THE CHARLES A. DANA CENTER
THE UNIVERSITY OF TEXAS AT AUSTIN
DEV 2.200 • 2901 North IH 35, Suite 2.200 • Austin, TX 78722 • 512-471-6190 • FAX 512-232-1855
Data to Inform the Discussion on the Fourth Year of Mathematics in High School
Texas Graduation Rates, College Enrollment Rates, and High School Mathematics Course Enrollment Rates
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.
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. On November 15–17, 2006, the
Texas State Board of Education will meet and decide the fate of the
proposed new requirements for high school graduation, which include
four credits of high school–level mathematics.
1
This document presents 11 tables of Texas data relevant to four
questions that have been raised about the proposed changes to
mathematics requirements for graduation in Texas. The questions are:
1. Why are we talking about a fourth year of mathematics?
2. Will additional mathematics requirements in high school increase
the dropout rate?
3. How many more students will take advanced mathematics if the
Algebra II prerequisite is enacted?
4. How many more teachers will be required to teach the additional
students in courses beyond Algebra II?
Our thanks for researching and writing this paper go to Cynthia L. Schneider, Ph.D., Dana Center research scientist associate. Reviewers included
Darlene Yañez, Ph.D., Dana Center research director; Garland Linkenhoger, M.Ed., mathematics consultant; and Jennifer Westrick, M.A., research consultant.
What does data tell us about the current discussion of policy changes surrounding a fourth year of mathematics for high school
graduation in Texas? The purposes of the proposed changes in policy are both
•
•
to increase the number of students who go to college and
to better prepare all students to succeed in mathematics in college or in the workforce.
In an attempt to quantify potential consequences of the proposed policy change, we collected data from
•
•
•
the Texas Education Agency’s Academic Excellence Indicator System (AEIS) (www.tea.state.tx.us/perfreport/aeis),
the Texas Higher Education Coordinating Board’s High School to College Linkages online reports
(www.txhighereddata.org/Interactive/HSCollLink.cfm), and
the Texas PK–16 Public Education Information Resource (www.texaseducationinfo.org/tpeir/Index.asp).
The Texas Education Agency’s Academic Excellence Indicator System reports for 2005–06 will become available at
www.tea.state.tx.us/perfreport/aeis in late November 2006. Thus, many of the data tables in this paper end with 2004–05 data. It
should be noted, however, that the AEIS reports for graduation completion and SAT / ACT data are a year behind. For instance, while
the 2004–05 AEIS data includes enrollment for 12th-graders in that year, the graduation completion rates and SAT / ACT scores are
for the graduating class of 2003–04 (identified as the class of 2004).
In the tables, most of the time we rounded percentages to the nearest tenth or whole number. As a consequence of this rounding, some
percentages, when added together, total slightly more or less than 100%. Also, whenever possible we tried to provide enough
information that our calculations can be checked; in some cases it was not possible to provide all the data for the calculations due to
limitations of space. For all data tables, we have provided the source from which we obtained the data.
In the abstract above are some of the key questions that have been raised as concerns about the proposed policy changes. In a
summary at the end of this document, these four questions are repeated, and each is followed by a response based on the data in the
tables that make up the body of this paper.
Observations on Table 1, Texas high school enrollment figures by grade level
Enrollment figures show a small increase from one school year to the next in the number of students in each grade level (for example,
from 2002–03 to 2003–04, the number of students in 9th grade grew 0.9%). The total number of students enrolled in high school
The Charles A. Dana Center at The University of Texas at Austin
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increased nearly 2% from 2002–03 to 2003–04. Between 2003–04 and 2004–05, total high school enrollment statewide increased
again at nearly 2%.
Table 1. Texas high school enrollment figures by grade level
School
year
Total students enrolled,
grades 9–12
Percentage
Percentage
Percentage
Percentage
Percentage
Number
increase over
Number
increase over
Number
increase over
Number
increase over
Number
increase over
previous year
previous year
previous year
previous year
previous year
2002–03 372,024
299,089
265,349
237,905
1,174,367
2003–04 375,225
0.9%
309,100
3.3%
267,553
0.8%
242,771
2.0%
1,194,649
1.7%
2004–05 383,353
2.2%
311,018
0.6%
274,815
2.7%
246,863
1.7%
1,216,049
1.7%
The number of students in this table is from the Texas Education Agency’s Academic Excellence Indicator System’s State Profile Reports’ Student Information,
www.tea.state.tx.us/perfreport/aeis (retrieved 10/19/06). The AEIS reports for 2005–06 will be online in late November 2006. We computed all percentages and
the totals in the column under “Total students enrolled, grades 9–12.”
9th-grade students
10th-grade students
11th-grade students
12th-grade students
Observations on Table 2, Decline in Texas high school enrollment by student cohort between grades
The number of students in 10th grade in 2003–04 was 17% less than the number of students in 9th grade in 2002–03. There was also
an 11% drop in the number of students enrolled in 11th grade in 2003–04 from the number enrolled in 10th grade in 2002–03, and a
9% drop in students enrolled in 12th grade in 2003–04 from the number enrolled in 11th grade in 2002–03. Similar rates of decline are
seen in the next set of years (2003–04 to 2004–05): a 17% drop in the number of students from 9th to 10th grade, an 11% drop from
10th to 11th grade, and an 8% drop from 11th to 12th grade.
