Chapter 5 First-Year Courses in Four-Year Colleges and Universities Tables in this chapter further explore topics from Tables S.7 to S.13 in Chapter 1 and Tables E.2 to E.9 of Chapter 3, presenting details by type of department on certain first-year mathematics courses in four- year colleges and universities—their enrollments, their teachers, and how they were taught. Courses studied include a spectrum of introductory-level courses, several first-year calculus courses, and elementary statistics courses. Among introductory-level math- ematics courses, the chapter focuses on: a) two general education courses (with names such as Finite Mathematics and Mathematics for Liberal Arts) that are specifically designed for students fulfilling a general education requirement, b) courses for pre-service elementary education teachers, and c) the cluster of precalculus courses with names such as College Algebra, Trigonometry, Algebra and Trigonometry, and Elementary Functions. First-year calculus courses are divided into “main- stream” and “non-mainstream” courses, where a calculus course is classified as “mainstream” if it typi- cally leads to upper-division mathematical sciences courses. That definition has been used in almost all CBMS surveys, and before 2005, it was roughly true to say that mainstream calculus courses were typically designed for mathematics, engineering, and physical sciences majors. By fall 2005, that rough characteriza- tion was less and less accurate. With the increasing national emphasis on mathematical biology, there was a growing body of calculus courses specifi- cally designed for students with biological interests that could fall into the “mainstream” classification. Whether a particular calculus course was classified as mainstream or non-mainstream was left up to responding departments, and based on calls and e- mails to the project directors in fall 2005, responding departments had few doubts about which calculus courses were mainstream and which were not. The final group of courses studied in this chapter are the elementary statistics courses, where the term “elemen- tary” refers only to the fact that such courses do not have a calculus prerequisite. Most of these courses are also part of the curriculum of two-year colleges, and details about the courses in the two-year-college setting appear in Chapter 6. Enrollments (Tables FY.2, FY.4, FY.6, FY.8, and FY.10 and Appendix I Tables A.1 and A.2) • Table A.1 in Appendix I shows that combined enrollments in Finite Mathematics and Liberal Arts Mathematics, two general education courses, increased markedly between fall 1995 and fall 2005, growing from 133,000 in 1995 to 168,000 in fall 2000 and finally to 217,000 in fall 2005. That is a 63% increase over ten years, and in fall 2005 combined enrollment in these two general education courses exceeded the total enrollment in Mainstream Calculus I. • Enrollments in first-year courses designed for pre-service elementary teachers rose between fall 1995 and fall 2000 and rose again by fall 2005. Table FY.2 shows an increase from roughly 59,000 in fall 1995 to about 72,000 in fall 2005, a 22% increase. • Enrollments in the cluster of four precalculus courses listed in c) above were roughly 368,000 in fall 1995, grew to about 386,000 in fall 2000, and declined to 352,000 in fall 2005, ending the decade more than 9% below 1995 levels. See Table FY.2. • Table A.2 in Appendix I shows that the combined enrollment in the Elementary Statistics course in mathematics and statistics departments (including distance-learning enrollments) grew from 132,000 in fall 1995 to 155,000 in fall 2000 and to 167,000 in fall 2005, an increase of about 27% between 1995 and 2005, with the rate of enrollment growth appearing to slow in the last five years of the decade. Mathematics departments taught almost three-quarters of the nation’s Elementary Statistics. Tables FY.8 and FY.10 display the non-distance- learning enrollments in this course in fall 2005. Who taught first-year courses? (Tables FY.1, FY.3, FY.5, FY.7, and FY.9) CBMS1995 and CBMS2000 presented data on the type of instructors assigned to teach first-year courses in terms of percentages of enrollments, but those enrollment estimates relied on certain assump- 111
Transcript
Chapter 5
First-Year Courses in Four-Year Colleges and Universities
Tables in this chapter further explore topics from Tables S.7 to S.13 in Chapter 1 and Tables E.2 to E.9 of Chapter 3, presenting details by type of department on certain first-year mathematics courses in four-year colleges and universities—their enrollments, their teachers, and how they were taught. Courses studied include a spectrum of introductory-level courses, several first-year calculus courses, and elementary statistics courses. Among introductory-level math-ematics courses, the chapter focuses on:
a) two general education courses (with names such as Finite Mathematics and Mathematics for Liberal Arts) that are specifically designed for students fulfilling a general education requirement,b) courses for pre-service elementary education teachers, and c) the cluster of precalculus courses with names such as College Algebra, Trigonometry, Algebra and Trigonometry, and Elementary Functions.
First-year calculus courses are divided into “main-stream” and “non-mainstream” courses, where a calculus course is classified as “mainstream” if it typi-cally leads to upper-division mathematical sciences courses. That definition has been used in almost all CBMS surveys, and before 2005, it was roughly true to say that mainstream calculus courses were typically designed for mathematics, engineering, and physical sciences majors. By fall 2005, that rough characteriza-tion was less and less accurate. With the increasing national emphasis on mathematical biology, there was a growing body of calculus courses specifi-cally designed for students with biological interests that could fall into the “mainstream” classification. Whether a particular calculus course was classified as mainstream or non-mainstream was left up to responding departments, and based on calls and e-mails to the project directors in fall 2005, responding departments had few doubts about which calculus courses were mainstream and which were not. The final group of courses studied in this chapter are the elementary statistics courses, where the term “elemen-tary” refers only to the fact that such courses do not have a calculus prerequisite. Most of these courses are also part of the curriculum of two-year colleges,
and details about the courses in the two-year-college setting appear in Chapter 6.
