Highest Math Course Completed in
High School
Summary
Highest math course completed in high school is associated with successful completion of a postsecondary credential. Controlling for socioeconomic status, the likelihood of students earning a bachelor’s degree varies directly with students taking and passing higher-level math courses in high school. Math coursework taken in high school is also a malleable factor over which policymakers and educators have some control. For purposes of the pilot, highest-level math includes the following categories: algebra 1 and below, geometry, algebra 2 and probability/statistics, algebra 3 (where applicable), higher math (including trigonometry or pre-calculus, IB Math, AP Probability and Statistics, non-AP/IB calculus, and some other courses of similar rigor), and non-AP/IB Calculus.
Background
The Common Core State Standards Initiative has defined the knowledge and skills with which students should graduate high school to succeed in entry-level, credit-bearing aca-demic college courses and in workforce training programs. The Initiative has published standards for kindergarten through high school in mathematics and English Language Arts. The high school mathematics standards cover a broad range of topics and domains, but do not dictate curriculum, pedagogy, or content delivery. In high school, mathematics is currently typically delivered through a sequence of courses, including either a tradi-tional course sequence (such as algebra 1, geometry, and algebra 2) or an integrated course sequence (such as mathematics 1, mathematics 2, and mathematics 3), followed by higher-level math courses.
Research Highlights
Completing a higher-level math course is associated with completing a bachelor’s degree (Adelman 2006), even after taking into account students’ prior ability in math along with demographic, academic, and school characteristics (Rose 2001). Among first-generation students, those taking a higher-level math course were about twice as likely to enroll in a 4-year college within two years of graduation compared with those whose highest math
level was algebra 2 (64 percent vs. 34 percent) (Horn 2000). Given these associations, opportunity to take high-level math is an important conditional factor associated with postsecondary opportunities. African American and Hispanic students from low socioec-onomic status backgrounds are less likely to attend high schools offering higher-level math courses and, when they do have the opportunity to take these classes, do so at a rate lower than that of white and Asian students (Adelman 2006; ACT 2005).
Indicator Details
A variety of coursetaking measures, including highest math course taken, were construct-ed for all high school students with complete course records in core subjects (English, mathematics, science, and social studies) in the state longitudinal data system (SLDS). All three pilot states had standard, statewide course classifications and maintained com-mon course catalogs, which allowed the uniform coding of courses for all students in the state. High school course codes for each state were first mapped to the Secondary School Taxonomy, available from the National Center for Education Statistics, which is particu-larly useful for cross-state transcript analysis.1 A second critical step was to define a complete course record (overall and in core subjects) based on state-specific high school graduation requirements. Only high school students with complete course records in core subjects were included in pilot coursetaking measures and related analyses. Course rec-ords may be incomplete due to varying submission practices over time or across districts, resulting in different levels of completeness in some years or locales, or due to student mobility and the lack of complete records for some students.
Operational Definition
This measure was operationally defined as the highest math course for which a student received at least one credit (one Carnegie unit) in high school,2 based on the following sequence of course categories from lowest to highest: algebra 1 and below, geometry, al-gebra 2 and probability/statistics, alal-gebra 3 (where applicable), higher math (including trigonometry or pre-calculus, IB Math, AP Probability and Statistics, non-AP/IB calculus, and some other courses of similar rigor), and AP/IB Calculus.3 State course codes were
1 See Bradby and Hoachlander (1999) and Bradby and Hudson (2007).
2 One Carnegie unit is awarded for a course that meets one period per day for the entire school
year, or the equivalent instructional time.
3 In some states, algebra I or geometry may be taken in the 8th grade rather than in high school.
State practices for counting these courses toward high school graduation requirements may also vary. It is important to consider state practices that may affect the definition of a complete high school course record and to reflect these practices in any constructed course measures. For exam-ple, it may be necessary to assume that a student who took geometry or algebra II in grade 9 took precursor math courses in middle school.
mapped to these categories using the Secondary School Taxonomy. Only high school students with complete course records in core subjects (English, mathematics, science, and social studies) were included in the measure and related analyses; students with in-complete course records were set to missing on the variable. Complete course records were defined based on state-specific high school graduation requirements.
Data Sources
Highest math course completed was constructed from high school course records that were included in the state longitudinal data system (SLDS). Complete transcripts were constructed for each high school student from annual course records. State course cata-logs were used to map state course codes to the federal Secondary School Taxonomy in order to create comparable coursetaking measures for the three pilot states.