Table 2. Decline in Texas high school enrollment by student cohort between grades
Decline in the
Percentage change
Decline in the
Percentage change
2003–04 to 2004–05
number of students
between grades
number of students
between grades
9th to 10th grade
-62,924
17% of 2002–03 9th-graders
9th to 10th grade
-64,207
17% of 2003–04 9th-graders
10th to 11th grade
-31,536
11% of 2002–03 10th-graders
10th to 11th grade
-34,285
11% of 2003–04 10th-graders
11th to 12th grade
-22,578
9% of 2002–03 11th-graders
11th to 12th grade
-20,690
8% of 2003–04 11th-graders
This data is from the numbers of students listed in Table 1, which are from the Texas Education Agency’s AEIS State Profile Reports’ Student Information,
www.tea.state.tx.us/perfreport/aeis (retrieved 10/19/06). For example, we subtracted Table 1’s number of students in 9th grade in 2002–03 (372,024) from the
number of students in 10th grade 2003–04 (309,100) to calculate the value of -62,924.
2002–03 to 2003–04
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Observations on Table 3, Texas completion-rate status
In 1996–97, 75.8% of the senior class graduated. In 2003–04, 84.6% graduated, an increase of 8.8% over seven years. It is probable
that a large part of this increase in graduation rates has come from (1) reducing the dropout rate, which was 9.3% in 1996–97 and only
3.9% in 2003–04, and (2) reducing the percentage of seniors receiving a GED from 8.2% in 1996–97 to 4.2% in 2003–04. Given the
controversy2 over the calculation of dropout rates, it is sufficient to observe that more students are graduating from our high schools.
Table 3. Texas completion-rate status*
Class of
Graduated
Received GED**
Continued high school***
Dropped out (4-year)****
1996–97
75.8%
8.2%
6.7%
9.3%
1997–98
78.7%
4.3%
8.2%
8.9%
1998–99
79.5%
4.0%
8.0%
8.5%
1999–00
80.7%
4.8%
7.3%
7.2%
2000–01
81.1%
4.8%
7.9%
6.2%
2001–02
82.8%
4.1%
8.0%
5.0%
2002–03
84.2%
3.3%
7.9%
4.5%
2003–04
84.6%
4.2%
7.3%
3.9%
The data in this table is from the Texas Education Agency’s Academic Excellence Indicator System reports, www.tea.state.tx.us/perfreport/aeis (retrieved
10/19/06). The AEIS reports for 2005–06 will be online in late November 2006.
*The AEIS completion rate indicator shows the status of a group (cohort) of students after four years in high school. For example, a cohort could consist of
students who first attended 9th grade in 1999–2000. They are followed through their expected graduation as the class of 2003. Any student who transferred
into the 1999–2000 cohort is added to it, and any student who transfers out of the cohort is subtracted from it. This definition was adapted from the “Glossary
for the Academic Excellence Indicator System, 2004–05,” at www.tea.state.tx.us/perfreport/aeis/2005/glossary.html#complete (retrieved 10/25/06).
**The General Educational Development (GED) certificate may be earned by Texas students who pass a high school equivalency examination.
***Continued high school refers to students still enrolled after four years of high school. For example, from the 1999–2000 cohort, continued high school would
be the percentage of students still enrolled in the fall of the 2003–04 school year. The percentage is calculated as follows: number of students from the cohort
who were enrolled for the 2003–04 school year divided by number of students in the 1999–2000 cohort. This definition was adapted from the “Glossary for
the Academic Excellence Indicator System, 2004–05,” at www.tea.state.tx.us/perfreport/aeis/2005/glossary.html#complete (retrieved 10/25/06).
****Dropped out (4-year) refers to students who dropped out within their cohort’s four years of high school and did not return by the fifth year. For example,
based on the 1999–2000 cohort, dropped out shows the percentage who dropped out and did not return by the fall of the 2003–04 school year. The dropout
2
See, for example, the Intercultural Development Research Association’s Attrition and dropout rates in Texas, retrieved October 23, 2006, from
www.idra.org/Research/Attrition. Note also at that site: Johnson, R. L. (2006, October). Texas public school attrition study, 2005–06: Gap continues to grow.
San Antonio, TX: Intercultural Development Research Association. Retrieved October 23, 2006, from www.idra.org/IDRA_Newsletters/October_2006_
School_Holding_Power/Texas_Public_School_Attrition_Study_2005-06. For current information on Texas dropout rates and their implications, see also
Deviney, F. (2006). The high cost of dropping out: How many? How come? How much?: A Texas Kids Count special report. Austin, TX: Center for Public
Policy Priorities. Retrieved October 23, 2006, from www.cppp.org/files/10/TKC_Report(S)%20-%20FINAL.pdf.
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rate for this cohort is calculated as follows: number of students from the cohort who dropped out before the fall of the 2003–04 school year, divided by
number of students in the 1999–2000 cohort. Note that the cohort in the denominator of the formula includes those students who graduated, continued in
school, received a GED, or dropped out. This cohort does not include some categories of “leavers” (students who were enrolled or in attendance in a given
district at any point during the prior year but who did not re-enroll the following fall) who, for example, died or moved to another district, state, or country.
Specifically, the cohort in the denominator of the formula does not include data errors or leavers with codes 03, 16, 19, 21, 22, 24, 30, 31, 60, 61, 63, 64, 66,
72, 78, 80, 81, 82, or 83. This definition was adapted from the “Glossary for the Academic Excellence Indicator System, 2004–05,”
www.tea.state.tx.us/perfreport/aeis/2005/glossary.html#complete and www.tea.state.tx.us/perfreport/aeis/2005/glossary.html#leaver (retrieved 10/25/06).
Observations on Table 4, Rates of graduation and rates of attendance in higher education under various Texas high school
graduation programs
The percentage of students graduating under Texas’s Recommended High School Program or Distinguished Achievement Program (or
Advanced Honors Program, the name for an earlier plan similar in requirements) increased about 32% from 1996–97 to 2004–05,
while the percentage of students graduating under the state’s Minimum High School Program (or Regular Education Graduation Plan
or Individual Education Graduation Plan) has decreased by the same amount over this eight-year period.