Enrollments (Tables FY.2, FY.4, FY.6, FY.8, and FY.10 and Appendix I Tables A.1 and A.2)
• Table A.1 in Appendix I shows that combined enrollments in Finite Mathematics and Liberal Arts Mathematics, two general education courses, increased markedly between fall 1995 and fall 2005, growing from 133,000 in 1995 to 168,000 in fall 2000 and finally to 217,000 in fall 2005. That is a 63% increase over ten years, and in fall 2005 combined enrollment in these two general education courses exceeded the total enrollment in Mainstream Calculus I.
• Enrollments in first-year courses designed for pre-service elementary teachers rose between fall 1995 and fall 2000 and rose again by fall 2005. Table FY.2 shows an increase from roughly 59,000 in fall 1995 to about 72,000 in fall 2005, a 22% increase.
• Enrollments in the cluster of four precalculus courses listed in c) above were roughly 368,000 in fall 1995, grew to about 386,000 in fall 2000, and declined to 352,000 in fall 2005, ending the decade more than 9% below 1995 levels. See Table FY.2.
• Table A.2 in Appendix I shows that the combined enrollment in the Elementary Statistics course in mathematics and statistics departments (including distance-learning enrollments) grew from 132,000 in fall 1995 to 155,000 in fall 2000 and to 167,000 in fall 2005, an increase of about 27% between 1995 and 2005, with the rate of enrollment growth appearing to slow in the last five years of the decade. Mathematics departments taught almost three-quarters of the nation’s Elementary Statistics. Tables FY.8 and FY.10 display the non-distance-learning enrollments in this course in fall 2005.
Who taught first-year courses? (Tables FY.1, FY.3, FY.5, FY.7, and FY.9)
CBMS1995 and CBMS2000 presented data on the type of instructors assigned to teach first-year courses in terms of percentages of enrollments, but those enrollment estimates relied on certain assump-
111
112 2005 CBMS Survey of Undergraduate Programs
tions that made standard errors difficult to calculate. To allow standard error calculations in this report, CBMS2005 expresses its conclusions in terms of percentages of sections. Consequently, direct numer-ical comparisons between CBMS2005 and earlier CBMS studies are problematic. Even if one assumes that percentage of sections converts linearly into percentage of enrollments, a conservative approach to making comparisons suggests drawing only tenta-tive conclusions.
In Chapter 5, as in previous CBMS surveys, tenured and tenure-eligible (TTE) faculty were combined into a single category. All other full-time faculty were put into the class called other full-time (OFT) faculty. To get a better picture of the mathematical qualifications of teachers in first-year courses, CBMS2005 subdi-vided the OFT faculty into those with doctoral degrees (OFT-doctoral) and those without doctorates. This was a new feature of CBMS2005. In order to maintain some degree of comparability with CBMS1995 and CBMS2000, tables in this chapter contain a column called “OFT (total)” as well as the column called “OFT (doctoral).”
• In fall 2005, about forty percent of introductory-level courses in bachelors- and masters-level depart-ments were taught by TTE or OFT-doctoral faculty, compared to about 17% in doctoral departments. Doctoral departments assigned about a third of introductory-level courses to graduate teaching assistants (GTAs), meaning that the GTAs were the instructors of record in those courses. See Table FY.1.
• Doctoral departments used a combination of TTE and OFT-doctoral faculty to teach about half of their Mainstream Calculus I sections. In masters-level departments, the combined percentage was closer to 75%, and in bachelors-level departments it was about 85%.
• Table FY.1 of CBMS2000 shows that doctoral mathematics departments taught 62% of their Mainstream Calculus I enrollment using TTE faculty in fall 1995, and 50% in fall 2000. Table FY.3 in CBMS2005 shows that in fall 2005, doctoral math-ematics departments used TTE faculty to teach 36% of their Mainstream Calculus I sections. With the usual caveat about comparing percentages of enrollment from CBMS2000 with percentages of sections in CBMS2005, Tables FY.1 in CBMS2000 and FY.3 in CBMS2005 suggest a marked trend in doctoral mathematics departments away from using TTE faculty in Calculus I.
• The percentage of Mainstream Calculus I sections taught by graduate teaching assistants (GTAs) in fall 2005 was only slightly lower than the percentage of enrollments in Mainstream Calculus I taught by
GTAs in fall 2000, and this suggests that there was not much change in the use of GTAs to teach Mainstream Calculus I between 2000 and 2005. See Table FY.1 in CBMS2000 and CBMS2005.
• There appears to be a continuing trend among mathematics departments to shift the teaching of the Elementary Statistics course from TTE faculty to OFT faculty. In mathematics departments, the percentage of Elementary Statistics sections taught by TTE faculty was below the percentage of enroll-ment taught by TTE faculty in 1995. At the same time, among bachelors- and masters-level math-ematics departments, the percentage of Elementary Statistics sections taught by OFT faculty in fall 2005 was more than double the percentage of enrollment in the same course taught by OFT faculty in fall 1995. Among doctoral mathematics departments, the fall 2005 percentage of sections taught by OFT faculty was almost four times as large as was the percentage of enrollment taught by OFT faculty in 1995. See Table FY.6 in CBMS2000 and Table FY.7 of this chapter.
How are first-year courses taught? (Tables FY.2, FY.4, FY.6, FY.8, and FY.10)
The CBMS1995 survey asked departments about the impact of the calculus reform movement on the way that their calculus courses were taught. In fall 1995, a meaningful question was “What percentage of your calculus sections are taught using a reform text?” By fall 2000, that question was no longer mean-ingful, with almost every publisher claiming to have incorporated calculus reform into every calculus text. To trace the continuing impact of calculus reform in fall 2000, the CBMS2000 survey focused atten-tion on a spectrum of pedagogical methods that had come to be thought of as “reform methods”. These were of two general types—those related to technology (the use of graphing calculators and computers), and those that were sometimes described as “humanistic pedagogies,” e.g., the use of writing assignments and group projects. Tables FY.2, FY.4, FY.6, FY.8, and FY.10 continue that study and suggest some conclusions about the spread of reform pedagogies during the 1995–2005 decade, once again subject to the caveat that comparing percentages of enrollment in CBMS1995 and CBMS2000 with percentages of sections in CBMS2005 leads to tentative conclusions at best.
