Mathematics in the Fourth Year of High School
Information Relevant to Proposed Changes to Mathematics Requirements for
Graduation in Texas
Compiled by staff1 of the
Charles A. Dana Center
an organized research unit of
The University of Texas at Austin
October 2006
Abstract
The Texas State Board of Education’s proposed changes to the Recommended High School
Program and Distinguished Achievement Program graduation plans are positive steps in better
preparing students for the workplace and college. Texas, along with a handful of other states, is
setting the standard for the rest of the nation.
This paper presents an introduction and four brief sections on issues related to four years of
mathematics in high school. The introduction—and each section—is followed by selected
citations for further information. The section headings are
•
High school mathematics preparation for college readiness and completion,
•
Mathematics for work readiness and college readiness,
•
Comparison of high school graduation requirements to college-readiness requirements, and
•
College-level mathematics remediation / developmental course-taking.
1
Our thanks for compiling and reviewing this information go to the following staff of the Charles A. Dana
Center: Susan Hull, Ph.D., director of mathematics, and Bryan Nankervis, M.S., graduate research assistant.
Reviewers included Danielle Seabold, M.A., senior program coordinator, and Cathy Seeley, Ed.D, research fellow.
On November 15–17, 2006, the Texas State Board of Education will meet and decide the fate of
proposed new requirements for high school graduation, which include four credits of high
school–level mathematics. At the first reading on September 15, 2006, the additional
requirement of taking mathematics each year of high school was removed from consideration.
Without this provision, it will be possible for students, especially those with high mathematics
aptitude, to avoid taking mathematics in the senior year, which is the most crucial year in terms
of preparing for the demands of college or the workplace.
Since the implementation of No Child Left Behind, states have focused with increased intensity
on developing statewide curriculum standards tied to common high-stakes tests. There is too
little consistency, however, in course rigor and expectations from school to school, too little
agreement about graduation requirements across states, and too little alignment between high
school curricula and the expectations of two- and four-year colleges and universities (American
Diploma Project, 2004).
Across the nation, only 34% of ninth-grade students—and even lower percentages of Latino
(20%) and African-American (23%) ninth-grade students—graduate on time and college ready
(Greene, 2005), and almost three out of ten first-year students in two- and four-year institutions
of higher education are placed into remedial courses in reading, writing, or mathematics (U.S.
Department of Education, National Center for Education Statistics, 2003). Worse yet, 51% of
students taking any remedial course fail to earn a bachelor’s degree (Adelman, 2006).
In response to this problem, many states have increased their high school graduation
requirements to include more advanced coursework. In mathematics, for example, a growing
number of states are requiring Algebra II for graduation, and a small number of vanguard states,
including Texas, have passed legislation to make four years of high school mathematics a
requirement for a diploma.
In Texas, the State Board of Education is currently considering the requirement of four credits of
mathematics (Algebra I, Geometry, Algebra II, and an additional course to be determined) for
graduation under both the Recommended High School Program and the Distinguished
Achievement Program.
However, in the September meeting, the Texas State Board of Education backed away from
requiring a mathematics course every year of high school. The effect of this action could allow
many students to forego taking mathematics during their senior year, thereby weakening their
transition to college or the workplace. In particular, it will affect students who take Algebra I
during middle school and complete their mathematics requirements in their junior year. Any
prolonged time away from using mathematics could result in students’ skills deteriorating. Such
a gap in students’ mathematics study could also lead to fewer students majoring in mathematicsor science-related fields.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
www.utdanacenter.org
2
Research cited
Adelman, C. (2006). The toolbox revisited: Paths to degree completion from high school through
college. Washington, DC: U.S. Department of Education. Retrieved October 10, 2006,
from http://www.ed.gov/rschstat/research/pubs/toolboxrevisit/index.html.
American Diploma Project. (2004). Ready or not: Creating a high school diploma that counts.
Washington, DC: Achieve, Inc. Retrieved October 10, 2006, from
http://www.achieve.org/files/ADPreport_7.pdf.
Greene, J. P., & Winters, M. A. (2005, February). Public high school graduation and collegereadiness rates: 1991–2002 (Manhattan Institute for Policy Research Education Working
Paper No. 8). Retrieved October 9, 2006, from http://www.manhattaninstitute.org/html/ewp_08.htm.
U.S. Department of Education, National Center for Education Statistics. (2003). Remedial
education at degree-granting postsecondary institutions in fall 2000: Statistical analysis
report (Publication number NCES 2004-010, by B. Parsad and L. Lewis). Washington,
DC: Author. Retrieved October 10, 2006, from http://nces.ed.gov/pubs2004/2004010.pdf.
Following are four brief sections on issues related to four years of mathematics in high school.
Each section is followed by selected citations for further information.