The percentage of students attending a two-year institution of higher education has remained the same over a seven-year timeframe
(1996–97 to 2002–03; more recent data were not yet available). The percentage of students attending a four-year higher education
institution has increased about 4% over this same time period.
The percentage of students meeting or exceeding the criteria set for college readiness on the SAT and/or ACT has remained stable at
around 27%. Tests that are norm-referenced,3 such as the ACT and SAT, are designed to produce stable or consistent results from year
to year.
The Texas Academic Skills Program (TASP) results over five years (1998–99 to 2002–03, when the TASP was discontinued and
replaced with other assessments) show the following trend: As more students graduated under the state’s Recommended High School
Program, more students (5% more over this time period) were passing the TASP in mathematics or were exempt from the TASP,
while fewer students graduating under the Minimum High School Program were passing or exempt (6% fewer over the five-year time
period in this table).
3
A norm-referenced exam is one in which an individual test-taker’s score is compared with the scores of all other test-takers. A criterion-referenced
test, in contrast, measures how well a test-taker has learned a specific body of knowledge and skills—thus, theoretically every test-taker could earn a passing
grade if he or she knows the tested material well enough. The Texas Assessment of Knowledge and Skills is a criterion-referenced test.
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Growth in the percentage of Recommended High School Program or Distinguished Achievement Program students meeting the new
state college-readiness indicator (that is, students attaining a scale cut-off score of at least 2200 on the 11th-grade mathematics Texas
Assessment of Knowledge and Skills), is showing a promising trend in that it demonstrates that increasing numbers of students (43%
in 2004–05 to 49% in 2006–07) are prepared for higher education.
Table 4. Rates of graduation and rates of attendance in higher education under various Texas high school graduation programs
Class of
Total
number
of
graduates
Participated in
Minimum High
School Program /
Regular / or
Individual
Education
Graduation
Program
Number
% of total
high
school
graduates
Participated in
Recommended High
School Program /
Distinguished
Achievement
Program / or (prior
to 2001) Advanced or
Advanced Honors
Program
Number % of total
high school
graduates
Enrolled in Texas higher education
institution the fall after high school
graduation
Texas 2-year
Texas 4-year
institution of higher
institution of higher
education
education
≥Collegereadiness
criteria
SAT /
ACT
Exempt from or passing
TASP-A* (1999–2003) or
scoring ≥ 2200 on 11thgrade Mathematics TAKS
(TSI Math** 2005–07)
Number
% of
students
who meet
or exceed
the criteria
% of students
in Min. /
Regular /
Indiv. Edu.
Program
% of total
high
school
graduates
Number
% of total
high
school
graduates
% of
students in
RHSP /
DAP /
Advanced
Program
1996–97 181,866
107,763
59.3%
74,103
40.7%
57,129
31.4%
39,055
21.5%
26.6%
1997–98 197,186
119,331
60.5%
77,855
39.5%
60,140
30.5%
41,849
21.2%
27.2%
1998–99 203,393
119,473
58.7%
83,920
41.3%
61,977
30.5%
41,631
20.5%
27.2%
10.9%
1999–00 212,925
128,104
60.2%
84,821
39.8%
63,461
29.8%
44,433
20.9%
27.3%
11.2%
2000–01 215,316
105,201
48.9%
110,115
51.1%
65,543
30.4%
45,751
21.2%
26.9%
7.8%
2001–02 225,167
94,163
41.8%
131,004
58.2%
65,720
29.2%
57,345
25.5%
26.6%
5.5%
2002–03 238,109
86,382
36.3%
151,727
63.7%
70,550
29.6%
59,014
24.8%
27.2%
3.7%
2003–04 244,165
77,194
31.6%
166,971
68.4%
****
****
****
****
27.0%
2004–05 238,759
66,034
27.7%
172,725
72.3%
****
****
****
****
****
43%
2005–06 ****
****
****
****
****
****
****
****
****
****
48%
2006–07
49%***
The data in this table are from the Texas PK–16 Public Education Information Resource at www.texaseducationinfo.org/tpeir/Index.asp (specifically, the High
School Graduates’ Longitudinal Analysis–Statewide—the combined data for ISD/CSD [Independent School District / Consolidated School District] and Open
Enrollment Charter School District); the Texas Higher Education Coordinating Board’s High School to College Linkages (available at
www.txhighereddata.org/Interactive/HSCollLink.cfm); and the Texas Education Agency’s Academic Excellence Indicator System reports (available at
www.tea.state.tx.us/perfreport/aeis; specifically, the SAT/ACT Results At/Above Criterion data and TAKS data). Retrieved 10/25/06.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
20.3%
18.2%
21.9%
23.8%
24.7%
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*TASP-A refers to the original college entrance examination known as TASP (Texas Academic Skills Program) and to other placement tests allowed after 1997,
such as the College Board’s ACCUPLACER and Multiple Assessment Programs and Services (MAPS) tests, and ACT’s ASSET and COMPASS tests.
**The Texas Success Initiative (TSI) is a program designed to improve student success in higher education; it began in 2003, after the state legislature replaced
the TASP with the TSI. The TSI requires that students be assessed in reading, writing, and mathematics before they enroll in an institution of higher
education, and that they be advised based on the results of that assessment. The TSI standard is set by the Texas Higher Education Coordinating Board; this
standard is the score that students must achieve on the exit-level TAKS (normally taken in 11th grade) to be considered college ready. Meeting the standard
exempts students from taking a test for the TSI. Under the TSI, as with the TASP, Texas institutions of higher education can use a variety of examinations to
determine if a student is college ready.
