Final report on the national survey of algebra teachers for the National Math Panel

Full text

FINAL REPORT ON THE NATIONAL
SURVEY OF ALGEBRA TEACHERS FOR
THE NATIONAL MATH PANEL
September 27, 2007
Thomas B. Hoffer
Lekha Venkataraman
E. C. Hedberg
Shobha Shagle
NORC at the University of Chicago
Presented to:
Marian Banfield and Tyrrell Flawn
National Math Panel
U.S. Department of Education
400 Maryland Avenue, S.W.
Washington, D.C. 20202-1200
Contact:
Tom Hoffer
National Opinion Research Center (NORC)
at the University of Chicago
1155 East 60th Street
Chicago, IL 60637
(773) 256-6097
(773) 753-7886 (Fax)
hoffer-tom@norc.uchicago.edu

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE I
TA B L E O F C O N T E N T S
Executive Summary..................................................................................................................iv
Teacher Background........................................................................................................................................... iv
Student Preparation ............................................................................................................................................ iv
Curriculum and Instruction................................................................................................................................ v
Conclusions........................................................................................................................................................ viii
Acknowledgments .................................................................................................................... x
Introduction ............................................................................................................................1
Analysis of Survey Variables......................................................................................................3
Teacher Background and Work Situation........................................................................................................ 3
Student Preparation ........................................................................................................................................... 10
Curriculum and Instruction.............................................................................................................................. 15
Views on Changing Secondary School Math Education ............................................................................. 26
Summary and Conclusions......................................................................................................33
Appendix A. Survey Methodology...........................................................................................36
Appendix B. Tables of Means for Survey Variables, by School Classification Variables.......44
Appendix C. Variables Used in the Regression Equations, and Tables of Regression
Estimates ..........................................................................................................53
Appendix D: Means and Confidence Intervals for Items in the National Survey of Algebra
Teachers ...........................................................................................................66
Appendix E: NSAT Questionnaire.........................................................................................80

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE II
LI S T O F T A B L E S A N D FI G U R E S
Table 1: Demographic and professional characteristics of Algebra I teachers: 2007 ..................4
Table 2: School characteristics of Algebra I teachers: 2007 ............................................................6
Table 3. Percentages of Algebra I teachers reporting various characteristics of their classes
and Schools: 2007 .....................................................................................................................................7
Table 4. Average time (in minutes) Algebra I teachers spent on various activities: 2007 ...........8
Table 5. Target Class Student Behavior: 2007...................................................................................9
Table 6. Class size of target class, by extent to which the teacher considers Large class sizes to
be a problem in the school: 2007 ...........................................................................................................9
Table 7. Teachers’ reports on student preparation for Algebra I: 2007 ......................................10
Figure 1. Percentage distribution of composite student preparation scale score: 2007..............11
Figure 2. Teachers’ Ratings of Student Problems in Various Areas of Mathematics: 2007.......13
Figure 3. Teachers’ Ratings of Local District Expectations for Student Proficiency with
Algebra I: 2007........................................................................................................................................16
Figure 4. Teachers’ Ratings of State or Local School District Mathematics Content Standards
for Algebra I: 2007..................................................................................................................................17
Figure 5. Teachers’ Ratings of State or Local School District Mathematics Assessments of
Algebra I Outcomes: 2007.....................................................................................................................17
Table 8. School Problems Reported by Algebra Teachers: 2007 ...........................................................18
Figure 6. Teachers’ Ratings of Various Aspects of the Algebra I Textbook Used in Target
Class: 2007 ...............................................................................................................................................19
Figure 7. Percentage distribution of composite textbook favorability ratings scale score: 2007...
.................................................................................................................................................20
Figure 8. Teachers’ Ratings on Helpfulness of Computer-Based Instructional Tools in Algebra
I Target Class: 2007 ................................................................................................................................21
Table 9. Frequency of using computers in the target class, by extent to which insufficient
access to computers is a problem in the school: 2007 .....................................................................22
Figure 9. Frequency of Using Various Instructional Materials and Tools in Algebra I, by Grade
Level of Target Class: 2007 ...................................................................................................................23
Table 10: Frequency of Graphing Calculator Use, by Grade Level of Target Class and
Urbanicity: 2007 ......................................................................................................................................24
Table 11. Frequency of using graphing calculators, by extent to which insufficient access to
graphing calculators is a problem in the school: 2007......................................................................25
Table 12: Frequency of Physical Object Use, by Grade Level of Target Class: 2007 ..........................26
Table 13. Teachers’ evaluation of professional development: 2007...............................................27
Figure 10. Distribution of teachers’ ratings of how well their pre-service education program
prepared them to teach Algebra I : 2007.............................................................................................27
Figure 11. Distribution of teachers’ ratings of how well their professional development
opportunities have helped them teach Algebra I: 2007.....................................................................28
Table 14. Teachers’ Ratings on Availability and Quality of Remedial Help for Algebra I
Students: 2007 .........................................................................................................................................29
Table 15. Percentage of Algebra I teachers reporting students with different abilities and skills
taking the same class is a problem, by whether school offers different levels based on ability:
2007 .................................................................................................................................................29

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE III
Figure 12. Extent to which students with different abilities and interests taking the same
Algebra I class is a problem: 2007........................................................................................................30
Figure 13. Extent to which too little parent/family support is a problem in school: 2007..........31
Table 16: Frequencies of Reported Challenges to Teaching Algebra I by Class Grade Level and
Type of School: 2007..............................................................................................................................32
Table 17: Reported Challenges to Teaching Algebra I by Years of Experience: 2007...............33
Table A.1. Numbers of Sampled Schools, Schools that Provided Rosters of Algebra I teachers,
and Algebra I teachers, by Sample Stratum: 2007..............................................................................39
Table A.2. Questionnaire and followup mailing dates and numbers of Algebra I teachers, by
mailout cohort: 2007 ..............................................................................................................................41
Table A.3. Number of Algebra I teachers sampled, ineligible, refusing, and completing the
questionnaire, and survey response rate, by sample variables: 2007 ...............................................42
Table A.4. Number of Algebra I teachers sampled, ineligible, refusing, and completing the
questionnaire, and survey response rate, by sample stratum: 2007 .................................................43
Table C.1 Regressions of teachers' summary ratings of student background preparation for
Algebra I on grade level and class size of the target class, and school and teacher demographic
variables, 2007. ........................................................................................................................................55
Table C.2 Regressions of teachers' summary ratings of importance-weighted preparation for
Algebra I on grade level and class size of the target class, and school and teacher demographic
variables, 2007. ........................................................................................................................................56
Table C.3 Regressions of teachers' summary ratings of content standards for Algebra I in their
state or local district on school grade level and class size of the target class, and school and
teacher demographic variables, 2007. ..................................................................................................57
Table C.4 Regressions of teachers' summary ratings of assessment standards for Algebra I in their
state or local district on school grade level and class size of the target class, and school and
teacher demographic variables, 2007. ..................................................................................................58
Table C.5 Regressions of teachers' summary ratings of Algebra I textbooks on grade level and class
size of the target class, and school and teacher demographic variables, 2007...............................59
Table C.6 Regressions of teachers' summary ratings of technology use in Algebra I on grade level
and class size of the target class, and school and teacher demographic variables, 2007. .............60
Table C.7a Regressions of teachers' summary ratings on the helpfulness of pre-service teacher
training in teaching Algebra I on grade level and class size of the target class, and school and
teacher demographic variables, 2007. ..................................................................................................61
Table C.7b Regressions of teachers' summary ratings on the helpfulness of professional
development for teaching Algebra I on grade level and class size of the target class, and school
and teacher demographic variables, 2007............................................................................................62
Table C.8 Regressions of teachers' summary ratings of remedial help for Algebra I students on
grade level and class size of the target class, and school and teacher demographic variables,
2007...........................................................................................................................................................63
Table C.9 Regressions of teachers' summary ratings of extent to which they see different levels of
students in the same Algebra I class as a problem in their school on grade level and class size of
the target class, and school and teacher demographic variables. .....................................................64
Table C.10 Regressions of teachers' summary ratings of family participation is a problem in Algebra
I on grade level and class size of the target class, and school and teacher demographic variables,
2007...........................................................................................................................................................65