High school mathematics preparation for college readiness and completion
Adding a fourth year of mathematics to the requirements for high school graduation is a positive
step in preparing students for college or the workplace. The most recent data from the College
Board reveals that on average, students with four years of high school–level mathematics score
63 points higher on the SAT-I quantitative section (which is a predictor of success in college)
than students with only three years of mathematics (College Board, 2006).
Further, students who take more than four years of mathematics (which would be the case for
students who take Algebra I in middle school and follow with mathematics each year in high
school) score 52 points higher on the SAT-I quantitative section than students with exactly four
years of mathematics. In terms of specific coursework, students who take precalculus or calculus
in high school score 50 to 90 points higher than those who complete just algebra or geometry,
and first-generation college-bound seniors score 96 points higher if they take precalculus in high
school and 116 points higher if they take calculus in high school (College Board, 2006).
The level of mathematics taken also has a strong influence on student completion of the
bachelor’s degree. The lifetime income of someone with a bachelor’s degree is about twice that
of a high school graduate, but on average only 40% of students whose highest level of high
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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school mathematics was Algebra II (that is, who meet the current graduation requirements in
Texas) finish their bachelor’s degree. However, if a student completes trigonometry, precalculus,
or calculus in high school, his or her chances for completing the bachelor’s degree grow to 62%,
74%, and 80%, respectively (Venezia, Kirst, & Antonio, 2003).
Selected research, including research cited (marked with a *)
Adelman, C. (2006). The toolbox revisited: Paths to degree completion from high school through
college. Washington, DC: U.S. Department of Education. Retrieved October 10, 2006,
from http://www.ed.gov/rschstat/research/pubs/toolboxrevisit/index.html.
*College Board (2006). 2006 College-bound seniors total group profile report. Retrieved
October 10, 2006, from
http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2006/nationa
l-report.pdf.
Dougherty, C., Mellor, L., & Jian, S. (2006, February). The relationship between Advanced
Placement and college graduation (2005 AP study series, Report 1). Austin, TX:
National Center for Educational Accountability. Retrieved October 10, 2006, from
http://www.nc4ea.org/files/NCEA_Report_Relationship_between_AP_and_College_Gra
duation_02-09-06.pdf.
Hussar, W. J., & Bailey, T. M. (2006). Projections of education statistics to 2015 (34th ed.)
(Publication number NCES 2006-084). U.S. Department of Education, National Center
for Education Statistics. Washington, DC: U.S. Government Printing Office. Retrieved
October 10, 2006, from http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2006084.
U.S. Department of Education, National Center for Education Statistics. (2006). The condition of
education 2006 (Publication number NCES 2006-071). Washington, DC: U.S.
Government Printing Office. Retrieved October 10, 2006, from
http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2006071.
*Venezia, A., Kirst, M. W., & Antonio, A. L. (2003). Betraying the college dream: How
disconnected K–12 and postsecondary education systems undermine student aspirations
(Final policy report from Stanford University’s Bridge Project). Stanford, CA: The
Stanford Institute for Higher Education Research. Retrieved October 10, 2006, from
http://www.stanford.edu/group/bridgeproject/betrayingthecollegedream.pdf.
Mathematics for work readiness and college readiness
The demands of the current job market also require higher levels of mathematics completion.
Whereas fifty years ago only a small percentage of jobs required skilled workers, today nearly
two-thirds of all jobs require people with strong academic skills. A report released this spring by
ACT, Inc., concluded that the expectations for students planning to go directly into the job
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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market looking “for jobs that are likely to offer both a wage sufficient to support a small family
and potential career advancement should be no different from students who choose to enter
college after high school graduation” (ACT, Inc., 2006).
Selected research, including research cited (marked with a *)
*ACT, Inc. (2006, May 8). High school graduates need similar math, reading skills whether
entering college or workforce training programs. Retrieved October 10, 2006, from
http://www.act.org/news/releases/2006/05-08-06.html. [Note related report accessible
from same site: Ready for college and ready for work: Same or different?]
American Diploma Project. (2004). Ready or not: Creating a high school diploma that counts.
Washington, DC: Achieve, Inc. Retrieved October 10, 2006, from
http://www.achieve.org/files/ADPreport_7.pdf.
Dougherty, C., Mellor, L., & and Jian, S. (2006, February). Orange juice or orange drink?
Ensuring that “advanced courses” live up to their labels (NCEA Policy Brief No. 1).
Austin, TX: National Center for Educational Accountability. Retrieved October 10, 2006,
from http://www.nc4ea.org/files/NCEA_Report_Orange_Juice_or_Orange_Drink_02-1306.pdf.
Education Trust. (2005). Gaining traction, gaining ground: How some high schools accelerate
learning for struggling students. Washington, DC: Author. Retrieved October 10, 2006,
from http://www2.edtrust.org/NR/rdonlyres/6226B581-83C3-4447-9CE731C5694B9EF6/0/GainingTractionGainingGround.pdf.