***The 2006–07 TSI percentage is from the Texas Assessment of Knowledge and Skills Summary Report—Test Performance (Grade 11 Exit Level)—the
section on Demographic Performance Summary—Mathematics, found at www.tea.state.tx.us/student.assessment/reporting/results/summary/
sum06/taks/gr11_apr06.pdf (retrieved 10/25/06). These results are released earlier than TEA’s Academic Excellence Indicator System report and are the
foundation of the AEIS reports’ achievement data. The rate of students scoring ≥ 2200 on the 11th-grade mathematics TAKS (TSI Math** 2005–07), when
computed with AEIS data only, will be slightly higher, as only an accountability subset of students is reported on the AEIS.
****Data for 2003–04, 2004–05, and 2005–06 were not available at the time this table was developed.
•
The 2007–08 Texas graduating class will be the first class required to complete the Recommended High School Program as the default graduation plan.
•
Not all graduates of the Recommended High School Program attend a four-year institution, nor do all graduates of the Minimum High School Program
attend a two-year institution.
•
The SAT / ACT are norm-referenced tests, while the TAKS is a criterion-referenced test.
Observations on Tables 5 through 8, High school mathematics course enrollment in Texas (2002–03 to 2005)
Student enrollment rates in various Texas high school mathematics courses have not shifted significantly over the four years
represented here. Nor have the percentages of students who received credit for completing the courses changed significantly. More
students are enrolled in each mathematics course each year, but not all students stay through the end of the course or receive credit for
it in the given year. For instance, only 62% of the students enrolled in Algebra I in spring 2003 received credit for the course in that
year. Thus 38% of those Algebra I students did not receive credit. Understanding the effect on the educational system of students who
repeat a mathematics course in high school is an important factor in the discussion of four years of high school mathematics.
The effect on student enrollment rates of the state’s requiring Algebra II as part of the Recommended High School Program4 will not
be seen until the enrollment figures for 2006–07 are available sometime in fall 2007. The effect of this Algebra II requirement on
4
Algebra II is currently required for students graduating under the Recommended High School Program if they entered 9th grade in 2004–05. Beginning
with the 2004–05 school year, a student entering grade 9 shall complete either the Recommended High School Program or the Distinguished Achievement
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graduation and college readiness rates will not be seen for several more years, when the high school juniors of 2006–07 enter college
in 2008–09, and the data becomes available about two years after that (2010–11). As with most policy implementation scenarios,
many schools try to shift to the new policy ahead of the deadline. For example, the senior class of 2006–07 may have been encouraged
to graduate under the Recommended High School Program, though they could graduate under the Minimum High School Program
without approvals. The policy currently under discussion—whether to require Algebra II as a prerequisite for the fourth mathematics
credit—would begin for 9th-graders next year (2007–08), and their fourth math credit would most likely occur in 2010–11. Note that
Algebra II enrollment in spring 2005 (263,097) is very close to the number of 11th-grade students for that year (274,815).
Although data is not available, considering Algebra I enrollment in middle school will help identify how many students are
progressing in a timely or accelerated manner through the high school mathematics curriculum. It would appear from the enrollment
data sets for fall and spring that students enrolled in 8th-grade Algebra I in the fall are coded differently in spring, as few middle
school campuses are represented in the spring data set.
Table 5. High school* mathematics course enrollment in Texas, 2002–03
Algebra I
Geometry
Algebra II
Mathematical
Models with
Applications
Precalculus
Advanced
Placement
Calculus AB
Advanced
Placement
Calculus BC
Advanced
Placement
Statistics
First
Independent
Study**
Fall 2002
370,398
293,422
223,979
54,425
84,363
21,343
3,743
7,064
5,010
enrolled
Spring 2003
308,448
321,262
243,713
69,254
90,295
21,649
4,678
6,481
6,799
enrolled
Spring 2003
265,542
286,135
221,801
57,516
81,625
19,198
4,400
5,729
6,057
completed
Spring 2003
192,559
231,057
187,304
49,995
74,849
18,187
4,284
5,444
5,324
received credit
% of spring
2003 enrolled
38%
28%
23%
28%
17%
16%
8%
16%
22%
who did NOT
receive credit
The enrollment data in this table was calculated by the Charles A. Dana Center based on a special-request course-enrollment report from the Texas Education
Agency. This special-request course-enrollment report was generated by TEA from the Public Education Information Management System (PEIMS) and
received by the Dana Center in June 2006.
Program; students must have parental and campus administrator approval to graduate under the Minimum High School Program. Under discussion by the State
Board of Education in November is whether to require Algebra II as a prerequisite for the fourth mathematics credit.
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8
*Enrollment figures may include middle school students. For example, many districts offer Algebra I at the 8th grade or earlier.
**Independent Study is listed in the K–12 Mathematics TEKS as “§111.52. Independent Study in Mathematics (One-Half to One Credit). (a) General
requirements. Students can be awarded one-half to one credit for successful completion of Independent Study in Mathematics. Required prerequisites:
Algebra II, Geometry. Students may repeat this course with different course content for a second credit. (b) Content requirements. Students will extend their
mathematical understanding beyond the Algebra II level in a specific area or areas of mathematics, such as theory of equations, number theory, non-Euclidean
geometry, advanced survey of mathematics, or history of mathematics. The requirements for each course must be approved by the local district before the
course begins. (c) If this course is being used to satisfy requirements for the Distinguished Achievement Program, student research/products must be
presented before a panel of professionals or approved by the student’s mentor.” (Retrieved 10/25/06, from www.tea.state.tx.us/rules/tac/chapter111.)
•
Does not include enrollment in Algebra I-4 of 12,076 and enrollment in another 24 courses with a total enrollment of 4,162. Algebra I-4 is a two-year
version of Algebra I that has been phased out. In it, students receive one local credit toward high school graduation and one credit for Algebra I for high
school graduation if districts request a waiver to offer this option. The other 24 courses include subjects such as linear programming and discrete math.