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE IV
EX E C U T I V E SU M M A R Y
This report presents findings from a study of a nationally-representative sample of public
school Algebra I teachers, the National Survey of Algebra Teachers (NSAT). A sample of 310
schools was selected from a comprehensive list of public schools which included the eighth grade or
higher. Of the 310 schools selected, 258 agreed to provide rosters of their Algebra I teachers. A total
of 1,026 teachers were identified on this basis, and 743 (72%) returned completed questionnaires by
the July 1, 2007 close of data collection. The report begins with a demographic and professional
profile of the public school Algebra I teachers, and then presents findings related to the research
questions identified by the National Mathematics Advisory Panel to guide the study.
TE A C H E R BA C K G R O U N D
The Algebra I teachers are predominately female (66%), white (91%), and had a median age
of 41 years old. The median years of teaching experience was 9 years and they had taught algebra
for a median of 6 years.
In terms of education, all had at least a baccalaureate degree and 51% had an MA/MS or
other advanced degree. About 44% majored in mathematics and another 24% minored in
mathematics during college; 8% earned an advanced degree in mathematics.
About 28% of the Algebra I teachers were teaching at the middle or junior high school level, while
almost all of the other 72% were teaching in high schools (less than 5% are in combined middle-
high schools).
ST U D E N T P R E P A R A T I O N
Research Question #1: How do the teachers rate the preparation of students coming into their
Algebra I classes? Are there widespread problems, or are problems confined to individual students?
The teachers generally rated their students’ background preparation for Algebra I as weak.
The three skill areas in which teachers report their students have the poorest preparation are rational
numbers, word problems, and study habits (Table 7).
The teachers’ ratings of student preparation generally did not vary much by school
demographic. The main point of difference was that teachers of classes that primarily enroll 7
th
or

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE V
8
th
graders rated their students’ backgrounds more highly, by 0.87 standard deviations (p<.001). The
grade level of the class is likely to be a proxy for the ability level of the class, with 8
th
grade being the
advanced group, 9
th
grade the average group, and 10
th
and higher the lower groups.
Research Question #2: To the degree that the teachers believe students need to be better prepared,
what are the major shortcomings?
The teachers were asked to rate the importance of a “solid foundation” in the each the 15
skill/knowledge areas asked about with respect to their target class students’ background
preparation. Since the same background skills and knowledge for which the teachers rated student
background as inadequate were also rated as important, the following areas emerge as the major
shortcomings: rational numbers, word problems, and study habits.
Research Question #3: Given their experience with in-coming students, would they change the
level of emphasis placed on mathematics topics at the elementary level? If so, how would they
change it?
 Would they put more or less emphasis on basic understandings or arithmetic and whole
number, fraction and decimals operations?
 Would they put more or less emphasis on helping students master basic concepts?
These questions are covered to some extent in the open-ended item III.2, “Please provide a
brief description of any changes you would like to see in the curriculum leading up to Algebra I in
your district.” Of the 743 teachers who returned completed questionnaires, 578 provided verbatim
responses to this item.
The most frequent type of suggestion among the 578 respondents was a greater focus in
primary education placed on mastery of basic mathematical concepts and skills.
CU R R I C U L U M A N D I N S T R U C T I O N
Research Question #4: How do they rate their state and local district curricular expectations in
algebra for PK-12? How do they rate the state or local school district mathematics standards and
math tests that they currently use?
 The modal response (67%) from teachers is that they feel that local expectations for student
proficiency in Algebra I are “about right”, while about equal numbers rated them as “too
high” (8%) or “too low” (11%) (see Figure 3).
 The teachers were also generally favorable about content standards for Algebra I in their
state or local district. A majority (53%) of teachers feel that the content standards are good

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE VI
and 16% rate them as excellent. Only about 5% rated their content standards as poor (see
Figure 4).
 Teachers were less positive about state and local assessment standards, but the modal
response (43%) was still that they were “good”. About 9% rated them as excellent and 15%
rated them as poor (see Figure 5).
Research Question #5: How do they rate their textbook (or textbooks in general) regarding algebra
instruction?
The questionnaire included several items asking for the teacher’s evaluation of the textbook
they use in the target class (items I.8a-i). For the most part, teachers were satisfied with their texts’
topics (Figure 7). The teachers rated their textbook least positively on the degree to which it is well
suited for the needs of a diverse population of students (Figure 6).
Research Question #6: How do the teachers rate online technology tools?
The questionnaire included questions asking how often the teachers used computer-based
instructional tools (item I.5f), the extent to which insufficient access to computers is a problem in
their school (item II.1a), and how much they agreed or disagreed with the proposition that
“Computer-based instructional tools (software) are helping Algebra I students in my Target Class”
(item I.6).
The data indicated that the average response to how frequently these tools are used was
about 1 (=“less than once a week”) on a scale that ranged from 0=never to 4=everyday (Table 9 and
Appendix D). The generally-low levels of computer use does not appear to be a reflection of
insufficient access. About half (49%) of the teachers reported that insufficient access to computers
was not a problem in their schools and another 28% reported insufficient access to be a minor
problem (Table 9). The teachers’ ratings of the helpfulness of computer-based instructional tools
were mixed, with 29% agreeing somewhat or agreeing strongly with the proposition that computers
were helpful and 38% disagreeing somewhat or disagreeing strongly (34% neither agreed nor
disagreed) (Figure 8).
Research Question #7: What is the role of the calculator in the algebra course?
Questionnaire item I.5d asked how often the teacher uses graphing calculators in her or his
target class. Overall, 33% of the teachers reported never using graphing calculators and another
29% report using them less than once a week. About 31% used them everyday (18%) or almost
everyday (13%) (Table 10). Teachers’ reports of insufficient access to graphing calculators was
correlated with reports of low usage (Table 11).
Research Question #8: To what extent do the Algebra I teachers use physical objects
(“manipulatives”) as instructional tools?

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE VI I
The relevant questionnaire item for this question asked how often the teacher uses physical
objects, commonly referred to as manipulatives, in her or his target class (item I.5e). Overall, use of
manipulatives on an occasional basis was widespread, but very few (9%) teachers report using them
more than once a week or everyday. About 12% of the teachers reported never using manipulatives,
and about 60% reported using them less than once a week (Table 12).
Research Question #9: How do they rate their professional training?
Questionnaire items pertaining to professional training and development included
questionnaire items III.4a,b and possibly IV.19; items II.1f and j are also relevant. We examined
these items by the teachers’ years of teaching experience, and school classification variables.
 The Algebra I teachers generally reported that their training is not a problem (see Table 13),
but they were less positive about their pre-service and during their careers. In contrast, they
feel more negative about their training than they do about their own experiences with pre-
service training and professional development opportunities. Figures 10 and 11 also show
that most teachers do not see training as a problem.
Research Question #10: Is there sufficient and effective remedial help for students who are
struggling in algebra? What sort of assistance-based interventions would struggling students benefit
from the most?
Questionnaire items II.8a-b asked the teachers to rate the availability and quality of tutoring
or other remedial services for students struggling with Algebra I in their school.
 On average, teachers were generally satisfied with the services available (Table 14).
 Controlling for other demographic variables, remedial services were rated somewhat higher
by teachers in schools with high minority enrollments. Also controlling for other
demographic variables, female and black teachers are less satisfied with their schools’
remedial services. This may reflect a tendency for these teachers to assume advocacy roles
on behalf of their students. (See Appendix Table C.8.)
Research Question #11: Would students learn more if they were grouped by ability for instruction,
or is this approach counter-productive?
Questionnaire item II.2 asked whether the school offers different levels of Algebra I based
on ability; and 46% of the teachers indicated their schools did differentiate. Questionnaire item
II.1h asked teachers to rate the extent to which they see different levels of students in the same class
as a problem in their school. A substantial number of teachers considered mixed-ability groupings to
be a “moderate” (28%) or “serious” (23%) problem (see Figure 12). Teachers in schools that did
not offer different levels of Algebra I based on ability were more likely than their counterparts in