Greene, J. P., & Winters, M. A. (2005, February). Public high school graduation and collegereadiness rates: 1991–2002 (Manhattan Institute for Policy Research Education Working
Paper No. 8). Retrieved October 9, 2006, from http://www.manhattaninstitute.org/html/ewp_08.htm.
Presley, J. B., & Gong, Y. (2005). The demographics and academics of college readiness in
Illinois (Policy Research Report: IERC 2005-3). Edwardsville, IL: Illinois Education
Research Council. Retrieved October 10, 2006, from
http://ierc.siue.edu/documents/College Readiness - 2005-3.pdf.
Comparison of high school graduation requirements to college-readiness
requirements
A recent survey of high school teachers and college professors provides some insight into their
different perceptions of how well students are prepared—and into the current misalignment of
high school graduation and college readiness requirements. While 36% of high school faculty
felt their students were very or extremely well prepared for college-level work, only 15% of
college faculty agreed (Sanoff, 2006). Another survey of college instructors found that 65% felt
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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their incoming students were not adequately prepared; 70% reported they had to spend class time
covering material and skills that should have been taught in high school (Peter D. Hart Research
Associates, 2005).
In Texas, according to the Texas Education Agency, only 49% of graduating students meet the
Texas Higher Education Coordinating Board standard for higher education readiness in
mathematics (Texas Education Agency, 2006). This general lack of college readiness on the part
of high school graduates is problematic, given that 56% of jobs today require some college
education, and 80% of the fastest growing jobs in the next ten years will require postsecondary
work (Texas Education Agency, 2006).
Research cited
*Peter D. Hart Research Associates / Public Opinion Strategies. (2005, February). Rising to the
challenge: Are high school graduates prepared for college and work? A study of recent
high school graduates, college instructors, and employers (Conducted for Achieve, Inc.).
Washington, DC: Author. Retrieved October 10, 2006, from
http://www.achieve.org/files/pollreport.pdf.
*Sanoff, A. P. (2006, March 10). A perception gap over students’ preparation. The Chronicle of
Higher Education, p. B9. Retrieved October 10, 2006, from
http://chronicle.com/weekly/v52/i27/27b00901.htm.
*Texas Education Agency. (2006). The high school allotment: Rulemaking for high school
completion and college readiness. [PowerPoint presentation.] Retrieved October 10,
2006, from http://www.tea.state.tx.us/HB1/HigSchAll.
College-level mathematics remediation / developmental course taking
Another indicator of the need to better prepare students in high school is the growth of
remediation for college freshmen. Nationwide, $1.4 billion a year is spent on remedial education
for recently graduated high school students. As a result, the nation’s economy loses another $2.3
billion annually because remedial students drop out at a higher rate (Alliance for Excellent
Education, 2006).
The percentage of first-time full-time freshmen needing developmental mathematics courses in
Texas was about 31% in 2004–05, up from about 25% in 1999–2000 (Texas Higher Education
Coordinating Board, 2005). The expansion of such remedial programs in higher education serves
to illustrate the acute need for better alignment between high school mathematics programs and
first-year undergraduate mathematics courses in Texas (Charles A. Dana Center, 2003). The
Alliance for Excellent Education estimates that by improving the high school curriculum and
thereby reducing the need for remediation in college, the state of Texas could save $88 million in
direct costs per year and that the result would be a total benefit to the state economy of $283
million a year (Alliance for Excellent Education, 2006).
The Charles A. Dana Center at The University of Texas at Austin
October 2006
www.utdanacenter.org
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Selected research, including research cited (marked with a *)
*Alliance for Excellent Education (2006, August). Paying double: Inadequate high schools and
community college remediation (Issue Brief). Retrieved October 10, 2006, from
http://www.all4ed.org/publications/remediation.pdf.
*Charles A. Dana Center, The University of Texas at Austin. (2003). Advanced mathematics
educational support: Support, recommendations, and resources for facilitating
collaboration between higher education mathematics faculty and Texas public high
schools. Austin, TX: Author. Retrieved October 10, 2006, from
http://www.utdanacenter.org/downloads/products/AMES.pdf.
*Texas Higher Education Coordinating Board. (2005, November). Developmental education:
Statewide data profile. Retrieved October 10, 2006, from
http://www.thecb.state.tx.us/OS/SuccessInitiatives/DevEd/DEData/Statewide.pdf.
U.S. Department of Education, National Center for Education Statistics. (2003). Remedial
education at degree-granting postsecondary institutions in fall 2000: Statistical analysis
report (Publication number NCES 2004-010, by Basmat Parsad and Laurie Lewis).
Washington, DC: Author. Retrieved October 10, 2006, from
http://nces.ed.gov/pubs2004/2004010.pdf.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
www.utdanacenter.org
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