• In fall 2005, none of the four reform pedagogies were universal in Calculus I (whether the mainstream version, or non-mainstream). Graphing calcula-tors were the most widely used reform pedagogy in Calculus I courses and were used about twice
First-Year Courses in Four-Year Colleges and Universities 113
as widely in Calculus I as computer assignments. See Table FY.4.
• The percentage of Calculus I sections taught using writing assignments and group projects was generally below 20%, and they were mostly in the single-digit range among doctoral-level departments. This is consistent with findings of CBMS2000. See Table FY.4.
• In contrast to the situation in Calculus I, a mark-edly larger percentage of Elementary Statistics sections used computer assignments compared to graphing calculators. In addition, while the use of writing assignments and group projects seems to have declined among Elementary Statistics sections taught in mathematics departments, it appar-ently increased markedly in Elementary Statistics sections taught in doctoral statistics departments. See Tables FY.8 and FY.10.
Earlier CBMS studies did not examine the peda-gogical methods used in introductory-level courses (such as College Algebra and Precalculus), so it is not possible to trace the spread of reform pedagogies over time in courses of that type. However, Table FY.2 does allow some comparisons between introductory-level and other first-year courses in fall 2005.
• The cluster of precalculus courses (namely College Algebra, Trigonometry, Algebra & Trigonometry (combined course), and Precalculus) resembled Mainstream Calculus I in pedagogical pattern, with graphing calculators being twice as commonly used
as computer assignments, and with writing assign-ments and group projects trailing far behind.
• Writing assignments and group projects were used much more extensively in Mathematics for Elementary Teachers than in any other introduc-tory-level course, while graphing calculators were used less.
A new question in CBMS2005 asked departments about the extent to which they used online resource systems in their first-year courses. The CBMS2005 questionnaires described these systems as online packages for generating and grading homework. In four-year colleges and universities, the percentage of first-year sections (i.e., introductory-level courses, Calculus I, or Elementary Statistics) using such systems was typically in the single digits in math-ematics departments. By contrast, it was closer to twenty percent in Elementary Statistics courses taught in doctoral statistics departments.
In fall 2005, reform pedagogies had been more widely adopted in two-year college courses than in the same courses at four-year colleges and universities, often by wide margins. See Table TYE.10 of Chapter 6 for details about the use of reform pedagogies and online resource systems in courses taught in two-year colleges.
Special Note on Chapter 5 Estimates: As can be seen from the Appendix on standard errors, many of the estimates in Chapter 5 had large standard error values so that the values in the entire population might be quite different from the estimates given in Chapter 5 tables.
114 2005 CBMS Survey of Undergraduate Programs
18 17 14 19 4 10 6 7 25 11
36 49 30 45 24 31 26 32 36 33
43 31 36 59 34 30 61 43 11 41
19 32 20 38 25 26 45 22 75 26
13 28 23 24 36 36 8 21 14 25
16 14 30 24 31 32 29 22 78 24
5 7 9 10 3 3 10 8 38 6
4 4 5 2 5 0 2 3 0 4
4 4 11 3 3 2 8 0 22 4
28 12 21 22 21 19 19 24 0 21
38 17 41 24 26 19 36 33 50 30
32 55 32 12 29 39 11 35 11 30
25 23 43 14 44 43 29 40 0 34
3 0 2 1 6 0 30 10 0 5
0 0 0 0 0 0 0 0 0 0
11 16 2 6 6 2 1 7 0 7
10 6 3 6 7 14 0 4 0 7
9 0 3 6 5 0 0 0 0 4
46 74 47 29 46 37 57 48 81 48
34 34 34 27 41 31 28 31 31 34
25 23 26 22 27 27 25 25 20 25
Mat
hem
atic
s fo
r Li
bera
l Art
s
Fin
ite M
athe
mat
ics
Bus
ines
s M
ath
(non
-cal
culu
s)
Mat
h fo
r E
lem
Sch
Tea
cher
s
Col
lege
Alg
ebra
Trig
onom
etry
Col
lege
Alg
& T
rig (
com
bine
d)
Ele
m F
unct
ions
, Pre
calc
ulus
Intr
o to
Mat
h M
odel
ing
To
tal A
ll In
tro
Lev
el C
ou
rses
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
Cou
rse
& D
epar
tmen
t Typ
e
Per
cent
age
of s
ectio
ns ta
ught
by
TA
BL
E F
Y.1
Per
cent
age
of s
ectio
ns (
excl
udin
g di
stan
ce-le
arni
ng s
ectio
ns)
of c
erta
in in
trod
ucto
ry-le
vel c
ours
es ta
ught
by
vario
us ty
pes
of in
stru
ctor
s in
mat
hem
atic
s de
part
men
ts in
fall
2005
, by
type
of d
epar
tmen
t. A
lso
aver
age
sect
ion
size
s.
Ave
rage
sect
ion
size
Ten
ured
/
te
nure
-
elig
ible
%
Oth
er
full-
time
(tot
al)
%
Par
t-tim
e
%
Gra
duat
e
teac
hing
assi
stan
ts
%
Unk
now
n
%
Not
e: 0
mea
ns le
ss th
an o
ne h
alf o
f 1%
.