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE VI II
schools that do use ability grouping to consider mixed-ability classrooms to be a moderate or serious
problem (Table 15).
Research Question #12: Do they find more parents helpful in encouraging students in their
mathematics studies, or do too many parents make excuses for their children’s lack of
accomplishment?
Questionnaire item II.1i asked teachers to rate the extent to which they see “too little
parent/family support” as a problem in their school. The responses indicate that about 28% of the
algebra teachers feel family participation is a serious problem and another 32% believe lack of family
participation is a moderate problem (Figure 13).
Research Question #13: What do they see as the single most challenging aspect of teaching Algebra
I successfully?
This question (IV.20) included 10 response options: explaining material to students, handling
accelerated students, teaching procedures, explaining concepts, using diagrams or models effectively,
interpreting student errors and difficulties, working with unmotivated students, working with
advanced students, helping students whose home language is not English, making mathematics
accessible and comprehensible, and an “other” option.
The overwhelmingly most frequent response to this question was “working with
unmotivated students.” This was chosen by 58% of the middle school teachers and 65% of the high
school teachers (Table 16). The next most frequent response was “making mathematics accessible
and comprehensible to all my students,” selected by 14% of the middle school teachers and 9% of
the high school teachers.
CO N C L U S I O N S
The Algebra I teachers generally reported that students were not adequately prepared for
their courses. The teachers rated as especially problematic students’ preparation in rational numbers,
solving word problems, and basic study skills. A lack of student motivation was by far the most
commonly-cited biggest challenge reported by the teachers. The problems the teachers identified
with the pre-Algebra I mathematics curriculum and instruction and with the lack of parental support
for mathematics were likely to be contributing factors to the lack of adequate student preparation
and motivation.
In contrast, the teachers generally held favorable views with respect to their own
professional preparation and the Algebra I curriculum and instructional services. Taken together

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE IX
with the generally negative ratings of students’ preparation and motivation suggests that careful
attention to pre-algebra curriculum and instruction in the elementary grades is needed, both to
remedy the specific skill deficiencies reported by the Algebra I teachers and to identify ways in
which negative attitudes toward mathematics develop and might be changed.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE X
AC K N O W L E D G M E N T S
This report draws on the data collected from 743 Algebra I teachers in public schools across
the United States in spring 2007 by the National Survey of Algebra Teachers (NSAT). We first want
to express our appreciation to these teachers for taking time from their busy schedules to complete
and return the questionnaires. We also want to thank the principals of the schools for supporting
the project and providing lists of the Algebra I teachers, and to the officials at the district offices
who granted access to the principals and teachers.
The content of the questionnaires primarily reflects the expertise and diligence of the
National Mathematics Advisory Panel members who served on the subcommittee directing the
NSAT: Tom Loveless, Chair; Francis “Skip” Fennel; Vern Williams; and Deborah Ball. The NSAT
project was staffed by Marian Banfield of the U.S. Department of Education, and the authors are
particularly indebted to her for guidance and encouragement throughout the project.
The questionnaire development process benefited greatly from reviews by Jenny Nagaoka of
the Consortium on Chicago School Research at the University of Chicago and by the mathematics
faculty at the University of Chicago Laboratory Schools.
At NORC, Tom Hoffer directed the project and Lekha Venkataraman managed the day-to-
day activities of instrument development and pretesting, sample recruitment, mailouts, and data
collection. Shobha Shagle developed reports for monitoring sample recruitment and data collection,
and combined, documented, and cleaned the data files. Michael Yang provided expert guidance on
the sample design and selection, as well as sample weighting. E. C. Hedberg built the sample frame
files and conducted the data analysis for this report. Hector Flores managed the mailout activities at
NORC’s Production Center. We were ably assisted throughout the sample recruitment and data
collection stages by research assistant Kirstin Millius of the University of Chicago. Imelda Demus
and Isabel Guzman-Barron provided expert assistance with the report formatting. The project is
indebted to Harrison Greene, Senior Vice President for Education and Child Development Studies
at NORC for additional support of staffing and for teacher incentive funding.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 1
IN T R O D U C T I O N
The National Survey of Algebra Teachers (NSAT) surveyed a national sample of public
school Algebra I teachers during the 2007 spring school semester. The survey was designed to
collect detailed information about the teachers’ views on student preparation, motivation, work
habits, and skills – as well as teachers’ insights on how math is now taught, how earlier math
education could be improved to prepare more children to succeed at algebra, and what would help
all math teachers do a better job. The survey was designed to shed light on the experiences of
algebra teachers in different kinds of school systems – for example, low-income, mainly minority
schools vs. higher income, mainly white schools. Learning algebra is often a turning point in a
student’s math education – when the student either thrives and moves forward or struggles and
perhaps gives up on math – and the algebra teachers have a unique perspective on math education
that is well worth understanding in some detail.
The NSAT was designed to provide a nationally-representative sample of Algebra I teachers
in public schools. A sample of 310 schools was selected from a comprehensive list of public schools
which included the eighth grade or higher. The list was stratified by the type of grade configuration
in the school (middle or junior high school, high school only, combined middle and high school),
the number of students from low-income households, the number of racial/ethnic minority students
enrolled in the school, and school location (urban, suburban, rural). Within the strata defined by
these variables, schools were selected with probabilities of selection proportional to the estimated
numbers of Algebra I teachers. Of the 310 schools selected, 258 agreed to provide rosters of their
Algebra I teachers. A total of 1,026 teachers were identified on this basis, and 743 (72.4%) returned
completed questionnaires by the July 1 close of data collection.
This report presents the survey results and provides initial analyses to identify important
sources of variability in the teacher reports. We begin with a demographic and professional profile
of the public school Algebra I teachers, and then present findings related to the research questions
identified by the National Mathematics Advisory Panel to guide the study. The survey methodology
and data collection results are described in Appendix A. A full set of tabulations of the main survey
variables is included in Appendix B. Charts and graphs are used throughout the report to improve
readability, and the numbers upon which they are based are displayed in the Appendix B tables.
Multiple regression models are estimated to provide compact summaries of the influences of several
variables on the outcomes focused on in the report, and the regression tables are included in
Appendix C along with a descriptions of the independent variables used in the models. Appendix D

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 2
is a copy of the questionnaire used to collect the data. The report concludes with a summary of the
main findings and a discussion of their implications.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 3
AN A L Y S I S O F SU R V E Y V A R I A B L E S
TE A C H E R BA C K G R O U N D A N D W O R K SI T U A T I O N
A profile of the demographic and professional backgrounds of the academic year 2006-2007
Algebra I teachers in U.S. public schools is shown in Table 1. These teachers were predominately
female (66%), white (91%), and had a median age of 41 years old. The Algebra I teachers’ median
years of teaching experience was 9 years and had taught algebra for a median of 6 years. In terms of
education, all had at least a baccalaureate degree and about half had an MA/MS or other advanced
degree. About 44% majored in mathematics and another 24% minored in mathematics during
college; about 15% of those who earned an advanced degree specialized in mathematics (Table 1).