Statewide enrollment levels in each of these 24 courses is typically less than fifty students; therefore, those data are not included in this table.
Table 6. High school* mathematics course enrollment in Texas, 2003–04
Algebra I
Geometry
Algebra II
Mathematical
Models with
Applications
Precalculus
Advanced
Placement
Calculus AB
Advanced
Placement
Calculus BC
Advanced
Placement
Statistics
First
Independent
Study**
Fall 2003
362,635
299,510
234,452
53,414
88,857
21,569
5,382
6,975
8,540
enrolled
Spring 2004
313,496
329,670
254,083
66,720
91,213
22,022
4,965
7,240
9,955
enrolled
Spring 2004
271,033
293,810
231,390
54,988
82,689
19,598
4,591
6,357
8,668
completed
Spring 2004
197,263
238,793
197,328
47,965
76,369
18,512
4,494
6,048
7,336
received credit
% of spring
2004 enrolled
37%
28%
22%
28%
16%
16%
9%
16%
26%
who did NOT
receive credit
The enrollment data in this table was calculated by the Charles A. Dana Center based on a special-request course-enrollment report from the Texas Education
Agency. This special-request course-enrollment report was generated by TEA from the Public Education Information Management System (PEIMS) and
received by the Dana Center in June 2006.
*Enrollment figures may include middle school students. For example, many districts offer Algebra I at the 8th grade or earlier.
**Independent Study—see note on Table 5.
•
Does not include enrollment in Algebra I-4 of 7,939 and enrollment in another 19 courses with a total enrollment of 3,791. Algebra I-4 is a two-year version
of Algebra I that has been phased out. In it, students receive one local credit toward high school graduation and one credit for Algebra I for high school
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October 2006
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9
graduation if districts request a waiver to offer this option. The other 19 courses include subjects such as linear programming and discrete math. Statewide
enrollment levels in each of these 19 courses is typically less than fifty students; therefore, those data are not included in this table.
Table 7. High school* mathematics course enrollment in Texas, 2004–05
Algebra I
Geometry
Algebra II
Mathematical
Models with
Applications
Precalculus
Advanced
Placement
Calculus AB
Advanced
Placement
Calculus BC
Advanced
Placement
Statistics
First
Independent
Study**
Fall 2004
374,993
306,598
249,955
55,257
92,300
23,383
4,908
8,428
7,724
enrolled
Spring 2005
323,607
331,483
263,097
65,383
94,493
22,680
5,200
8,468
9,214
enrolled
Spring 2005
281,851
297,578
239,636
53,255
85,584
20,336
4,870
7,537
6,696
completed
Spring 2005
205,896
240,640
204,840
45,947
78,382
19,161
4,707
7,145
6,016
received credit
% of spring
2005 enrolled
36%
27%
22%
30%
17%
16%
9%
16%
35%
who did NOT
receive credit
The enrollment data in this table was calculated by the Charles A. Dana Center based on a special-request course-enrollment report from the Texas Education
Agency. This special-request course-enrollment report was generated by TEA from the Public Education Information Management System (PEIMS) and
received by the Dana Center in June 2006.
*Enrollment figures may include middle school students. For example, many districts offer Algebra I at the 8th grade or earlier.
**Independent Study—see note on Table 5.
•
Does not include enrollment in Algebra I-4 of 6,532 and enrollment in another 21 courses with a total enrollment of 3,682. Algebra I-4 is a two-year version
of Algebra I that has been phased out. In it, students receive one local credit toward high school graduation and one credit for Algebra I for high school
graduation if districts request a waiver to offer this option. The other 21 courses include subjects such as linear programming and discrete math. Statewide
enrollment levels in each of these 21 courses is typically less than fifty students; therefore, those data are not included in this table.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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10
Table 8. High school* mathematics course enrollment in Texas, 2005
Algebra I
Geometry
Algebra II
Mathematical
Models with
Applications
Precalculus
Advanced
Placement
Calculus
AB
Advanced
Placement
Calculus
BC
Advanced
Placement
Statistics
First
Independent
Study**
Fall 2005
383,115
311,423
256,550
54,412
95,903
23,743
5,086
9,366
9,949
enrolled***
The enrollment data in this table was calculated by the Charles A. Dana Center based on a special-request course-enrollment report from the Texas Education
Agency. This special-request course-enrollment report was generated by TEA from the Public Education Information Management System (PEIMS) and
received by the Dana Center in June 2006.
*Enrollment figures may include middle school students. For example, many districts offer Algebra I at the 8th grade or earlier.
**Independent Study—see note on Table 5.
***The data available from the Texas Education Agency as of June 2006 included enrollment only through fall 2005. Enrollment and course completion data for
the end of the 2005–06 school year should be available sometime in 2006–07.
•
Does not include enrollment in another 19 courses with a total enrollment of 2,308. The other 19 courses include subjects such as linear programming and
discrete math. Algebra I-4 is not listed here because there were no students enrolled in it in fall 2005. Statewide enrollment levels in each of these 19 courses
is typically less than fifty students; therefore, those data are not included in this table.
Observations on Table 9, Texas student enrollment in 11th and 12th grade compared to enrollment in advanced high school
mathematics
If one assumes that the majority of students in advanced high school mathematics courses—that is, Precalculus, AP Calculus AB, AP
Calculus BC, AP Statistics, and First Independent Study (requires Algebra II and Geometry prerequisite)—are either seniors or juniors
and seniors, then somewhere between one-half of the seniors and three-quarters of the juniors and seniors are not enrolling in these
advanced courses. To serve this not-enrolling population, we would need to double or triple the number of advanced mathematics
teachers. The data in Table 9 are supported by data that Dr. Clifford Adelman, a senior research analyst with the U.S. Department of
Education,5 presented to the Texas Higher Education Coordinating Board on October 9, 2006, showing that only 24% of students in
high school took mathematics beyond Algebra II during the 1990s in a geographic area that includes Texas, Arkansas, Louisiana, and
Oklahoma. Texas represented 64% of the student population in this area.
