the proportion of true positives in each outcome level, to compare the performance of the models. We found recall measures of.58 and.60 for the nonselective category for RF and MLR, respectively. The recall for nonselective 4‐year and 2‐year college or fewer categories was low for both models. The precision index, which measures the number of true positives among the total predicted positives, ranged between.35 and.50 within categories. Finally, the <emph>F</emph>1 index, which provides a balance between recall and precision, ranged between.25 and.51. Examining the low scores on the recall, we see that RF and MLR did not perform well enough to differentiate the nonselective 4‐year college enrollment from other categories using only the information coming from course‐taking trajectories.</p> <p>7 Table Prediction Performance of Models for Test Data</p> <p> <ephtml> <table><thead><tr><th>Category</th><th>Accuracy</th><th>Recall</th><th>Precision</th><th><italic>F</italic>1 score</th></tr></thead><tbody><tr><td>Logistic regression</td></tr><tr><td>Overall</td><td>.45</td><td /><td /><td /></tr><tr><td>No college</td><td>.70</td><td>.59</td><td>.49</td><td>.53</td></tr><tr><td>Not selective 4 years</td><td>.60</td><td>.60</td><td>.44</td><td>.51</td></tr><tr><td>Selective 4 years</td><td>.62</td><td>.32</td><td>.50</td><td>.39</td></tr><tr><td>Two years or less</td><td>.54</td><td>.19</td><td>.35</td><td>.25</td></tr><tr><td>Random forests</td></tr><tr><td>Overall</td><td>.44</td><td /><td /><td /></tr><tr><td>No college</td><td>.68</td><td>.52</td><td>.50</td><td>.51</td></tr><tr><td>Not selective 4 years</td><td>.60</td><td>.58</td><td>.46</td><td>.51</td></tr><tr><td>Selective 4 years</td><td>.62</td><td>.31</td><td>.48</td><td>.37</td></tr><tr><td>Two years or less</td><td>.56</td><td>.30</td><td>.35</td><td>.33</td></tr></tbody></table> </ephtml> </p> <p>8 <emph>Data source</emph>: U.S. Department of Education, National Center for Education Statistics, High School Longitudinal Study of 2009.</p> <p>We repeated the RF and MLR analyses by adding variables, including gender, race/ethnicity, high school grade point average, parental education, and family income to course‐taking sequence information. Results showed that accuracy increases for MLR and RF to.53 and.52, respectively (Prediction performances of MLR models that include demographics and demographics with the course‐taking variables are shown in Table A13 in the supplemental materials).</p> <hd id="AN0164231921-19">Discussion</hd> <p>The availability of transcript data provides an opportunity to go beyond single snapshots of students' course‐taking and explore their high school curriculum as sequences of courses. Sequential accumulation of the coursework provides further insights on students' course‐taking experiences that cannot be observed in other ways. We adopt common basic (e.g., length) and complex (e.g., entropy) measures used to identify the diversity of and variation in sequences to study course‐taking sequences. We find that, on average, mathematics and English course‐taking sequences are more complex than the science course‐taking sequences. Examining the sequence characteristics by student groups shows that whereas White students, Asian students, and students from higher SES families tend to have more advanced typical course‐taking sequences, other students, including students of color and students from low‐SES families, have less advanced course sequences. Given the relationship between advanced course sequences and postsecondary enrollment, course‐taking variation may be one of the factors contributing to the underrepresentation of these students in postsecondary institutions.</p> <p>When students take several courses and transition between them, the course‐taking sequences become complex. This situation leads to a common problem in the study of course‐taking sequences—a large number of unique course sequences. To identify common pathways in course‐taking sequences, we employ sequence clustering to classify the sequences. We use hierarchical clustering to group together sequences with similar features to help understand the differences in the course‐taking patterns of the students. Unlike the earlier studies (e.g., Bozick & Ingels, [<reflink idref="bib8" id="ref35">8</reflink>]; Schiller & Hunt, [<reflink idref="bib24" id="ref36">24</reflink>]), however, we show that it is possible to capture the richness in the diversity of the students' course‐taking using these clustering methods. In mathematics, the representative sequence in the first cluster is in line with previous studies where the courses include Algebra I, geometry, and Algebra II. The other two clusters include advanced courses like precalculus and other advanced mathematics. The latter clusters are more associated with 4‐year college enrollment than the former cluster. We find that students can be classified into separate pathways in science and ELA as well. The complexity of course sequences in science and literature is higher for those clusters with higher college enrollment. An examination of course‐taking clusters across subjects shows that students in the advanced math cluster are also more likely to be in the conventional science and ELA clusters. This finding may indicate the emphasis placed on advanced math course‐taking by current curriculum practices or the perception of students, parents, and counselors.