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 4
TABLE 1: DEMOGRAPHIC AND PROFESSIONAL CHARACTERISTICS OF ALGEBRA I
TEACHERS: 2007
ITEM
VALUES
VALID N
WEIGHTED %
Teacher is female
0-1
733
65.5
Teacher Racial/Ethnic Background:
Hispanic
0-1
727
5.7
American Indian or Alaska Native
0-1
715
2.1
Native Hawaiian or other Pacific Islander
0-1
715
0.2
Asian
0-1
715
2.5
Black or African American
0-1
715
3.6
White
0-1
715
91.0
Teacher age (quartiles)
1st: 22-30 yrs
27.4
2nd: 31-40 yrs
21.6
3rd: 41-50 yrs
25.1
4th: 51-65 yrs
26.0
All
729
100.0
Teacher’s total years teaching experience (quartiles)
1st: 0-3 yrs
31.1
2nd: 4-9 yrs
30.6
3rd: 10-18 yrs
21.6
4th: 19-41 yrs
16.7
All
733
100.0
Teachers years teaching Algebra (quartiles)
1st: 0-2 yrs
24.4
2nd: 3-6 yrs
24.4
3rd: 7-14 yrs
26.4
4th: 15-40 yrs
24.8
All
733
100.0
Teacher’s highest degree
Bachelors
51.4
Masters
40.9
Other advanced degree
7.7
All
737
100.0
Baccalaureate math background
Math major
738
43.6
Math minor
729
24.2
Graduate degree math background
Math specialty
400
15.2
Teacher Has Regular or Standard State Certification
0-1
733
82.4
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers,
2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 5
The distribution of Algebra I teachers by grade level (8
th
-12
th
) and by the main school-level
classification variables used throughout the report is shown in Table 2. The first three of these
school-level variables largely reflect student enrollment patterns across the country:
 Type of locale: the standard 3-level indicator of urban (27%), suburban (39%), and rural (34%)
school location.
 Percentage of students receiving free or reduced-price lunch: the percentage variable was recoded into
quartiles of the distribution of Algebra I teachers (median was 10% of the students are
eligible).
 Percentage of students who are black or Hispanic: the percentage variable was recoded into quartiles
of the distribution of Algebra I teachers (median is 27% of the students are black or
Hispanic).
The grade level variable at the bottom of Table 2 indicates that 32% of the algebra teachers were
teaching at the middle or junior high school level, while 50% were teaching in high schools and 18%
were in combined middle-high schools.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 6
TABLE 2: SCHOOL CHARACTERISTICS OF ALGEBRA I TEACHERS: 2007
SCHOOL CHARACTERISTICS
VALUES
UNWTD.
N
WTD. N
WTD. %
School urbanicity
Urban
252
23,088
26.9
Suburban
381
33,796
39.4
Rural
110
28,891
33.7
Total
743
85,775
100
Percent minority - quartiles
Low thru 10 percent
119
22,923
26.7
11 thru 27 percent
184
20,100
23.4
28 thru 48 percent
265
24,549
28.6
49 thru 81 percent
175
18,202
21.2
Total
743
85,775
100
Percent free/reduced lunch status - quartiles
Low thru 3 percent
219
21,998
25.6
4 thru 10 percent
227
24,537
28.6
11 thru 40 percent
182
22,318
26
41 thru 82 percent
103
16,358
19.1
Total
731
85,210
99.3
School grade level
Middle, junior high, or K-8
school
128
27,508
32.1
High school (9-12 or 10-12)
532
43,234
50.4
Other schools
83
15,033
17.5
All schools
743
85,775
100
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra
Teachers, 2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 7
The Algebra I teachers were asked to report several characteristics about a “target” Algebra I class
they were currently teaching. The following table shows the portion of algebra teachers and their
classes that fit various criteria. Most teachers report that their class meets everyday (83%) and that
they have enough time to teach algebra adequately (77%). About half of the teachers’ schools offer
different levels of algebra based on student needs and about one-third of teachers report that their
class is part of block scheduling in their school.
The teachers were asked which student grade levels they were currently teaching in their Algebra I
classes. The ninth grade was reported most often, by 58% of all the algebra teachers. Tenth grade
was next (43%), followed by 8
th
grade (38%) and 11
th
grade (28%). A significant portion taught
seniors (17%), and only 7% reported teaching 7
th
graders. A significant number of the teachers
(15%) reported teaching special education students in their Algebra I class(es). (See Table 3.)
TABLE 3. PERCENTAGES OF ALGEBRA I TEACHERS REPORTING VARIOUS
CHARACTERISTICS OF THEIR CLASSES AND SCHOOLS: 2007
Classes and School
LOWER 95%
CI
MEAN
HIGHER 95%
CI
Target class meets everyday
76.1%
82.8%
89.4%
Feel they have enough time to adequately teach
70.7%
76.3%
81.9%
School offers different levels of Algebra I based on ability
39.3%
46.6%
54.0%
Target class is part of block scheduling
26.4%
33.9%
41.4%
Teachers Who Teach Algebra I to . . .
7th graders
3.7%
6.7%
9.7%
8th graders
31.2%
38.4%
45.7%
9th graders
50.6%
57.5%
64.5%
10th graders
36.9%
43.2%
49.5%
11th graders
22.3%
27.6%
32.8%
12th graders
12.3%
16.8%
21.3%
Special-education students
10.8%
15.1%
19.4%
Teachers’ estimates of how many students will fail their Algebra I course. . .
None of the students in target class
15.6%
21.7%
27.9%
1-10% of the students in target class
33.9%
40.7%
47.4%
11-20% of the students in target class
12.4%
18.0%
23.6%
21-30% of the students in target class
5.3%
8.3%
11.4%
31-40% of the students in target class
3.5%
5.6%
7.6%
41-50% of the students in target class
2.2%
3.3%
4.4%
50% or more of the students in target class
1.4%
2.5%
3.7%
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 8
With regards to rates of failing Algebra I, 22% of the teachers believed that none of the students in
their target class would fail, and another 41% expected 1-10% of their students would fail. A
substantial proportion of the teachers (20%) expected to fail more than 20% of their students.
Time allocations. Teachers were asked to report the number of minutes spent on various
activities. On average, a class period of algebra lasts about 1 hour. Teachers also averaged about 1
hour per day preparing for their classes during the school day. Teachers also spend time outside of
school in preparation, averaging 54 minutes per day. In comparison, teachers expect their students
to spend about 25 minutes per day on their Algebra I homework.
TABLE 4. AVERAGE TIME (IN MINUTES) ALGEBRA I TEACHERS SPENT ON VARIOUS
ACTIVITIES: 2007
Activity
LOWER 95% CI
MEAN
HIGHER 95% CI
In class per period
59.28
62.14
65.00
In preparation during a school day
57.25
61.16
65.07
In preparation for algebra outside of school
50.14
54.38
58.62
Expected time needed for target class students to complete
homework per day
23.28
24.81
26.33
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
As for the students in their target class, teachers are generally satisfied with their in-class behavior.
On average, teachers feel that most of their students come to class on time and attend class
regularly. Teachers also feel that more than half of their students generally come to class prepared,
pay attention, participate, take notes, and care about the grades they receive. Disruptions do not
appear be a major problem, as teachers report that few of their students create behavior problems.
Finally, teachers feel that few of their students have serious difficulties reading English.
In further analyses we found that teachers in urban schools were more likely to report that their
students presented behavior problems, while teachers in rural schools reported the best-behaved
students.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 9
TABLE 5. TARGET CLASS STUDENT BEHAVIOR: 2007
Item
LOWER 95% CI
MEAN
HIGHER 95% CI
Come to class on time
3.49
3.57
3.65
Attend class regularly
3.39
3.46
3.54
Come to class prepared with appropriate supplies and books
2.79
2.92
3.05
Create serious behavior problems
0.53
0.61
0.69
Regularly pay attention in class
2.70
2.82
2.93
Actively participate in class activities
2.57
2.69
2.80
Take notes
2.59
2.72
2.86
Have serious difficulties reading English
0.41
0.47
0.54
Care about what grade they receive
2.78
2.90
3.02
Scale: 0 = None, 1 = Some, 2 = About Half, 3 = Most, 4 = Nearly All
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
Size of target class. Most teachers have classes between 15 and 30 students, with 21-25 students
reported most often. However, we found a strong correlation (r = 0.54) between the size of a
teacher’s target class and whether or not they felt that class size is a problem (see Table 6). Of those
that felt is was not a problem, 90% of those teachers had class sized of 25 students or below. Of
those that felt it was a serious problem, almost 75% of those teachers had a class size above 25
students. There is a clear connection between class size and teachers’ feelings that it is a problem;
this correlation is across the board.
TABLE 6. CLASS SIZE OF TARGET CLASS, BY EXTENT TO WHICH THE TEACHER
CONSIDERS LARGE CLASS SIZES TO BE A PROBLEM IN THE SCHOOL: 2007
How much of a problem is class size?
SIZE OF TARGET CLASS
NOT A
PROBLEM
MINOR
PROBLEM
MODERATE PROBLEM
SERIOUS
PROBLEM
ALL
TEACHERS
Less than 15 students
19.19%
4.05%
2.00%
0.41%
9.90%
15-20 students
40.44%
21.93%
11.24%
4.24%
26.11%
21-25 students
29.56%
41.89%
24.07%
19.84%
30.82%
26 - 30 students
7.58%
28.13%
51.19%
38.46%
24.37%
31 - 35 students
1.99%
2.78%
10.05%
30.37%
6.90%
More than 36 students
1.24%
1.21%
1.45%
6.67%
1.90%
Total
100%
100%
100%
100%
100%
Chi-square = 296.6 (p<0.000), Correlation = 0.54 (p<0.00)
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 10
ST U D E N T P R E P A R A T I O N
Research Question #1: How do the teachers rate the preparation of students coming into their
Algebra I classes? Are there widespread problems, or are problems confined to individual students?
As noted in the previous section, the teachers were asked to report several characteristics
about a “target” Algebra I class they were currently teaching. The questionnaire items asking about
students’ preparation are in Section 1, question #4 (items 4a-4o). The topics are listed in Table 7
and ranked from the biggest problem (on the bottom) to the smallest (the top). These items range
from 1= excellent [preparation] to 4= poor [preparation].
TABLE 7. TEACHERS’ REPORTS ON STUDENT PREPARATION FOR ALGEBRA I: 2007
95% CI
Based on your experience with in-coming Algebra I students in
your Target Class, how would you rate students’ background in
each of the following areas of mathematics?
MEAN
LOW
HIGH
Whole numbers and operations with whole numbers
1.86
1.80
1.92
Working cooperatively with other students
2.32
2.26
2.37
Plotting points, and graphing lines on the four-quadrant coordinate plane
2.44
2.37
2.51
The concept of variables
2.48
2.42
2.54
Computation skills
2.53
2.47
2.60
Positive & negative integers and operations with positive & negative integers
2.58
2.51
2.64
Working independently
2.58
2.52
2.64
Solving simple linear equations and inequalities
2.80
2.74
2.86
Measurement formulas of basic geometric shapes
2.81
2.75
2.87
Manipulation of variables
2.82
2.76
2.88
Ratios, percents, rates, and proportions
2.83
2.77
2.90
Ability to use math in context that are identified as real world situations
2.94
2.89
3.00
Basic study skills and work habits necessary for success in math
3.00
2.94
3.06
Rational numbers and operations involving fractions and decimals
3.10
3.04
3.16
Solving word problems
3.26
3.20
3.32
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
As Table 7 shows, the three skill areas in which teachers report their students have the
poorest preparation are solving word problems, rational numbers and operations involving fractions
and decimals, and basic study skills and work habits. Student preparation is relatively strong in
whole numbers and operations with whole numbers, working cooperatively with other students, and
plotting points and graphing lines on the four-quadrant coordinate plane.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 11
The teachers’ responses to the various items in this battery are highly correlated with one
another and can be combined into a single “student preparation” summary scale. As is evident in
Figure 1, teachers generally feel their students are fair-to-poorly prepared for their algebra class
(alpha = 0.94).
FIGURE 1. PERCENTAGE DISTRIBUTION OF COMPOSITE STUDENT PREPARATION
SCALE SCORE: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
Differences in the teachers’ scale scores associated with types of classes and schools were
assessed using regression analysis. The estimated regression coefficients of the class-type and school-
level covariates are reported in Appendix Table C.1.
 The most consistent finding from the analyses is that, holding other factors constant,
teachers of classes that primarily enroll 7
th
or 8
th
graders rated their students’ backgrounds
more highly, by 0.88 standard deviations (p<.001). The grade level of the class is likely to be
a proxy for the ability level of the class, with 8
th
grade being the advanced group, 9
th
grade
the average group, and 10
th
and higher the lower groups.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 12
The regression analysis also finds that some school-level covariates were associated with
whether teachers feel their students are prepared. Teachers in schools with a high concentration of
minority students (greater than 81%) felt that their incoming students were less prepared, but this
difference was reduced and not statistically significant in the full regression equation. Interestingly,
there was only a weak association of teacher ratings with the schools’ free/reduced lunch
concentrations. Teachers’ opinions of their students’ preparations varied across urban-suburban-
rural lines, with urban teachers having the lowest opinion and rural teachers having the best, but
these differences were not significant in the full regression.
Research Question #2: To the degree that the teachers believe students need to be better prepared,
what are the major shortcomings?
The teachers were asked to rate the importance of a “solid foundation” in the each the 15
skill/knowledge areas asked about with respect to their target class students’ background preparation
(see questionnaire items III.1a-o). We addressed this research question by combining the teachers’
responses to the 15 student preparation items (I.4a-o) with teacher responses to the questionnaire
items asking how important each of the preparation items is for success in Algebra I (III.1a-o).
Information from the two batteries was combined to weight the preparation rating by its
importance. A “preparation problem” score for each item was calculated by multiplying the
teacher’s rating of his or her students’ preparation by that teacher’s rating of the importance of a
solid foundation in that particular area to students’ success in Algebra I.
 Referring to Figure 2, we find that when we weight each topic by the teachers’ level of
importance, a similar pattern to that shown in Table 7 for the teachers’ ratings of student
backgrounds emerges, with only minor differences in the ordering of the items.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 13
FIGURE 2. TEACHERS’ RATINGS OF STUDENT PROBLEMS IN VARIOUS AREAS OF
MATHEMATICS: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
The set of preparation-problem items are highly intercorrelated and, like the background-
preparation items, can be combined into a summary scale to facilitate analysis of factors related to
differences among teachers in their ratings. We constructed a summary “preparation problem” scale
using the full set of weighted items and regressed it on the standard classroom and school
classification variables.
 The regressions of this scale on the classroom, school, and teacher variables also confirm the
patterns from the ratings of background preparation — students in the 7
th
-8
th
grade Algebra
I classes are better prepared than those taking Algebra I in grade 9 and higher (see Appendix
Table C.2).
The consistency of Table 7 and Figure 2 reflects the fact that virtually all of the “how
important” items (III.1a-n) were rated as “very important” or “extremely important” by almost all
respondents. Because these are largely invariant across the whole sample, the weighting method just