Data Limitations
In order to interpret coursetaking measures appropriately, information should be available to users on the extent of any missing or incomplete course data for their school, district, or state; the definition used for a complete transcript in the state context; and the specific state courses included each variable category. Ideally, state and local stakeholders will have participated in determining, or will have reviewed, the many decision rules required to construct valid coursetaking measures.
Related Measures
A goal of the pilot was to create common cross-state measures, and the following addi-tional coursetaking measures were constructed for each of the three pilot states based on national benchmarks for college preparatory coursework. State-specific measures can al-so be constructed from course data in SLDS.
Completed 4 years of high school math, including algebra 1: whether students earned credit for 4 years of non-remedial high school math, including algebra 1;4
Completed 4 years of high school math, including algebra 1, geometry, and algebra 2: whether students earned credit for 4 years of non-remedial high school math, including algebra 1, geometry, and algebra 2;5
4 For this measure, it is critical to consider whether students may have taken algebra 1 and/or
geometry in middle school.
Completed 4 years of high school math, including geometry, algebra 2, and an advanced math course: whether students earned credit for 4 years of non-remedial high school math, including geometry, algebra 2, and at least one higher math course;6
Completed a math course during senior year: whether students earned credit for a non-remedial math course during their senior year of high school;
Rigor of high school math courses: average academic rigor of high school math courses completed, based on course rigor designations in the Secondary School Taxonomy (func-tional/exceptional, basic, regular, honors/advanced, and AP/IB);
Number of math credits above the basic level earned in high school: number of credits students earned in high school math courses above the basic level (that is, at the regular, honors/advanced, or AP/IB levels) as designated in the Secondary School Taxonomy.
How to Use the Measure
Math coursework taken in high school is a malleable factor over which policymakers and educators have some control. Higher-level math courses are associated with successful completion of a postsecondary credential, particularly a bachelor’s degree. Highest math course completed can be used to determine whether there are any systematic differences in postsecondary outcomes associated with students’ highest level of math taken in the local or state context. The measure can also be used to examine whether the relationship between highest math course taken and postsecondary outcomes is the same for all groups of students.
It is important to provide information about data limitations, such as the extent of any missing or incomplete course data, along with results so that users may interpret the data appropriately.
Prompting Questions
Users may find it helpful to think about the following questions:
What appears to be the relationship between highest math course taken and college enrollment?
Is there a steady upward relationship or do outcomes vary by course type? Is there a threshold where completing the next highest math course is associated with a large change in college enrollment?
6 For this measure, it is critical to consider whether students may have taken geometry in
Is the pattern consistent for all demographic groups?
Is the pattern consistent when controlling for prior mathematics achievement, such as measured by the state 8th-grade mathematics assessment?
What factors may contribute to these patterns?
Presentation
This section describes how information about the highest match course taken in high school can be presented effectively to state, district, and school audiences. State and local staff who are considering how to use the rich source of information in their state longitu-dinal data systems (SLDS) may find the examples presented here a useful guide for their own practice. These examples were developed through extensive conversations with, and iterative review by, stakeholder advisory groups in the three participating pilot states.
Standard Display
The standard reports included in the pilot web tool, Advance, combine a graphical dis-play, a table containing demographic detail, the option to switch between percentages and counts, state-specific variable definitions, notes about the data and interpretation, ques-tions to prompt thought and action, and the ability to export results to a PDF document or Excel spreadsheet. As seen on the next page, the bar chart shows the percentage of 2010 high school graduates who enrolled in postsecondary education immediately after gradua-tion according to their highest math course completed in high school. Below the graph, a table shows additional detail, first repeating the overall result (total row) and then dis-aggregating results by three student demographic characteristics of general interest: gen-der, race/ethnicity, and economic disadvantage status. Definitions of terms and symbols and other related information appear to the right of the graph and table to provide context and support in understanding and interpreting the results. See the Sample Advance Report to view all standard report components.
To protect student privacy, results based on less than a state-defined minimum number of students were suppressed and replaced with a footnote indicating small numbers. Typically, the state practice for suppressing assessment results in public reporting was followed (a minimum of either five or ten students for the states participating in the pilot). Users can toggle between “Percentages” and “Counts” in the table to obtain the number of students upon which each percentage is based. This helps users interpret results appropriately, since results based on small numbers may be more volatile than those based on larger numbers.