</p> <p>When clusters of course‐taking sequences are used together in classification tree analyses to visualize their relationship to college enrollment, results show that course‐taking sequences that include more advanced courses such as calculus, AP literature, or general physics and higher diversity are predictive of enrolling in 4‐year selective colleges. This finding is not surprising given that the evidence in the literature points to the importance of advanced course‐taking (e.g., Byun et. al., [<reflink idref="bib10" id="ref37">10</reflink>]; Long et al., [<reflink idref="bib20" id="ref38">20</reflink>]).</p> <p>Overall, we found that advanced course‐taking was associated with postsecondary enrollment. This finding may have implications for policy and practice because the course‐taking behaviors can be influenced by several different stakeholders. The research shows that academic advising is associated with retention and completion (e.g., Bettinger & Baker, 2014; Hatch & Garcia, [<reflink idref="bib17" id="ref39">17</reflink>]) and learning analytics dashboard incorporating comparative and predictive analyses that use course‐taking information was useful for decision making, especially for advisors with limited experience (Gutierrez et al., [<reflink idref="bib15" id="ref40">15</reflink>]). The academic advising on course‐taking has the potential to increase students' postsecondary enrollment. In a small‐scale study, Oripova ([<reflink idref="bib21" id="ref41">21</reflink>]) using data from 44 high school students enrolled in a Texas charter school showed that students' commitments levels for postsecondary attainment increased after receiving academic advising services. Combined together, these results suggest change of course‐taking behavior through different means has the potential to increase students' postsecondary enrollment. At the individual level, students can change their course‐taking behavior, as corroborated by the increase in the number of students enrolling in rigorous courses (e.g., calculus). School districts and academic advisors may also guide students to take more advanced courses. At the system level, policy changes that aim to increase curriculum standards could increase the number of students who could finish high school with more advanced courses through initiatives like the Algebra for All movement, requiring students to take Algebra I in middle school. Similarly, s states can adopt requirements for students to go through a specific curriculum, such as a college and career‐ready curriculum, and change graduation requirements like increasing the minimum number of mathematics credits required to graduate from high school, which in turn could lead students to take more advanced courses.</p> <p>This study has a few limitations. First, we limit the definition of course‐taking to include only those courses that students earned a passing grade in and therefore received a credit. We do not differentiate between students receiving an A versus a D, for example. Second, we simplify the course‐taking sequences by aggregating the courses taken within a subject in a given school year to a single course to account for the differences in school systems (e.g., semester versus trimester). Using more grained duration, like semester instead of school year, to create the course‐taking sequences can provide richer information about the sequences. Third, we used a cluster‐based approach to create small groups of sequences. This approach is suitable for uncovering structures in complex data such as sequences; however, it requires a number of decisions—some of them at will. For example, we identified the number of clusters from a practical perspective, but this approach may introduce ambiguities in interpreting the clusters. Sequence clustering does not provide further information about how likely it is that individual sequences belong to different clusters, which might influence conclusions about representative sequences within clusters. Fourth, we pick the neighborhood density, the proportion of courses within a given radius, to extract the representative sequences for each subject; however, other measures such as sequence frequency might lead to different results. Finally, the complexity measures we compute for the sequences do not necessarily translate into rigor but only indicate that students have taken several courses, which may or may not be difficult or challenging courses. Despite these limitations, this study provides important tools for researchers and practitioners by demonstrating that the analysis and interpretation of course sequences can provide further insights into studying course‐taking, guiding course selection, and developing curricula.