Oth
er
full-
time
(doc
tora
l)
%
Jan
9, 0
7;N
ov
8; O
ct 2
3; A
ug
ust
24,
200
6; A
pri
l 23,
200
7
First-Year Courses in Four-Year Colleges and Universities 115
Univ (PhD) Univ (MA) Coll (BA)
0
10
20
30
40
50
60
70
80
90
100
Tenured/tenure-eligible
Other full-time
Part-time
Graduate teaching assistants
FIGURE FY.1.1 Percentage of sections (excluding distance-learning sections) in introductory-level
mathematics courses (including College Algebra and Precalculus) taught in mathematics
departments by various kinds of instructors in fall 2005, by type of department. (Deficits from 100%
represent unknown instructors.)
Jan 9,07; Nov 8; Oct 23; August 22, 2006
116 2005 CBMS Survey of Undergraduate Programs
14
47
31
32
47
25
39
38
41
51
57
50
59
44
14
47
70
19
77
48
42
36 4 1 4 2 25 7
58
13
18 4 6 59
23
55 3 5 0 13
44
21
10
18
12 2 6 0 12
13 3 0 0 2 0 4
20 5 5 0 11
59
12
3 18
15
12
17 0 10
2 6 0 0 2 0 3
2 7 5 0 4 4 4
25 4 1 0 2 13 6
31 3 7 4 7 0 10
43 3 5 0 9 56
17
15
71
17
18
47 1
16
9
20
63 6 7 20 4
12
0
37
62 7 9 25 3
14
3
29
46
37
57
48
81
44
27
41
31
28
31
31
34
22
27
27
25
25
20
25
Math
em
atics f
or
Ele
m S
chool T
ea
ch
ers
Colle
ge A
lgebra
Trigonom
etr
y
Colle
ge A
lgebra
& T
rig (
com
bin
ed
)
Ele
menta
ry F
unctions,
Pre
calc
ulu
s
Intr
o t
o M
ath
em
atical M
odelin
g
All
cours
es in F
Y.2
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AC
ours
e &
Depart
ment
Typ
e
Gra
ph
ing
ca
lcu
lato
rs
%
Writin
g
assig
nm
en
ts
%
Co
mp
ute
r
assig
nm
en
ts
%
Gro
up
pro
jects
%
En
rollm
en
t
in 1
00
0s
Ave
rag
e
se
ctio
n
siz
e
Pe
rce
nta
ge
of
se
ctio
ns in
ce
rta
in I
ntr
od
ucto
ry L
eve
l co
urs
es ta
ug
ht u
sin
g
TA
BL
E F
Y.2
Perc
enta
ge o
f se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in c
ert
ain
in
tro
du
cto
ry-le
ve
l co
urs
es ta
ug
ht u
sin
g v
ario
us r
efo
rm m
eth
od
s in
math
em
atics d
epart
ments
in f
all
20
05
, b
y t
yp
e o
f d
ep
art
me
nt. A
lso
to
tal e
nro
llme
nts
(in
10
00
s)
an
d a
ve
rag
e s
ectio
n s
ize
.
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
-15
, a
nd
le
ss t
ha
n 5
00
in
th
e E
nro
llme
nt
co
lum
ns.
O
n-lin
e
reso
urc
e
syste
ms
%
No
v 8
; O
ct
23
; A
ug
us
t 2
2,
20
06
First-Year Courses in Four-Year Colleges and Universities 117
42
42
28
36
51
38
34
42
38
72
78
71
73
63
70
78
73
73
62
83
94
79
79
96
10
0
94
83
31
19
21
25
29
20
25
26
25
16 5 16
12 0 7 12 8 11
24 9 0 12
18 4 0 6 10
19
10
14
15
20
14
13
16
15
3 1 6 4 0 4 12 7 5
17 5 0 7 4 4 0 3 6
6 5 12 8 4 6 14 8 8
2 5 8 6 21
13 4 10 7
14 5 6 7 0 0 0 0 5
9 32
29
22 7 36
18
17
20
0 4 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0
11 2 11 9 8 1 9 7 9
11 7 5 7 16 9 6 9 7
0 2 0 2 4 0 0 1 1
65
25
37
46
64
26
38
47
46
29
24
34
29
23
22
31
25
28
23
21
33
22
19
20
35
20
22
Main
str
eam
Calc
ulu
s I
Lectu
re/
recitation
Regula
r section <
31
Regula
r section >
30
To
tal M
ain
str
eam
Calc
ulu
s I
Main
str
eam
Calc
ulu
s II
Lectu
re/
recitation
Regula
r section <
31
Regula
r section >
30
To
tal M
ain
str
ea
m C
alc
ulu
s II
To
tal M
ain
str
ea
m C
alc
ulu
s I &
II
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AC
ours
e &
Depart
ment
Typ
e
Ave
rag
e
se
ctio
n
siz
eU
nkn
ow
n
%
Gra
du
ate
tea
ch
ing
assis
tan
ts
%
Pa
rt-t
ime
%
Oth
er
full-
tim
e
(do
cto
ral)
%
Oth
er
full-
tim
e
(to
tal)
%
Te
nu
red
/
ten
ure
-
elig
ible
%
TA
BL
E F
Y.3
Perc
enta
ge o
f se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in M
ain
str
ea
m C
alc
ulu
s I a
nd
Ma
instr
ea
m C
alc
ulu
s II ta
ug
ht b
y v
ario
us typ
es
of
instr
ucto
rs in f
our-
year
math
em
atics d
ep
art
me
nts
in
fa
ll 2
00
5,
by s
ize
of
se
ctio
ns a
nd
typ
e o
f d
ep
art
me
nt. A
lso
ave
rag
e s
ectio
n s
ize
s.
Pe
rce
nta
ge
of
se
ctio
ns t
au
gh
t b
y
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
th
rou
gh
18
.