5
Adelman is the author most recently of the 2006 U.S. Department of Education report, The toolbox revisited: Paths to degree completion from high
school through college (Washington, DC: U.S. Department of Education), available at www.ed.gov/rschstat/research/pubs/toolboxrevisit.
The Charles A. Dana Center at The University of Texas at Austin
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October 2006
11
Table 9. Texas student enrollment in 11th and 12th grade compared to enrollment in advanced high school mathematics
Total number of students* in the following
advanced mathematics courses combined:
Precalculus, AP Calculus AB, AP Calculus
BC, AP Statistics, and First Independent
Study (requires Algebra II prerequisite)
Number of students
in 12th grade
Difference between
number of students in
12th grade and number
of students in advanced
mathematics
Number of students in
11th and 12th grade
Difference between
number of students in
11th and 12th grade
and number of students
in advanced
mathematics
373,352 (74%)
374,929 (73%)
381,632 (73%)
Spring 2003
129,902
237,905
108,003 (45%)
503,254
Spring 2004
135,395
242,771
107,376 (44%)
510,324
Spring 2005
140,055
246,863
106,808 (43%)
521,678
Fall 2005
144,047
**
**
The data in this table for number of 11th- and 12th-grade students is taken from Table 1 (which is from the Texas Education Agency’s Academic Excellence
Indicator System reports, www.tea.state.tx.us/perfreport/aeis, retrieved 10/19/06). The enrollment data in this table was calculated by totaling the numbers in the
last five columns in each of Tables 5 through 8. The differences and percentages were computed by the Charles A. Dana Center.
*Not all students in advanced mathematics are juniors or seniors.
**Data not yet available.
Observations on Table 10, Percentage of total Texas student enrollment receiving mathematics course credit
In any one year, about two out of three Texas high school students receive credit in a mathematics course. For example, potentially
67% of the total enrolled students in grades 9–12 in 2004–05 received credit in a high school mathematics course. (We say potentially
because this percentage may be smaller if any of the students receiving credit in this count are in middle school.) The data in this table
show the extent of the dropout or repeat problem.
For many students, it will take more than four years to complete four years of high school mathematics. The enrollment data presented
thus far does not address those students enrolled in dual-enrollment (high school and college) courses. Data on the number of students
in dual-enrollment mathematics courses was not available—instead, the far-right column in Table 10 reflects the percentage of high
school students completing a dual-enrollment course of any kind (not just mathematics). It is reasonable to estimate that dual
enrollment in College Algebra is behind student dual enrollment in more popular courses such as English/Language Arts,
Government, History, and Biology. In other words, based on this assumption and the figures reported below (which include students
receiving credit in advanced high school mathematics courses) there are not a significant number of students receiving credit for dualenrollment mathematics courses statewide. Thus, we estimate that close to one-third of Texas high school students are not receiving a
mathematics credit in high school in a given year. Table 11 will attempt to address the number of students not enrolled in any
mathematics course in high school.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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12
Table 10. Percentage of total Texas student enrollment receiving mathematics course credit
Received
Completion of
Total who received
credit in
all advanced
credit in advanced high Total received
Year
Mathematical
courses and
school mathematics*
credit
Models with
dual
courses
Applications
enrollment**
Percentage of
Percentage of
Percentage of
Percentage of
Percentage of
Percentage of
Percentage of
Number
Number
total enrolled
total enrolled
total enrolled
total enrolled
total enrolled
total enrolled
total enrolled
9–12
9–12
9–12
9–12
9–12
9–12
9–12
2002–03
1,174,367
16%
20%
16%
4%
108,088
9%
65%
20%
2003–04
1,194,649
17%
20%
17%
4%
112,759
9%
67%
20%
2004–05
1,216,049
17%
20%
17%
4%
115,411
9%
67%
***
The data in this table for total students enrolled in grades 9–12 is taken from Table 1. The Dana Center computed the “received-credit” percentages for each
separately listed mathematics course by dividing the number of students who received credit in a given course each year, as recorded in Tables 5 through 7, by
the total number of students enrolled in grades 9–12 for that year. The credit data for advanced high school mathematics courses in Table 10 was calculated by
totaling the numbers of students who received credit in the last five columns in each of Tables 5 through 7 and dividing by the total number of students enrolled
in grades 9–12 for the corresponding year. For example, to calculate the “total who received credit in advanced high school mathematics courses” in 2002–03, we
added the numbers in the last five columns in the “Spring 2003 received credit” row in Table 5, which totaled 108,088. Then we divided 108,088 by the total
students enrolled in grades 9–12 for 2002–03, 1,174,367, to calculate 9%. The second to the last column on the right of Table 10 is the sum of the percentages
that precede it in each row. The far-right column in Table 10 is from the Texas Education Agency’s Academic Excellence Indicator System State Profile Reports’
Student Information, www.tea.state.tx.us/perfreport/aeis (retrieved 10/19/06).
*Advanced high school mathematics courses here means the same advanced courses as listed in Table 9: Precalculus, AP Calculus AB, AP Calculus BC, AP
Statistics, and First Independent Study (requires Algebra II and Geometry prerequisite).