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 14
outlined did not yield different results than the analysis of the preparation items discussed under
research question #1.
Research Question #3: Given their experience with incoming students, would they change the level
of emphasis placed on mathematics topics at the elementary level? If so, how would they change it?
 Would they put more or less emphasis on basic understandings or arithmetic and whole
number, fraction and decimals operations?
 Would they put more or less emphasis on helping students master basic concepts?
These questions are covered to some extent in the open-ended item III.2, “Please provide a
brief description of any changes you would like to see in the curriculum leading up to Algebra I in
your district.” Of the 743 teachers who returned completed questionnaires, 578 provided verbatim
responses to this item.
A substantial number of the 578 would like to see a greater focus in primary education
placed on mastery of basic mathematical concepts. For example:
"Students need to be better prepared in basic math skills and not be quite so calculator dependent. Also, more training
in thinking skills."
"Make sure the 1st-8th grade teachers teach the foundations of math and that the students know their basic skills."
"More focus on basics-students should already know order of operations, positive vs. neg. numbers, fractions, and
decimals."
"Stronger basic math facts, less rigor and rushing to higher math and more arithmetic."
"Please do not allow students to use calculators, especially fraction calculators."
As these examples suggest, responses to this item will also be the best source in the
questionnaire for answers to the National Math Panel’s research question “What are the teachers’
views on students using calculators in the early grades?” Of those that wrote an answer for item
III.2, (N=578), 13% (N=75) specifically mentioned that they would like to see less use of calculators
before students take their Algebra I class.
Additionally, 8% of the teachers (N=46) also mentioned changing pre-algebra standards.
These responses not only include teachers stating that students need to prove their pre-algebra
competence before entering Algebra I, but also indicate that pre-algebra is not even offered to all
students before entering Algebra I. For example:

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 15
“Make pre-alg or alg I a requirement for middle schools.”
“I would like to see a pre-algebra class as a requirement prior to taking Algebra.”
“Most students in my class have a different curriculum in middle school, so they do not officially have pre-algebra. A
better diagnostic and year end assessment is essential. Many students are dependent on calculators.”
“The curriculum issue is being address next year. We are adding general math and pre-algebra and we will hopefully
insist on mastery before allowing students to take Algebra I.”
“Students should have at least 80% proficiency in pre-algebra skills. Class for high schools students not proficient in
these skills. Alternative classes or students with behavior and/or attendance issues.”
“Student mastery of pre-alg concepts before enrolling in Alg.”
“Mandatory success in a pre-algebra course.”
CU R R I C U L U M A N D I N S T R U C T I O N
Research Question #4: How do the Algebra I teachers rate their state and local district curricular
expectations in algebra for PK-12? How do they rate the state or local school district mathematics
standards and math tests that they currently use? Are they setting the right expectations? Too low or
unrealistically high? Clear and helpful, or confused and counter-productive? (This combines two
separate research questions as requested by the NMP subcommittee).
The questionnaire included one item asking the teachers to rate their local district’s
expectations for student proficiency in Algebra I (III.3) and two items asking about state standards
and assessment tools (III.7a,b). A fourth related question asked whether students are required to
pass Algebra I in order to graduate high school (III.6). We examined these responses by the school
classification variables.
 The modal response (67%) from teachers is that they feel that local expectations for student
proficiency in Algebra I are “about right”, while about equal numbers rated them as “too
high” (8%) or “too low” (11%) (see Figure 3).

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 16
FIGURE 3. TEACHERS’ RATINGS OF LOCAL DISTRICT EXPECTATIONS FOR STUDENT
PROFICIENCY WITH ALGEBRA I: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
The teachers were also generally favorable about content standards for Algebra I in their
state or local district. A majority (54%) of teachers felt that the content standards are good and 19%
rate them as excellent. Only about 3% rated their content standards as poor (see Figure 4).
However, the regression analysis shows that teachers who teach in schools in the second quartile of
minority student population also feel that the standards are better (.37 sd), compared with the
feelings of teachers with low levels of minority students (see Appendix Table C.3).

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 17
FIGURE 4. TEACHERS’ RATINGS OF STATE OR LOCAL SCHOOL DISTRICT
MATHEMATICS CONTENT STANDARDS FOR ALGEBRA I: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
Teachers were less positive about state and local assessment standards, but the modal
response was still that they were “good” (see Figure 5). The regression analysis did not find any
differences based on teacher or school characteristics (see Appendix Table C.4).
FIGURE 5. TEACHERS’ RATINGS OF STATE OR LOCAL SCHOOL DISTRICT
MATHEMATICS ASSESSMENTS OF ALGEBRA I OUTCOMES: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 18
School Problems. The NSAT questionnaire also included a battery of questions regarding
possible problems with the teacher’s school, and the next table reports the means and 95%
confidence intervals for these items. From poor computer access to inadequate administrative
support, examination of the confidence intervals show that teachers have a problem with each
aspect of their school to a similar degree. On average, teachers feel that each aspect is, on average,
a minor problem.
TABLE 8. SCHOOL PROBLEMS REPORTED BY ALGEBRA TEACHERS: 2007
ASPECT
LOWER 95% CI
MEAN
HIGHER 95% CI
Insufficient access to computers
1.68
1.86
2.04
Inadequate access to graphing calculators
1.58
1.70
1.81
Poor quality or out-of-date textbooks
1.43
1.59
1.75
Too large class sizes
1.84
1.97
2.10
Too little coordination between classes in the mathematics
1.62
1.75
1.87
Lack of teacher planning time
1.63
1.74
1.85
Inadequate administrative support
1.52
1.64
1.75
Scale: 1 = Not a problem, 2 = Minor, 3 = Moderate, 4 = Serious problem
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
Research Question #5: How do they rate their textbook (or textbooks in general) regarding algebra
instruction?
The questionnaire included several items asking for the teacher’s evaluation of the textbook
they use in the target class (items I.8a-i). We examine these, first, item-by-item and then assess
whether they form a scale. The items and scale are then broken down by school classification
variables and grade level of the Algebra I class.
 Figure 6 shows, item by item, how strongly the teacher agreed that their textbook was well
suited for a specific task. This figure shows there is little variation across items. For the
most part, teachers are satisfied with their texts’ list of topics. The only point of (possible)
contention is that some teachers feel that their textbook is not well suited for the needs of a
diverse population of students.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 19
FIGURE 6. TEACHERS’ RATINGS OF VARIOUS ASPECTS OF THE ALGEBRA I
TEXTBOOK USED IN TARGET CLASS: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
The data indicate that the nine items form a strong scale, with reliability of alpha=.90.
Figure 7 shows the average composite scale score of the textbook rating questions across
respondents. As is clear, the majority of the teachers have a positive view of their text.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 20
FIGURE 7. PERCENTAGE DISTRIBUTION OF COMPOSITE TEXTBOOK FAVORABILITY
RATINGS SCALE SCORE: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
 The regression results for this composite scale show that teachers of smaller classes had
more favorable ratings of their textbooks (Appendix Table C.5). Teachers with small classes
(15 or fewer) like their text more by 0.56 standard deviations. Likewise, teachers in rural
schools also like their books more, in this case by 0.35 standard deviations. However,
teachers in schools with a high concentration of minority students have a less favorable view
of their texts. On average, they like their texts less by .52 standard deviations.
This generally positive evaluation was corroborated by the teachers’ responses to an item
asking them to rate the extent to which “poor quality or out-of-date textbooks” are a problem in
their school. On a scale that ranged from 1=not a problem to 4=serious problem, the average rating
was 1.59, indicating that poor textbooks are considered about midway between 1= “not a problem”
and 2 = “a minor problem” (Table 8).
Research Question #6: How do the teachers rate online technology tools?
The questionnaire included questions asking how often the teachers used computer-based
instructional tools (item I.5f), the extent to which insufficient access to computers is a problem in
their school (item II.1a), and how much they agreed or disagreed with the proposition that
“Computer-based instructional tools (software) are helping Algebra I students in my Target Class”
(item I.6). We examined these responses by the grade level of the class and the standard school
classification variables in the regression analysis (see Appendix Table C.6).
The data indicated that the average response to how frequently these tools are used was
about 1 (=“less than once a week”) on a scale that ranged from 0=never to 4=everyday. The