No
v 2
5;
No
v 8
; S
EP
T 1
5;
Au
gu
st
24
, 2
00
6
118 2005 CBMS Survey of Undergraduate Programs
Univ (PhD) Univ (MA) Coll (BA)
0
10
20
30
40
50
60
70
80
90
100
Tenured/tenure-eligible
Other full-time
Part-time
Graduate teaching assistants
FIGURE FY.3.1 Percentage of sections (excluding distance learning) in Mainstream Calculus I in
four-year mathematics departments by type of instructor and type of department in fall 2005. (Deficits
from 100% represent unknown instructors.)
Dec 8;Nov 8; Oct 23; August 17, 2006
Univ (PhD) Univ (MA) Coll (BA)
0
5
10
15
20
25
30
35
40
45
Graphing calculators
Writing assignments
Computer assignments
On-line resource systems
Group projects
FIGURE FY.2.1 Percentage of sections (excluding distance enrollment) in introductory-level mathematics courses
in Table FY.2 (including College Algebra and Precalculus) taught in mathematics departments using various reform
methods in fall 2005, by type of department.
Dec 8;Nov 8; Oct 23; August 22, 2006
First-Year Courses in Four-Year Colleges and Universities 119
37
44
42
40
23
42
37
32
38
69
66
36
52
75
54
44
53
52
57
59
65
59
64
47
86
52
57
5 2 5 5 4 6 1 3 4
9 27
18
20 0 12 8 8 16
25
16
14
18
25
15
28
17
18
14 9 26
18 8 17
15
13
16
39
10 4 12
46 6 16
16
14
33
25
32
27
43
31
57
34
29
10 4 11 9 6 3 8 6 8
6 1 0 2 0 0 0 0 1
0 2 0 2 0 2 0 2 2
4 5 11 7 1 3 2 2 5
0 19
10
11 0 12 8 8 10
27 6 32
12
28 4 28 9 11
60
11
34
105
31 6 16
54
159
5 8 17
30 2 4 6 12
42
14
44 7 65 3 15 1 19
84
65
25
37
46
64
26
38
47
46
29
24
34
29
23
22
31
25
28
23
21
33
22
19
20
35
20
22
Main
str
ea
m C
alc
ulu
s I
Lectu
re/r
ecitation
Regula
r section <
31
Regula
r section >
30
To
tal M
ain
str
ea
m C
alc
ulu
s I
Main
str
ea
m C
alc
ulu
s II
Lectu
re/r
ecitation
Regula
r section <
31
Regula
r section >
30
To
tal M
ain
str
eam
Calc
ulu
s II
To
tal M
ain
str
eam
Calc
ulu
s I&
II
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AC
ours
e &
Depart
ment
Typ
e
Gra
ph
ing
ca
lcu
lato
rs
%
Writin
g
assig
nm
en
ts
%
Co
mp
ute
r
assig
nm
en
ts
%
Gro
up
pro
jects
%
En
rollm
en
t
in 1
00
0s
Ave
rag
e
se
ctio
n
siz
e
Pe
rce
nta
ge
of
Ma
instr
ea
m C
alc
ulu
s I
& I
I se
ctio
ns ta
ug
ht u
sin
g
TA
BL
E F
Y.4
Perc
enta
ge o
f se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in M
ain
str
ea
m C
alc
ulu
s I &
II ta
ug
ht u
sin
g v
ario
us r
efo
rm m
eth
od
s in
math
em
atics d
epart
ments
by t
yp
e o
f se
ctio
n a
nd
typ
e o
f d
ep
art
me
nt
in f
all
20
05.
Als
o t
ota
l e
nro
llme
nts
(in
10
00
s)
an
d a
ve
rag
e s
ectio
n s
ize
.
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
th
rou
gh 1
5,
an
d le
ss t
ha
n 5
00
in
th
e E
nro
llme
nt
co
lum
ns.
On
-lin
e
reso
urc
e
syste
ms
%
No
v 8
; S
ep
t 1
5;
Au
gu
st
16
, 2
00
6
120 2005 CBMS Survey of Undergraduate Programs
Univ (PhD) Univ (MA) Coll (BA)
0
10
20
30
40
50
60
Graphing calculators
Writing assignments
Computer assignments
On-line resource systems
Group projects
FIGURE FY.4.1 Percentage of sections (excluding distance-learning sections) in Mainstream Calculus I taught
using various reform methods in four-year mathematics departments by type of department in fall 2005.
Jan 9, 07; Dec 8;Nov 8; Oct 23; August 17, 2006
Univ (PhD) Univ (MA) Coll (BA)
0
10
20
30
40
50
60
70
Graphing calculators
Writing assignments
Computer assignments
On-line resource systems
Group projects
FIGURE FY.4.2 Percentage of sections (excluding distance-learning sections) in Mainstream Calculus II taught
using various reform methods in four-year mathematics departments by type of department in fall 2005.
Jan 9, 07; Dec 8;Nov 8; Oct 23; August 17, 2006
First-Year Courses in Four-Year Colleges and Universities 121
16 7 21
17
25
18
27
46
40
42
47
42
40
47
75
51
100
52
33
24
27
28
31
29
9 7 27
18
13
18
60
20 6 19 0 19
13 4 11
10 9 10
9 1 8 5 0 5
0 5 3 4 0 4
11
12
24
17
20
18
0 27
31
28
40
28
0 20
19
19 0 19
11
36
27
24
22
23
0 0 0 0 0 0
0 13 0 10 0 10
29
20 1 14 1 12
64
20 2 12 0 12
0 0 0 0 0 0
72
26
53
52
56
53
28
23
39
33
18
32
22
24
28
25
14
25
No
n-M
ain
str
eam
Calc
ulu
s I
Lectu
re/ re
citation
Reg. section <
31
Reg. section >
30
To
tal N
on
-Mn
str
m C
alc
ulu
s I
To
tal N
on
-Mn
str
m C
alc
ulu
s II
To
tal N
on
-Mn
str
m C
alc
ulu
s I &
II
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
PhD
MA
BA
Cours
e &
Depart
ment T
ype
Tenure
d/
tenure
-
elig
ible
%
Oth
er
full-
tim
e
(tota
l)
%
Oth
er
full-
tim
e
(docto
ral)
%
Part
-tim
e
%
Gra
duate
teachin
g
assis
tants
%
Unknow
n
%
Avera
ge
section
siz
e
TA
BL
E F
Y.5
Perc
enta
ge o
f sections (
exclu
din
g d
ista
nce-learn
ing s
ections)
in N
on-M
ain
str
eam
Calc
ulu
s I a
nd II ta
ught by v
arious types o
f in
str
ucto
rs
in m
ath
em
atics d
epart
ments
in fall
2005, by s
ize o
f sections a
nd type o
f depart
ment. A
lso a
vera
ge s
ection s
ize.