**Advanced course / dual enrollment completion: This indicator is based on a count of students who complete and receive credit for at least one advanced course
in grades 9–12. The definition of advanced courses includes dual enrollment courses. Dual enrollment courses are those for which a student gets both high
school credit and college credit. Deciding who gets credit for which college course is described in Texas Administrative Code §74.25: “To be eligible to
enroll and be awarded credit toward state graduation requirements, a student must have the approval of the high school principal or other school official
designated by the school district. The course for which credit is awarded must provide advanced academic instruction beyond, or in greater depth than, the
essential knowledge and skills for the equivalent high school course. Appendix C lists all courses identified as advanced, with the exception of courses
designated only as dual enrollment. These are not shown, as the list could potentially include a large proportion of all high school courses.” This definition
was adapted from the Glossary for the Academic Excellence Indicator System, 2004–05, at www.tea.state.tx.us/perfreport/aeis/2005/glossary.html#advcourse
(retrieved 10/26/06). Appendix C, “Advanced Academic Courses: 2004–05 Academic Excellence Indicator System” (retrieved 10/27/06 from
www.tea.state.tx.us/perfreport/aeis/2005/glossary.html#appendc) lists advanced mathematics courses as Calculus AB, Calculus BC, AP Statistics,
Mathematical Methods Subsidiary Level, Mathematical Studies Subsidiary Level, Mathematics Higher Level, Advanced Mathematics Subsidiary Level,
Precalculus, Independent Study in Mathematics (1st time), Independent Study in Mathematics (2nd time).
Total students
enrolled,
grades 9–12
•
Received
credit in
Algebra I
Received
credit in
Geometry
Received
credit in
Algebra II
Data on the number of students in dual enrollment mathematics courses was not available; instead, dual enrollment here reflects the percentage of Texas high
school students completing a dual-enrollment course of any kind (not just mathematics). It is reasonable to estimate that dual enrollment in College Algebra
is behind student dual enrollment in more popular courses such as English/Language Arts, Government, History, and Biology. By definition, the last column
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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13
must include the 9% of students receiving credit in advanced mathematics courses. Therefore, the number of students that complete a college mathematics
course during high school may be relatively small.
***Data for 2004–05 were not available at the time this table was developed.
Observations on Table 11, Texas high school enrollment figures by grade level compared to high school mathematics
enrollment
The small percentage of students not enrolled in mathematics (7%) is not a complete picture of how many high school students are not
enrolled in mathematics. Because the high school mathematics course enrollment figures in Table 11 may include middle school
students who are taking high school mathematics, the actual number of high school students not enrolled in mathematics is probably
larger—perhaps as much as 10% of high school students are not enrolled in a mathematics course in a given year.
Further, as mentioned above, many more do not receive credit for the course in which they enrolled. Table 11 contains the same data
as Table 1, Texas high school enrollment figures by grade level, but adds the three columns on the far right about enrollment in high
school mathematics.
Table 11. Texas high school enrollment figures by grade level compared to high school mathematics enrollment
School
year
9th-grade students
Number
Percentage
increase over
previous
year
10th-grade
students
Number
Percentage
increase
over
previous
year
11th-grade
students
Number
Percentage
increase
over
previous
year
12th-grade
students
Number
Percentage
increase
over
previous
year
Total students
enrolled, grades 9–12
Number
Percentage
increase over
previous year
Total
enrolled
in high
school
math*
Number
Difference between
total enrolled and
total enrolled in
mathematics
Number
% of total
enrolled who
are not in
mathematics
2002–03 372,024
299,089
265,349
237,905
1,174,367
1,088,817 85,550
7.3%
2003–04 375,225
0.9%
309,100
3.3%
267,553
0.8%
242,771
2.0%
1,194,649
1.7%
1,111,094 83,555
7.0%
2004–05 383,353
2.2%
311,018
0.6%
274,815
2.7%
246,863
1.7%
1,216,049
1.7%
1,133,839 82,210
6.8%
The data in all but the three far-right columns of this table duplicate the data in Table 1. The data in the three far-right columns about enrollment in high school
mathematics was calculated by the Charles A. Dana Center based on a special-request course-enrollment report from the Texas Education Agency. This specialrequest course-enrollment report was generated by TEA from the Public Education Information Management System (PEIMS) and received by the Dana Center
in June 2006. The differences and percentages in the far-right column were computed by the Charles A. Dana Center.
*The total number of students enrolled in high school mathematics courses includes students at the middle school level.
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October 2006
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14
Summary
1. Why are we talking about a fourth year of mathematics?
Table 4 (Rates of graduation and rates of attendance in higher education under various Texas high school graduation programs) shows
the discrepancy between the number of students who enroll in a Texas higher education institution and the number of students who—
according to the SAT / ACT college-readiness criteria or the TASP-A or TSI mathematics standard—may be prepared for collegelevel mathematics.
If Texas wants to increase the number of high school graduates, increase the number of college-going high school graduates, and
increase the number of students prepared for college-level mathematics, we clearly must help a large portion—51% of the Texas high
school student population if using 2006–07 figures, and 71% if using 2002–03 figures—to become adequately prepared in
mathematics. Numerous studies6 show that the more mathematics completed, the more prepared students are for success in higher
education and the workplace.
2. Will additional mathematics requirements in high school increase the dropout rate?
The data from Table 3 (Texas completion-rate status)—which show from 1996–97 to 2003–04 an increase in the graduation rate of
nearly 9% and a decrease in the dropout rate of more than 5%—do not support the argument that increased mathematics requirements
will increase dropouts. Further, since 1996–97, the state’s implementation of the Texas Essential Knowledge and Skills (TEKS) has
increased the rigor of our K–12 mathematics curriculum, and the state’s implementation of the Texas Assessment of Knowledge and
Skills (TAKS) has increased the rigor of our statewide test. Yet even with this increased rigor, the percentage of dropouts has declined
(5%), and the percentage of high school graduates has increased (9%). It will be valuable to see the effect on dropout rates and high
school graduation rates of requiring all students to take Algebra II (Algebra II is currently required for students graduating under the
Recommended High School Program if they entered 9th grade in 2004–05; see footnote 4 for more information), but we have not had
time to see the outcome of this policy.