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 21
teachers’ ratings of the helpfulness of computer-based instructional tools were mixed, with 29%
agreeing somewhat or agreeing strongly with the proposition that computers were helpful and 38%
disagreeing somewhat or disagreeing strongly (34% neither agreed nor disagreed).
FIGURE 8. TEACHERS’ RATINGS ON HELPFULNESS OF COMPUTER-BASED
INSTRUCTIONAL TOOLS IN ALGEBRA I TARGET CLASS: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
Use of computers and access. The generally-low levels of computer use does not appear
to be a reflection of insufficient access. About half (49%) of the teachers reported that insufficient
access to computers was not a problem in their schools and another 28% reported insufficient
access to be a minor problem. Similar portions of those who do not feel access is a problem use
computers less than once a week or never (74%) as those who feel access is a serious problem
(72%). This suggests that if those without access did get computers they would not use them much.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 22
TABLE 9. FREQUENCY OF USING COMPUTERS IN THE TARGET CLASS, BY EXTENT TO
WHICH INSUFFICIENT ACCESS TO COMPUTERS IS A PROBLEM IN THE
SCHOOL: 2007
How much of a problem is insufficient access to
computers?
USE OF COMPUTERS AND
SOFTWARE
NOT A
PROBLEM
MINOR
PROBLEM
MODERATE
PROBLEM
SERIOUS PROBLEM
USE
TOTAL
Never
40.75%
46.80%
38.69%
51.72%
43.40%
Less than once a week
33.42%
33.17%
46.79%
20.58%
33.66%
About once a week
10.76%
9.49%
9.37%
9.02%
10.03%
Several times a week
6.62%
3.30%
1.14%
2.53%
4.52%
Everyday
8.47%
7.24%
4.00%
16.15%
8.39%
Total
100%
100%
100%
100%
100%
Chi-square = 27.1 (p=0.46), Correlation = 0.03 (p=0.73)
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 23
Figure 9 shows the frequency of use of various materials across grades. As the chart shows,
the level of use for texts and technology generally remains constant across grades. In other words,
no matter what the age is of the students, the level of use for each material is about the same.
Software is used least of all.
FIGURE 9. FREQUENCY OF USING VARIOUS INSTRUCTIONAL MATERIALS AND
TOOLS IN ALGEBRA I, BY GRADE LEVEL OF TARGET CLASS: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
Research Question #7: What is the role of the calculator in the algebra course?
Questionnaire item I.5d asked how often the teacher uses graphing calculators in her or his
target class. Overall, 33% of the teachers report never using graphing calculators and another 29%
report using them less than once a week About 31% use them everyday (18%) or almost everyday
(13%). (See Table 10).
Table 10 shows rates of graphing calculator use by grade and urbanicity. Teachers in urban
schools were less likely to use graphing calculators than their suburban and rural counterparts, and
teachers of 8
th
grade Algebra I were more likely than others to use them in all three types of locale.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 24
TABLE 10: FREQUENCY OF GRAPHING CALCULATOR USE, BY GRADE LEVEL OF
TARGET CLASS AND URBANICITY: 2007
Total Sample
FREQUENCY OF USE
GRADE 7 & 8
GRADE 9
GRADE 10-
12
TOTAL
Never
22.8%
39.4%
38.7%
33.0%
Less Than Once a Week
41.9%
22.6%
15.6%
29.4%
About Once a Week
7.1%
5.7%
8.5%
6.4%
Several Times a Week
10.1%
14.2%
17.5%
13.2%
Everyday
17.4%
18.1%
19.7%
18.0%
Total
100%
100%
100%
100%
Sample Size (Total)
128
518
73
719
Urban
Never
18.6%
39.4%
44.3%
31.8%
Less Than Once a Week
44.4%
22.8%
17.8%
30.7%
About Once a Week
8.6%
6.4%
13.6%
7.4%
Several Times a Week
20.9%
19.9%
9.0%
20.0%
Everyday
7.5%
11.6%
15.3%
10.1%
Total
100%
100%
100%
100%
Sample Size (Urban)
37
202
10
249
Suburban
Never
30.3%
44.8%
36.5%
38.6%
Less Than Once a Week
43.3%
18.8%
10.1%
26.7%
About Once a Week
9.5%
7.2%
11.6%
8.6%
Several Times a Week
7.6%
11.3%
22.1%
11.2%
Everyday
9.3%
17.9%
19.7%
15.0%
Total
100%
100%
100%
100%
Sample Size (Suburban)
66
247
55
368
Rural
Never
18.0%
32.9%
42.1%
27.2%
Less Than Once a Week
38.4%
27.0%
27.5%
31.8%
About Once a Week
3.3%
3.2%
0.0%
3.0%
Several Times a Week
6.9%
12.2%
9.5%
9.9%
Everyday
33.4%
24.8%
20.9%
28.1%
Total
100%
100%
100%
100%
Sample Size (Rural)
25
69
8
102
Note: Cells are weighted percentages within each urbanicity.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 25
Use of graphing calculators and access. While only about 30% of teachers use graphing
calculators more than about once a week, many of those who use them with less frequency do
report that access to this technology is a problem (Table 11). Of those that feel that access is not a
problem, only 26% never use them. This contrasts with the over 50% that never use them among
those who report insufficient access is a moderate or serious problem. The correlation coefficient
summarizing the linear relationship between the two items is moderately high (r = 0.32). This
suggests that that if they had access, more – though by no means all – of the Algebra I teachers
would use graphing calculators.
TABLE 11. FREQUENCY OF USING GRAPHING CALCULATORS, BY EXTENT TO WHICH
INSUFFICIENT ACCESS TO GRAPHING CALCULATORS IS A PROBLEM IN THE
SCHOOL: 2007
How much of a problem is insufficient access to graphing
calculators?
USE OF GRAPHING
CALCULATORS
NOT A PROBLEM
MINOR
PROBLEM
MODERATE PROBLEM
SERIOUS PROBLEM
USE
TOTAL
Never
25.9%
32.1%
50.0%
58.1%
32.7%
Less than once a week
22.7%
42.7%
35.4%
23.2%
29.6%
About once a week
7.8%
2.7%
8.6%
4.7%
6.5%
Several times a week
14.6%
18.4%
2.3%
4.6%
13.3%
Everyday
29.0%
4.1%
3.7%
9.4%
18.0%
Total
100%
100%
100%
100%
100%
Chi-square = 121.6 (p<.000), Correlation = 0.32 (p<0.000)
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
Research Question #9 What about the use of manipulatives as instructional tools?
The relevant questionnaire item for this question asked how often the teacher uses physical
objects (“manipulatives”) in her or his target class (item I.5e). Overall, use of manipulatives on an
occasional basis is widespread, but very few (9%) teachers report using them more than once a
week. About 12% of the teachers reported never using manipulatives, and about 60% reported
using them less than once a week (Table 12). As evident in Table 12, there does not seem to be a
relationship between the class grade level and the frequency of use.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 26
TABLE 12: FREQUENCY OF PHYSICAL OBJECT USE, BY GRADE LEVEL OF TARGET
CLASS: 2007
FREQUENCY OF USE
GRADE 7 & 8
GRADE 9
GRADE 10 -
12
TOTAL
Never
11.4%
12.9%
12.8%
12.3%
Less Than Once a Week
62.1%
57.8%
53.7%
59.1%
About Once a Week
19.2%
18.5%
28.9%
19.5%
Several Times a Week
7.4%
10.1%
3.9%
8.6%
Everyday
0.0%
0.7%
0.7%
0.4%
Total
100%
100%
100%
100%
Sample Size
128
518
73
719
Note: Cells are weighted percentages
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
VI E W S O N C H A N G I N G S E C O N D A R Y SC H O O L MA T H ED U C A T I O N
Research Question #9: How do they rate their professional training?
Questionnaire items pertaining to professional training and development include items
III.4a,b and possibly IV.19; items II.1f and j are also relevant. We examined these items by the
teachers’ years of teaching experience, and school classification variables. With one exception, we
did not find that satisfaction with training varied by teacher characteristics. Hispanic teachers
reported more satisfaction with pre-service training by .64 standard deviations.
Looking at Table 13, we generally see that although teachers feel that their training is not a
problem (the first two rows), they do however feel less positive about their training, both before
service and during their careers. In contrast, they feel more negative about their training than they
do about their own experiences with pre-service training and professional development
opportunities. Figures 10 and 11 also show that most teachers do not see training as a problem.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 27
TABLE 13. TEACHERS’ EVALUATION OF PROFESSIONAL DEVELOPMENT: 2007
95% CI
ITEM
SCALE
MEAN
LOW
HIGH
Inadequately Prepared Teachers
1 = Not a Problem . . . 4 = Serious Problem
1.49
1.43
1.55
Inadequate Opportunities for
Professional Development
1 = Not a Problem . . . 4 = Serious Problem
1.65
1.59
1.71
Rating of Own Pre-service Teacher
Education
1 = Prepared Teacher Very Well . . .4 = Very
Poorly
1.96
1.89
2.02
Rating of Own Professional
Development Opportunities
1 = Help Teach Very Well . . .4 = Very Poorly
1.98
1.91
2.04
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design effects
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
FIGURE 10. DISTRIBUTION OF TEACHERS’ RATINGS OF HOW WELL THEIR PRE-
SERVICE EDUCATION PROGRAM PREPARED THEM TO TEACH ALGEBRA I :
2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 28
FIGURE 11. DISTRIBUTION OF TEACHERS’ RATINGS OF HOW WELL THEIR
PROFESSIONAL DEVELOPMENT OPPORTUNITIES HAVE HELPED THEM
TEACH ALGEBRA I: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
Research Question #10: Is there sufficient and effective remedial help for students who are
struggling in algebra? What sort of assistance-based interventions would struggling students benefit
from the most?
Questionnaire items II.8a-b asked the teachers to rate the availability and quality of tutoring
or other remedial services for students struggling with Algebra I in their school. We examine the
average ratings by the school classification variables.
 On average, looking at Table 14, teachers were generally satisfied with the services available,
even if not extremely so.
 These services were rated more favorably by teachers in high minority schools
 Female and black teachers are less satisfied with their schools’ remedial services. This may
reflect a tendency for these teachers to assume advocacy roles on behalf of their students.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 29
Table 14. Teachers’ Ratings on Availability and Quality of Remedial Help for
Algebra I Students: 2007
Evaluation of Remedial Help
Lower 95% CI
Mean
Higher 95% CI
Availability of remedial help
2.35
2.52
2.69
Quality of remedial help
2.26
2.42
2.58
Scale: 1= Excellent, 2= Good, 3=Fair, 4=Poor;
CI = confidence interval, calculated as +/- two standard errors from the mean. Standard errors adjusted for design
effects.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.
Research Question #11: Do teachers believe that students would learn more if they were grouped by
ability for instruction, or is this approach counter-productive?
Questionnaire item II.2 asked whether the school offers different levels of Algebra I based
on ability; 46% of the teachers indicated their schools did differentiate. Questionnaire item II.1h
asked teachers to rate the extent to which they see different levels of students in the same class as a
problem in their school.
A substantial number of teachers considered mixed-ability groupings to be a “moderate”
(28%) or “serious” (23%) problem (see Figure 12). Teachers in schools that did not offer different
levels of Algebra I based on ability were more likely than their counterparts in schools that do use
ability grouping to consider mixed-ability classrooms to be a moderate or serious problem (Table
15).
TABLE 15. PERCENTAGE OF ALGEBRA I TEACHERS REPORTING STUDENTS WITH
DIFFERENT ABILITIES AND SKILLS TAKING THE SAME CLASS IS A
PROBLEM, BY WHETHER SCHOOL OFFERS DIFFERENT LEVELS BASED ON
ABILITY: 2007
LEVEL OF PROBLEM
AVAILABLE AT
TEACHERS’ SCHOOL
NOT AVAILABLE AT
TEACHERS’ SCHOOL
ALL TEACHERS
Not a problem
21.3%
19.3%
20.2%
Minor problem
33.4%
25.9%
29.4%
Moderate problem
26.2%
29.5%
27.9%
Serious Problem
19.2%
25.4%
22.5%
Total
100%
100%
100%
Note: Twelve respondents did not know whether or not their school mixed ability levels.
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 30
FIGURE 12. EXTENT TO WHICH STUDENTS WITH DIFFERENT ABILITIES AND
INTERESTS TAKING THE SAME ALGEBRA I CLASS IS A PROBLEM: 2007
Evaluation of Ability Group Mixing
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
35.00%
Not a Problem Minor Problem Moderate Problem Serious Problem
How Much of a Problem
Percentage
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
Looking at Appendix Table C.9, we see that larger classes and high school teachers do feel
that it is a problem. We also found that Black teachers were more favorable of the practice.
Although we must remember that these are teachers describing their feelings about the practice in
general. Teachers with larger classes and later grades are less likely to feel that it is a good practice.
Research Question #12: Do they find more parents helpful in encouraging students in their
mathematics studies, or do too many parents make excuses for their children’s lack of
accomplishment?
Questionnaire item II.1i asked teachers to rate the extent to which they see “too little
parent/family support” as a problem in their school. The data in Figure 13 shows that more teachers
feel that family participation is a moderate (32%) or serious (28%) problem than feel it is a minor
problem (26%) or not a problem at all (14%).