Jan
9,0
7;N
ov 8
; O
ct
23;
Sep
t 15;
Sep
t 5, 2006
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
th
rou
gh
18
.
Perc
enta
ge o
f section
s taught by
S
ee
dis
cu
ssio
n o
f th
is p
erc
en
tag
e in
th
e t
ext
of
rep
ort
.
T
he
sa
mp
le s
ize
fo
r th
is c
ell
wa
s v
ery
sm
all.
1
1 1
2
2
22
22
22
Special Note on Table FY.5: Table FY.5 asserts that thirteen percent of smaller sections of the Non-main-stream Calculus I course taught in bachelors-level mathematics departments were taught by graduate teaching assistants (GTAs), and that seems anomalous. Part of that thirteen percent figure can be accounted for by the fact that some bachelors-level departments borrow GTAs from graduate science departments at
their universities and assign the borrowed GTAs to teach mathematics courses. However, follow-up calls revealed that the bulk of that figure was caused by the inclusion of some M.A.T. programs in the bach-elors-level universe of the CBMS2005 study. Such departments assigned M.A.T. students to teach some of their calculus courses, and the statistical calcu-lations used this raw data to make the national projection of thirteen percent.
122 2005 CBMS Survey of Undergraduate Programs
Tenured/tenure eligible
Other full-time
Part-time
Graduate teaching assistants
0 10 20 30 40 50 60
Univ (PhD)
Univ (MA)
Coll (BA)
FIGURE FY.5.1 Percentage of sections (excluding distance-learning sections) in Non-mainstream Calculus I in
four-year mathematics departments taught by various kinds of instructors, by type of department in fall 2005. (See
the text of the report for discussion of the use of GTAs in bachelors-only departments.)
Jan 9, 07; Nov 8; Oct 23; Sept 15; Sept 5, 2006
First-Year Courses in Four-Year Colleges and Universities 123
60
45
31
43
36
44
47
45
80
75
35
68
4 1 6 4
0 2 9 6
60 0 6 3
10 1 7 7
0 0 0 0
0 7 0 6
8 1 6 6
0 0 0 0
0 5 13 6
5 1 4 4
0 0 7 4
0 1 6 2
26 5 30
61
1 5 15
21
1 20 5 26
72
26
53
52
28
23
39
33
22
24
28
25
Non-m
ain
str
eam
Calc
ulu
s I
Lectu
re/r
ecitation
Regula
r section <
31
Regula
r section >
30
To
tal N
on
-main
str
eam
Calc
ulu
s I
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AC
ours
e &
Depart
ment
Type
Gra
ph
ing
ca
lcu
lato
rs
%
Writin
g
assig
nm
en
ts
%
Co
mp
ute
r
assig
nm
en
ts
%
On
-lin
e
reso
urc
e
syste
ms
%
Gro
up
pro
jects
%
En
rollm
en
t
in 1
00
0s
Ave
rag
e
se
ctio
n
siz
e
Pe
rce
nta
ge
of
No
n-m
ain
str
ea
m C
alc
ulu
s I
se
ctio
ns t
au
gh
t u
sin
g
TA
BL
E F
Y.6
Perc
enta
ge o
f sectio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in N
on
-ma
instr
ea
m C
alc
ulu
s I ta
ug
ht u
sin
g v
ario
us r
efo
rm m
eth
od
s in
fo
ur-
year
math
em
atics d
epart
ments
in f
all
20
05
, b
y t
yp
e o
f se
ctio
n a
nd
typ
e o
f d
ep
art
me
nt. A
lso
to
tal e
nro
llme
nts
(in
10
00
s)
an
d a
ve
rag
e s
ectio
n s
ize
.
Ja
n 9
,07
; N
ov
8;
Se
pt
15
; S
ep
t 5
, 2
00
6
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
th
rou
gh
15
, a
nd
le
ss t
ha
n 5
00
in
th
e E
nro
llme
nt
co
lum
ns.
124 2005 CBMS Survey of Undergraduate Programs
Graphing calculators
Writing assignments
Computer assignments
On-line resource systems
Group projects
0 10 20 30 40 50 60 70
PhD
MA
BA
FIGURE FY.6.1 Percentage of sections (excluding distance-learning sections) in Non-mainstream
Calculus I taught using various reform methods in four-year mathematics departments by type of
department in fall 2005.
Jan 9,07; Dec 8;Nov 8; Oct 23; August 17, 2006; Sept 5, 2006
First-Year Courses in Four-Year Colleges and Universities 125
15 1 31
21
25
21
13
35
53
45
53
47
41
61
54
57
15
53
58
51
25
38
29
37
14
28
20
21
17
20
17 8 13
10
27
12
32
22 5 14 2 13
9 4 2 3 5 4
0 3 5 3 4 3
14
14
12
13
37
17
63
31
22
28
25
27
34
29
27
29
58
32
9 33
26
24
10
22
0 6 1 2 0 2
0 0 0 0 0 0
4 0 6 4 0 3
9 0 3 3 6 4
8 2 6 4 0 3
70
24
48
46
49
47
37
26
41
37
33
36
22
24
36
27
23
26
Ele
men
tary
Sta
tisti
cs
(n
on
-Ca
lcu
lus)
Lectu
re/
recitation
Regula
r section <
31
Regula
r section >
30
To
tal E
lem
en
tary
Sta
tis
tic
s
To
tal P
rob
ab
ilit
y &
Sta
tisti
cs
(n
on
-Ca
lcu
lus)
To
tal b
oth
co
urs
es
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AM
ath
em
atics D
epart
me
nts
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
th
rou
gh
18
.