</p> <hd id="AN0164231921-20">Acknowledgments</hd> <p>The research reported herewas supported by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A190073 to the American Institutes for Research(AIR). The opinions expressed are those of the authors and do not representviews of the Institute or the U.S. Department of Education.</p> <p>GRAPH: Diving into Students' Transcripts: High School Course‐Taking Sequences and Postsecondary Enrollment</p> <ref id="AN0164231921-21"> <title> Footnotes </title> <blist> <bibl id="bib1" idref="ref11" type="bt">1</bibl> <bibtext> Although we aimed to have one course per subject per grade, in some cases this was not possible because of students taking more than one course for a given subject. For example, if a student in a school with a trimester system takes Algebra I in trimesters 1 and 2 and geometry in trimester 3, then that student would have Algebra I‐geometry as the course‐taking sequence for that grade.</bibtext> </blist> <blist> <bibl id="bib2" idref="ref12" type="bt">2</bibl> <bibtext> Our examination various measures of the quality of partition (e.g., average Silhouette score, Hubert's gamma) did not differ notably for various number of clusters. Therefore, we adopted the approach described in the text.</bibtext> </blist> <blist> <bibl id="bib3" idref="ref1" type="bt">3</bibl> <bibtext> If a student did not enroll in or receive any credits for any course in a given subject, then that student does not have a course‐taking sequence in that subject. Similarly, if a student does not take a course in a given subject in a grade, we do not include a "no course" in that student's sequence. For example, if a student takes Algebra I‐geometry‐no math‐Algebra II, then the student's math‐taking sequence in our analyses is Algebra I‐geometry‐Algebra II.</bibtext> </blist> <blist> <bibl id="bib4" idref="ref2" type="bt">4</bibl> <bibtext> Throughout this article, the student level sample sizes are rounded to nearest 10 to comply with IES rules on reporting results from restricted use data.</bibtext> </blist> </ref> <ref id="AN0164231921-22"> <title> References </title> <blist> <bibtext> Aassve, A., Billari, F. C., & Piccarreta R. (2007). Strings of adulthood: A sequence analysis of young British women's work‐family trajectories. European Journal of Population, 23, 369 – 388.</bibtext> </blist> <blist> <bibtext> Abbott, A., & Tsay, A. (2000). Sequence analysis and optimal matching methods in sociology: Review and prospect. Sociological Methods and Research, 29 (1), 3 – 33</bibtext> </blist> <blist> <bibtext> Adelman, C. (1999). Answers in the toolbox: Academic intensity, attendance patterns, and bachelor's degree attainment. U.S. Department of Education.</bibtext> </blist> <blist> <bibtext> Attewell, P., & Domina, T. (2008). Raising the bar: Curricular intensity and academic performance. Educational Evaluation and Policy Analysis, 30 (1), 51 – 71.</bibtext> </blist> <blist> <bibl id="bib5" idref="ref5" type="bt">5</bibl> <bibtext> Bastedo, M. N., & Jaquette, O. (2011). Running in place: Low‐income students and the dynamics of higher education stratification. Educational Evaluation and Policy Analysis, 33 (3), 318 – 339.</bibtext> </blist> <blist> <bibl id="bib6" idref="ref26" type="bt">6</bibl> <bibtext> Bergner, Y., Shu, Z., & von Davier, A. (2014). Visualization and confirmatory clustering of sequence data from a simulation‐based assessment task. In Proceedings of the 7th Annual International Conference on Educational Data Mining [EDM2014].</bibtext> </blist> <blist> <bibl id="bib7" type="bt">7</bibl> <bibtext> Bettinger, & Baker, R. B. (2014). The effects of student coaching: An evaluation of a randomized experiment in student advising. Educational Evaluation and Policy Analysis, 36 (1), 3 – 19. https://doi.org/10.3102/0162373713500523</bibtext> </blist> <blist> <bibl id="bib8" idref="ref4" type="bt">8</bibl> <bibtext> Bozick, R., & Ingels, S. J. (2008). Mathematics coursetaking and achievement at the end of high school: Evidence from the Education Longitudinal Study of 2002 (ELS:2002) (NCES 2008–319). U.S. Department of Education, National Center for Education Statistics.</bibtext> </blist> <blist> <bibl id="bib9" idref="ref32" type="bt">9</bibl> <bibtext> Breiman, L. (2017). Classification and regression trees. Routledge.</bibtext> </blist> <blist> <bibtext> Byun, S., Irvin, J. M., & Bell, A. B. (2015). Advanced math course taking: Effects on math achievement and college enrollment. Journal of Experimental Education, 83, 439 – 468.