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 31
FIGURE 13. EXTENT TO WHICH TOO LITTLE PARENT/FAMILY SUPPORT IS A PROBLEM
IN SCHOOL: 2007
SOURCE: U.S. Department of Education, National Mathematics Advisory Panel, National Survey of Algebra Teachers, 2007
To estimate relationships between the teachers’ family participation rating and the teacher
and school background variables, we used regression analysis (see Appendix Table C.10). High
school teachers were much more likely than middle school and other teachers to report lack of
family participation as a problem (the effect size is 0.65 SD units). Also, teachers in schools with
higher percentages of free and reduced priced lunch students also felt that lack of family
participation was more of a problem, the 2
nd
quartile by .31 standard deviations, the 3
rd
by .46 SD
units, and the 4
th
quartile by .54 SD units. Female teachers, on the other hand, feel that lack of
family participation is less of a problem by .22 standard deviations.
Research Question #13: What do they see as the single most challenging aspect of teaching Algebra
I successfully?
This question (IV.20) included 10 response options: explaining material to students, handling
accelerated students, teaching procedures, explaining concepts, using diagrams or models effectively,
interpreting student errors and difficulties, working with unmotivated students, working with
advanced students, helping students whose home language is not English, making mathematics
accessible and comprehensible, and an “other” option.

FINAL REPORT ON THE
NATIONAL SURVEY OF ALGEBRA TEACHERS FOR THE NATIONAL MATH PANEL
SEPTEMB ER 27, 2007
PAGE 32
Table 16 shows the percentages of each response within high schools or middle/other
schools. The overwhelmingly most frequent response to this question was “working with
unmotivated students.” This was chosen by 65% of the high school teachers and 58% of the middle
school teachers.
TABLE 16: FREQUENCIES OF REPORTED CHALLENGES TO TEACHING ALGEBRA I BY
CLASS GRADE LEVEL AND TYPE OF SCHOOL: 2007
HIGH
SCHOOLS
MIDDLE/OTHER
SCHOOLS
ALL
TEACHERS
Working with unmotivated