Ja
n 9
,07
; D
ec
8;
No
v 2
5;
No
v 8
; S
ep
t 1
5;
Se
pt
12
; A
ug
us
t 2
2,
20
06
T
en
ure
d/
t
en
ure
-
elig
ible
%
Pe
rce
nta
ge
of
se
ctio
ns t
au
gh
t b
y
Oth
er
full-
tim
e
(to
tal)
%
Oth
er
full-
tim
e
(do
cto
ral)
%
Pa
rt-t
ime
%
Gra
du
ate
tea
ch
ing
assis
tan
ts
%
Un
kn
ow
n
%
Ave
rag
e
se
ctio
n
siz
e
TA
BL
E F
Y.7
Perc
enta
ge
of
se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in E
lem
en
tary
Sta
tistics (
no
n-C
alc
ulu
s)
an
d P
rob
ab
ility
an
d S
tatistics
(non-C
alc
ulu
s)
taught
by v
ario
us t
yp
es o
f in
str
ucto
rs in
ma
the
ma
tics d
ep
art
me
nts
in
fa
ll 2
00
5, b
y s
ize
of se
ctio
ns a
nd
typ
e o
f d
ep
art
me
nt. A
lso
avera
ge s
ection s
ize.
126 2005 CBMS Survey of Undergraduate Programs
Univ (PhD) Univ (MA) Coll (BA)
0
10
20
30
40
50
60
Tenured/ tenure-eligible
Other full-time
Part-time
Graduate teaching assistants
FIGURE FY.7.1 Percentage of sections (excluding distance-learning sections) in Elementary
Statistics (non-Calculus) in four-year mathematics departments, by type of instructor and type of
department in fall 2005.
Jan 9, 07;Nov 8; Oct 23; August 17, 2006
First-Year Courses in Four-Year Colleges and Universities 127
0 0 36
21
19
21
33
59
39
43 3 34
62
29
52
37
35
37
0 3 24
14 8 13
67
27
12
21 0 16
62
31
26
33
79
37
69
57
17
36
85
43
67
35
40
41
13
35
92
58
64
62
61
62
0 0 0 0 0 0
0 7 1 2 0 2
0 4 3 4 0 3
0 0 12 7 19 8
0 25 6 10 0 7
65
20 2 20
53
23
7 3 14
23 4 27
1 4 20
24 7 31
5 47
23
74 7 81
70
24
48
46
49
43
37
26
41
35
33
32
22
24
36
27
23
26
Ele
men
tary
Sta
tisti
cs
(no
n-C
alc
ulu
s)
Lectu
re/r
ecitation
Regula
r section <
31
Regula
r section >
30
To
tal E
lem
en
tary
Sta
tisti
cs
To
tal P
rob
ab
ilit
y &
Sta
tisti
cs
(no
n-
Calc
ulu
s)
To
tal b
oth
co
urs
es
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AP
hD
MA
BA
Ph
DM
AB
AM
ath
em
atics D
epart
ments
Gra
ph
ing
ca
lcu
lato
rs
%
Writin
g
assig
nm
en
ts
%
Co
mp
ute
r
assig
nm
en
ts
%
Gro
up
pro
jects
%
En
rollm
en
t
in 1
00
0s
Ave
rag
e
se
ctio
n
siz
e
Pe
rce
nta
ge
of
Sta
tistics &
Pro
ba
bili
ty (
no
n-C
alc
ulu
s)
se
ctio
ns ta
ug
ht u
sin
g
TA
BL
E F
Y.8
Perc
enta
ge o
f se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in E
lem
en
tary
Sta
tistics (
no
n-C
alc
ulu
s)
an
d P
rob
ab
ility
& S
tatistics (
no
n-
Calc
ulu
s)
taught
usin
g v
arious r
efo
rm m
eth
od
s in
fo
ur-
ye
ar
ma
the
ma
tics d
ep
art
me
nts
in
fa
ll 2
00
5,
by typ
e o
f se
ctio
n a
nd
typ
e o
f d
ep
art
me
nt.
Als
o to
tal
enro
llments
(in
1000s)
and a
vera
ge
se
ctio
n s
ize
.
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
th
rou
gh
15
.
On
-lin
e
reso
urc
e
syste
ms
%
Ja
n 9
,07
; N
ov
8;
Se
pt
15
; A
ug
us
t 1
6,
20
06
128 2005 CBMS Survey of Undergraduate Programs
Graphing calculators
Writing assignments
Computer assignments
On-line resource systems
Group projects
0 10 20 30 40 50 60 70
Univ (PhD)
Univ (MA)
Coll (BA)
FIGURE FY.8.1 Percentage of sections (excluding distance-learning sections) in Elementary Statistics (non-
Calculus) taught using various reform methods in four-year mathematics departments by type of department in fall
2005.