Percentage of 2010 high school graduates who enrolled in postsecondary education by the fall following graduation, by highest math course completed
16% 30% 59% 43% 79% 94% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Algebra 1 & below Geometry Algebra 2 & probability/ statistics
Algebra 3 Higher math AP/ IB Calculus
16% 30% 59% 43% 79% 94% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Algebra 1 & below Geometry Algebra 2 & probability/ statistics
Algebra 3 Higher math AP/ IB Calculus
Percentage of 2010 high school graduates who enrolled in postsecondary education by the fall following graduation, by highest math course completed
Reading the table: Sixteen percent (16%) of the 2009 high school graduates who com-pleted algebra 1 or below as their highest math course in high school enrolled in postsec-ondary education by the fall following graduation. In comparison, 92% of the 2009 graduates who completed AP or IB Calculus as their highest math course enrolled imme-diately in postsecondary education. Sixteen percent (16%) of the female 2009 high school graduates who completed algebra 1 or below as their highest course enrolled immediately in postsecondary education, compared with 17% of their male classmates who completed this level of math course.
Digging Deeper
In addition to offering a set of standard reports, the pilot web tool, Advance, also made it possible for users to create their own tables in order to investigate their own questions or dig deeper into results. The table below shows postsecondary remediation rates in math based on the highest math course students took in high school. Remediation rates in math decreased as the highest level of math course completed increased.
Did not take remedial math
30% 35% 67% 89% 98% 2% AP/ IB Calculus 11% Higher math 33% Algebra 2 & probability/
statistics
65% Geometry
70% Algebra 1 & below
Highest high school math course for which student earned at least one credit.
Took remedial math
Percentage of 2008 high school graduates who took remedial math, of those who enrolled in an in-state public institution, by highest high school math course
Reading the table: Thirty percent (30%) of the 2008 high school graduates who complet-ed algebra 1 or below as their highest math course in high school and enrollcomplet-ed in state public postsecondary institutions within 12 months of graduation did not take a postsec-ondary-level remedial math course, while 70% took a remedial math course. At the other end of the spectrum, 98% of the 2008 graduates who completed AP or IB Calculus in high school and enrolled in state public postsecondary institutions within 12 months did not take a remedial math course, while 2% did take a remedial math course.
Digging deeper, the user examined the relationship between math remediation and high-est math course taken when controlling for the prior math achievement of students. This investigation showed a more complex relationship between math remediation rates and highest math course taken, which varied depending on a student’s proficiency level on the 8th grade state math assessment.
Not Proficient Proficient Advanced
74% 66% 33%
71% 58% 30%
66% 37% 11%
60% 18% 3%
25% 3% 1%
Proficiency on 8th grade math assessment
Percentage of 2008 high school graduates who took remedial math, of those who enrolled in an in-state public institution, by highest high school math course and proficiency on the state 8th grade math assessment
AP/ IB Calculus Higher math
Algebra 2 & probability/ statistics
Geometry
Algebra 1 & below
Highest high school math course for which student earned at least one credit.
Reading the table: Among the 2008 high school graduates who enrolled in state public postsecondary institutions within 12 months, postsecondary remediation rates in math de-creased as their performance on the state’s 8th grade math assessment inde-creased. For ex-ample, among the 2008 graduates who completed algebra 1 or below as their highest math course in high school, 74% of those who did not score proficient on the state’s 8th-grade math assessment took a postsecondary-level remedial math course; 66% of those who scored proficient on the 8th grade math assessment took a remedial math course; and 33% of those who score advanced on the 8th grade math assessment took such a course.
Sources
ACT (2005). Courses Count: Preparing Students for Postsecondary Success.
Adelman, C. (2006). The Toolbox Revisited: Paths to Degree Completion From High School Through College. Washington, D.C.: U.S. Department of Education. Bradby and Hoachlander (1999).
Bradby and Hudson (2007).
Dalton, B., Ingels, S.J., Downing, J., and Bozick, R. (2007). Advanced Mathematics and Science Coursetaking in the Spring High School Senior Classes of 1982, 1992, and 2004 (NCES 2007-312). National Center for Education Statistics, Institute of Educa-tion Sciences, U.S. Department of EducaEduca-tion. Washington, DC.
Horn, L and A. Nuñez (2000). Mapping the Road to College: First-Generation Students’ Math Track, Planning Strategies, and Context of Support,. U.S. Department of Edu-cation. National Center for Education Statistics. Washington, DC.
Rose, H. and J. Betts (2001). Math Matters: The Link Between High School Curriculum, College Graduation, and Earnings. Public Policy Institute of California. Retrieved 12/14/2012 from www. ppic.org/content/pubs/report/R_701JBR.pdf.