The data from Table 1 (Texas high school enrollment figures by grade level), Table 2 (Decline in Texas high school enrollment by
student cohort between grades), and Table 10 (Percentage of total Texas student enrollment receiving mathematics course credit) point
6
See, for example, many of the studies cited in the Dana Center’s companion to this paper: “Mathematics in the Fourth Year of High School:
Information Relevant to Proposed Changes to Mathematics Requirements for Graduation in Texas,” available at
www.utdanacenter.org/mathtoolkit/support/mathrequirements.php.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
www.utdanacenter.org
15
to a serious problem in students dropping out between 9th and 10th grade. This is a well-known phenomenon, and efforts have been
made and are being made to address the problem (such as moving 9th-graders to their own campus).
Tables 5 through 7 (High school mathematics course enrollment in Texas, 2002–03 to 2004–05) show that a high percentage of
students do not receive credit in Algebra I (typically a freshman course). At least 36% did not receive credit in the three years for
which we have data. Thus, if Texas wants to continue to decrease the dropout rate (see the far-right column in Table 3, Texas
completion-rate status), then improving the rate at which 9th-graders receive credit for Algebra I would help. Without increased
student success rates in Algebra I, our educational system will continue to struggle to provide opportunities for students to access—
and succeed in—the mathematics courses that follow.
3. How many more students will take advanced mathematics if the Algebra II prerequisite is enacted?
Table 9 (Texas student enrollment in 11th and 12th grade compared to enrollment in advanced high school mathematics) reflects that
potentially 57% of 12th-grade students in 2004–05 (spring 2005) enrolled in an advanced mathematics course. That is, in spring 2005,
140,055 students enrolled in an advanced mathematics course, out of a total 12th-grade student enrollment of 246,863—but as the
table notes, some students enrolled in advanced mathematics might be grade 11 students or below. Continuing with the assumption
that those receiving credit in advanced mathematics courses are all 12th-graders, then the percentage of 12th-graders receiving credit
in 2004–05 is 47%: 115,411 (total received credit in advanced high school mathematics courses, from Table 10) divided by 246,863
(number of students in 12th grade in spring 2005, from Table 9). Thus, from these two numbers above—the 57% enrolled in an
advanced mathematics course, less the 47% receiving credit—it could be approximated that 10% of those enrolled did not receive
credit, assuming they were all 12th-graders.
From Table 11 (Texas high school enrollment figures by grade level compared to high school mathematics enrollment), one can see
that in each school year from 2002–03 to 2004–05, about 7% of high school students are not enrolled in any high school mathematics
course. If one assumes that the majority of these non-enrolled students are seniors, and assumes further that they have finished four
years of mathematics, that still leaves at least 36% (100% minus 57% enrolled in advanced mathematics minus 7% not enrolled in any
mathematics) of students currently enrolled in Algebra II or lower mathematics courses.
If we wish to reduce the percentage of students graduating with the Minimum High School Program to between 0% to 15%, we would
need to see an additional 46% of the graduating class pass an advanced mathematics class (this is made up of the 36% not enrolled in
advanced mathematics classes, plus the 10% not passing advanced mathematics classes in which they are enrolled). If the 7% of
students not enrolled in mathematics (Table 11) have not actually completed a fourth high school mathematics credit or a course
beyond Algebra II, then the 46% who need to pass an advanced mathematics class must be increased by 7%.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
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16
4. How many more teachers will be required to teach the additional students in courses beyond Algebra II?
If the state mandates that students pass an Algebra II prerequisite before they can take the fourth mathematics credit for graduating
under the Recommended High School Program, then this prerequisite for advanced mathematics courses will require that the number
of highly qualified teachers be doubled for those courses for the 12th-grade class.
Estimating this number of needed additional teachers based on the size of the fall 2005 advanced course enrollment (Table 9—
144,047), a class size of 30 students, and a teaching load of 6 classes a day (so one teacher can serve 180 students), this would amount
to another 800 mathematics teachers (or more) statewide, certified at the high school level.
If Algebra II is not made a prerequisite for students to pass before they can pursue the fourth mathematics credit, then the increase in
teachers needed to teach a fourth year of mathematics in all Texas high schools is difficult to determine. If we assume that more
students will be taking more high school mathematics than ever before, then we will need more mathematics teachers, with or without
the Algebra II prerequisite.
If one assumes that the 7–10% (per Table 11 and the observations on Table 11) of students not enrolled in a high school mathematics
course during high school should be enrolled in mathematics, then conservatively we need enough teachers to serve this 7%.
Estimating this number of needed additional teachers based on 7% of the 2004–05 total enrolled in high school (Table 11—total
enrolled is 1,216,049, so 7% is 85,123 students), and based on a class size of 30 students and a teaching load of 6 classes per day,
would amount to another 472 mathematics teachers statewide.
If the students not enrolled in mathematics have completed their four required credits because they enrolled in high school
mathematics during middle school, then there is no increase needed to the number of high school mathematics teachers. We do not yet
know the effect of the current state policy of requiring that most or all Texas high school students complete the Recommended High
School Program to graduate. There should have been an increase in the number of Algebra II teachers this school year (2006–07) due
to this policy change. Without current (2006–07) data, it is not possible to estimate well the additional number of teachers we need for
a fourth year of mathematics.
The Charles A. Dana Center at The University of Texas at Austin
October 2006
www.utdanacenter.org
17