Jan 9,07; Nov 8; Oct 23; August 17, 2006
First-Year Courses in Four-Year Colleges and Universities 129
18
31
18
19
41
20
13
19
26
40
58
46
25
44 0 43
21 8 11
17
19
17
22
17
63
60
20
37
63
39
67
40
8 8 10 9 13 9 12 9
0 60 4 6 63
11
33
12
16 8 18
16 0 16
10
14
11 0 17
14 0 13
33
13
20
28
48
30
28
29
20
27
0 0 0 0 0 0 0 0
25
24 5 18
13
18
35
23
0 0 5 3 13 4 0 4
75
21
58
67
95
64
61
68
12
1
29
38
66
30
62
94
63
Ele
men
tary
Sta
tisti
cs
(no
n-C
alc
ulu
s)
Lectu
re/r
ecitation
Regula
r section <
31
Regula
r section >
30
To
tal E
lem
en
tary
Sta
tis
tic
s
Pro
ba
bilit
y &
Sta
tisti
cs
(n
on
-Calc
ulu
s)
To
tal E
lem
en
tary
Sta
tis
tic
s a
nd
Pro
ba
bilit
y &
Sta
tisti
cs
Sta
tisti
cs L
itera
cy
To
tal all c
ou
rse
s in
Tab
le F
Y.9
Ph
DM
AP
hD
MA
Ph
DM
AP
hD
MA
Ph
DM
AP
hD
MA
Ph
DM
AS
tatistics D
epart
ments
Pe
rce
nta
ge
of
se
ctio
ns t
au
gh
t b
y
Ave
rag
e
se
ctio
n
siz
e
T
en
ure
d/
ten
ure
-
e
ligib
le
%
Oth
er
full-
tim
e
(to
tal)
%
Pa
rt-t
ime
%
Gra
du
ate
tea
ch
ing
assis
tan
ts
%
Un
kn
ow
n
%
No
te:
In t
he
firs
t 1
2 c
olu
mn
s,
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
%.
TA
BL
E F
Y.9
Perc
enta
ge o
f se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in E
lem
en
tary
Sta
tistics (
no
n-C
alc
ulu
s)
an
d P
rob
ab
ility
an
d S
tatistics (
no
n-
Calc
ulu
s)
taught
by instr
ucto
rs o
f va
rio
us t
yp
es in
sta
tistics d
ep
art
me
nts
in
fa
ll 2
00
5,
by s
ize
of se
ctio
ns a
nd
typ
e o
f d
ep
art
me
nt. A
lso
ave
rag
e s
ectio
n
siz
e.
Oth
er
full-
tim
e
(do
cto
ral)
%
Ja
n 9
,07
; D
ec
8;N
ov
8;
Se
pt
15
; S
ep
t 1
2;
Au
gu
st
24
, 2
00
6
130 2005 CBMS Survey of Undergraduate Programs
Univ (PhD) Univ (MA)
0
5
10
15
20
25
30
35
40
45
50
Tenured/ tenure-eligible
Other full-time
Part-time
Graduate teaching assistants
FIGURE FY.9.1 Percentage of sections (excluding distance-learning sections) in Elementary
Statistics (non-calculus) taught in statistics departments in fall 2005, by type of instructor and type of
department. (Deficits from 100% represent unknown instructors.)
Jan 9,07; Oct 23; August 22, 2006
First-Year Courses in Four-Year Colleges and Universities 131
10 2 2 7
0 0 0 0
37
24
62
44
74 0 48
54
56
82
43
54
74
10
0
67
71
28
20 0 18
15
80 2 11
29
20 6 20
41 0 48
43
22 0 9 31
7 0 4 11
75
21
58
67
12
1
29
38
66
Ele
men
tary
Sta
tisti
cs
(no
n-C
alc
ulu
s)
Lectu
re/r
ecitation
Regula
r section <
31
Regula
r section >
30
To
tal E
lem
en
tary
Sta
tis
tic
s
Ph
DM
AP
hD
MA
Ph
DM
AP
hD
MA
Ph
DM
AP
hD
MA
Ph
DM
AS
tati
sti
cs D
ep
art
me
nts
Gra
ph
ing
ca
lcu
lato
rs
%
Writin
g
assig
nm
en
ts
%
Co
mp
ute
r
assig
nm
en
ts
%
Gro
up
pro
jects
%
En
rollm
en
t
in 1
00
0s
Ave
rag
e
se
ctio
n
siz
e
Pe
rce
nta
ge
of
Ele
me
nta
ry S
tatistics (
no
n-C
alc
ulu
s)
se
ctio
ns ta
ug
ht u
sin
g
TA
BL
E F
Y.1
0P
erc
en
tag
e o
f se
ctio
ns (
exclu
din
g d
ista
nce
-le
arn
ing
se
ctio
ns)
in E
lem
en
tary
Sta
tistics (
no
n-C
alc
ulu
s)
tau
gh
t u
sin
g v
ario
us r
efo
rm
meth
ods in s
tatistics d
ep
art
me
nts
in
fa
ll 2
00
5,
by t
yp
e o
f se
ctio
n a
nd
typ
e o
f d
ep
art
me
nt. A
lso
to
tal e
nro
llme
nts
(in
10
00
s)
an
d a
ve
rag
e s
ectio
n s
ize
.
No
te:
0 m
ea
ns le
ss t
ha
n o
ne
ha
lf o
f 1
% in
co
lum
ns 1
-12
an
d le
ss t
ha
n 5
00
in
th
e E
nro
llme
nt
co
lum
ns.On
-lin
e
reso
urc
e
syste
ms
%
Ja
n 9
, 0
7;
No
v 8
; S
ep
t 1
5;
Au
gu
st
16
, 2
00
6
132 2005 CBMS Survey of Undergraduate Programs
Graphing calculators
Writing assignments
Computer assignments
On-line resource systems
Group projects
0 10 20 30 40 50 60 70 80
Univ (PhD)
Univ (MA)
FIGURE FY.10.1 Percentage of sections (excluding distance-learning sections) in Elementary Statistics (non-
Calculus) taught using various reform methods in statistics departments, by type of department in fall 2005.