</bibtext> </blist> <blist> <bibtext> Finkelstein, N., Fong, A., Tiffany‐Morales, J., Shields, P., & Huang, M. (2012). College bound in middle school and high school? How math course sequences matter. The Center for the Future of Teaching and Learning at WestEd.</bibtext> </blist> <blist> <bibtext> Gabadinho, A., & Ritschard, G. (2013). Searching for typical life trajectories applied to childbirth histories. In R. Levy & E. D. Widmer (Eds.), Gendered life courses—Between individualization and standardization. A European approach applied to Switzerland (pp. 287 – 312). LIT Verlag.</bibtext> </blist> <blist> <bibtext> Gabadinho, A., Ritschard, G., Mueller, N. S., & Studer, M. (2011). Analyzing and visualizing state sequences in R with TraMineR. 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The impact of intrusive college academic advising on high school students' college degree attainment commitment levels : A quantitative quasi‐experimental study. ProQuest Dissertations Publishing.</bibtext> </blist> <blist> <bibtext> Ritschard, G. (2021). Measuring the nature of individual sequences. Sociological Methods & Research. https://doi.org/10.1177/00491241211036156</bibtext> </blist> <blist> <bibtext> Ritschard, G., Gabadinho, A., Muller, N. S., & Studer, M. (2008). Mining event histories: A social science perspective. International Journal of Data Mining, Modelling and Management, 1 (1), 68 – 90.</bibtext> </blist> <blist> <bibtext> Schiller, K. S., & Hunt, D. J. (2011). Secondary mathematics course trajectories: Understanding accumulated disadvantages in mathematics in Grades 9–12. Journal of School Leadership, 21 (1), 87 – 118.</bibtext> </blist> <blist> <bibtext> Stevenson, D. L., Schiller, K. S., & Schneider, B. (1994). Sequences of opportunities for learning. Sociology of Education, 67, 184 – 198</bibtext> </blist> </ref> <aug> <p>By Burhan Ogut and Ruhan Circi</p> <p>Reported by Author; Author</p> </aug> <nolink nlid="nl1" bibid="bib20" firstref="ref3"></nolink> <nolink nlid="nl2" bibid="bib24" firstref="ref7"></nolink> <nolink nlid="nl3" bibid="bib11" firstref="ref9"></nolink> <nolink nlid="nl4" bibid="bib25" firstref="ref10"></nolink> <nolink nlid="nl5" bibid="bib19" firstref="ref17"></nolink> <nolink nlid="nl6" bibid="bib18" firstref="ref19"></nolink> <nolink nlid="nl7" bibid="bib13" firstref="ref23"></nolink> <nolink nlid="nl8" bibid="bib14" firstref="ref24"></nolink> <nolink nlid="nl9" bibid="bib22" firstref="ref25"></nolink> <nolink nlid="nl10" bibid="bib23" firstref="ref27"></nolink> <nolink nlid="nl11" bibid="bib12" firstref="ref29"></nolink> <nolink nlid="nl12" bibid="bib16" firstref="ref33"></nolink> <nolink nlid="nl13" bibid="bib10" firstref="ref37"></nolink> <nolink nlid="nl14" bibid="bib17" firstref="ref39"></nolink> <nolink nlid="nl15" bibid="bib15" firstref="ref40"></nolink> <nolink nlid="nl16" bibid="bib21" firstref="ref41"></nolink>
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  Data: Diving into Students' Transcripts: High School Course-Taking Sequences and Postsecondary Outcomes
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  Data: <searchLink fieldCode="AR" term="%22Burhan+Ogut%22">Burhan Ogut</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-1729-1396">0000-0003-1729-1396</externalLink>)<br /><searchLink fieldCode="AR" term="%22Ruhan+Circi%22">Ruhan Circi</searchLink> (ORCID <externalLink term="https://orcid.org/0000-0003-3854-1796">0000-0003-3854-1796</externalLink>)
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  Data: <searchLink fieldCode="SO" term="%22Grantee+Submission%22"><i>Grantee Submission</i></searchLink>. 2023.
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  Data: 10.1111/emip.12554
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  Data: The purpose of this study was to explore high school course-taking sequences and their relationship to college enrollment. Specifically, we implemented sequence analysis to discover common course-taking trajectories in math, science, and English language arts using high school transcript data from a recent nationally representative survey. Through sequence clustering, we reduced the complexity of the sequences and examined representative course-taking sequences. Classification tree, random forests, and multinomial logistic regression analyses were used to explore the relationship between the course sequences students complete and their postsecondary outcomes. Results showed that distinct representative course-taking sequences can be identified for all students as well as student subgroups. More advanced and complex course-taking sequences were associated with postsecondary enrollment. [This paper was published in "Educational Measurement: Issues and Practice" v42 n2 2023.]
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