Mathematics Program Review Report
2004-2005
California Baptist University
Department of Natural and Mathematical Sciences
June 8, 2005
Compiled by: Thomas E. Ferko, Ph.D., Department Chair
Wb1/asmt/stoOt/687287644
2
Introduction
This Mathematics Program Review is being performed as part of the regular assessment of
academic programs at California Baptist University (CBU). The following aspects are contained
within this report this following:

A comprehensive analysis of all of the accumulated Student Outcomes Assessments
including a comparative review of “industry standard” outcomes data against CBU
students.

A comparison of our curriculum to other universities, including 2 comparable Christian
universities, 1 dissimilar Christian university, and 2 dissimilar secular universities.

A report from an on-site visit by Dr. Wil Clarke, Professor of Mathematics at La Sierra
University.

A detailed discussion about the state of the Mathematics program including proposed
changes.
Analysis of Student Outcomes Assessments
As part of our ongoing assessment of the mathematics major at CBU we have established four
Program Student Outcomes (PSOs) that we hope for 1) all students to attain while completing their
mathematics major at CBU and 2) be able to quantitatively measure. These PSOs are:
1) Students should have a solid foundation of mathematical processes at the level of a
student entering a graduate program in mathematics. Processes should include (but
are not limited to) a proficiency in logic, problem solving, and methods of proof.
2) Students will demonstrate their ability to apply mathematics in other fields at an
appropriate level and demonstrate their ability to apply knowledge acquired from
their major to real world models.
3) Students will demonstrate mastery of abstract mathematical concepts and critical
reasoning.
4) Students should acquire the up-to-date skills of computer programming necessary for
future career choices.
During the 2002-2003 academic year the 1st PSO was assessed and during the 2003-2004 and
2004-2005 academic years the 1st and 2nd PSOs were assessed. The 3rd and 4th PSOs have not been
assessed as of this date.
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Program Student Outcome #1
One of our Math goals has always been to adequately prepare students for advanced study in
mathematics at the graduate level, should they choose to pursue such studies. The standard
evaluation tool for such study is the Graduate Record Exam (GRE) in Mathematics which is
published by the Educational Testing Service (ETS). However, we have instead chosen to utilize the
Major Field Test (MFT) in mathematics. This exam, also published by ETS, was developed from a
similar knowledge base but is designed for assessment. Results from the MFT mathematics exam
are provided for each student and include not only a total test score but also assessment indicators in
Calculus, Algebra, Routine, Nonroutine, and Applied areas of mathematics. Based on information
posted on the ETS web site, the Calculus area of the exam (30%) covers material in the first 3
semesters of calculus, the Algebra area (30%) covers topics in Linear Algebra and Abstract Algebra
and the remainder of exam (40%) covers 10 ‘additional topics’ that would be covered in upper level
courses. Material on the exam was also classified into 3 cognitive levels: Routine (55%),
Nonroutine (25%), and Applied (20%). Characteristics of problems classified into each of these
areas are as follows:
Routine involves:
 two or three definitions and no more than a 2-step reasoning process
 standard techniques from courses that most majors take
Nonroutine includes:
 all items that are considered ‘insightful’
 items that include several steps of reasoning
 items that require either the use of several definitions or a ‘new’ definition which the
student would not be expected to know.
 may require bridging techniques from two or more areas to bear on one problem.
Applied includes:
 all ‘real world’ settings
A total test mean score for all CBU Math students who took the exam (currently only
seniors) is also provided along with tables that permit us to estimate percentile scores on both the
total test and each assessment indicator for the average graduating CBU Math major. Such data, if
they can be correlated to specific courses, should permit us to both assess the effectiveness of the
MFT in evaluating our program and determine areas in which we need to make changes to improve
our students’ performance on this measure.
As shown in Table 1, six seniors took the MFT at the end of the 2002-2003 academic year
and averaged 138.7 (10th percentile) for the total exam, with individual scores ranging from a high of
147 (35th percentile) to 128 (5th percentile). Five seniors took the MFT at the end of the 2003-2004
year and averaged 139.1 (10th percentile) for the total exam, with individual scores ranging from a
high of 152 (50th percentile) to 120 (5th percentile). At the end of the 2005-2006 year 11 seniors
took the MFT and averaged 146.1 (25th percentile) for the total exam, with individual scores ranging
from a high of 169 (80th percentile) to 123 (5th percentile). The total possible score range is 120200 and national means are 152.4 (individual) and 151.9 (institution); median scores are 149.4
(individual) and 151.8 (institutional).
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Table 1: Student scores and percentiles for 2003-2005 mathematics seniors.
Score
147
141
141
136
136
128
Average:
138.7
2003
Percentile
35th
25th
25th
15th
15th
5th
10th
Score
152
147
141
131
120
Average:
139.1
2004
Percentile
50th
35th
25th
5th
5th
10th
Score
169
164
164
155
149
149
140
137
134
131
123
Average:
146.1
2005
Percentile
80th
75th
75th
60th
40th
40th
25th
20th
10h
5th
5th
25th
Our goal for the MFT during the first 2 years that the MFT was administered was for
students to average at or near the 50th percentile compared to national results. However, only one
out of eleven students reached this national average and our institutional average was closer to the
10th percentile. Having established this as base line, we re-set our goal of reaching the 50th
percentile in the long-term while setting more modest short-term goals. For the 2004-2005 academic
year we set a goal of reaching the 20th percentile. Our results for 2004-2005 met this goal since we
were at the 25th percentile and this is a marked increase over the 10th percentile that we attained in
each of the last 2 years. Next year we will revise this goal to the 30th percentile with the goal of
attaining the 50th percentile within 3 years.
For the 2004-2005 academic year we further establish goals of having all students score at or
above the 10th percentile and having 20% of students score at or above the 50th percentile for the
2004-2005 academic year. We partially met this goal since 36% of our students (4 out of 11) scored
at or above the 50th percentile but 2 out of 11 students scored in the lowest 5th percentile; this is
identical to the combined total over the first 2 years (2 out of 11 students in the lowest 5th
percentile).
We are very pleased with the trend of higher performance of our individual students. Over
the first 2 years only 1 out of 11 students scored at or above the 50th percentile and in 2004-2005
36% scored in this range. Two additional students were one point below the 50th percentile (scoring
149 out of 200 when 150 defined the 50th percentile) and including them we would have had 6 out of
11 (55%) scoring at or above the 50% percentile; this would be at the national average. However,
the rather large percentage (5 out of 22, or 23%) of students scoring at or below the 5th percentile
nationally is of some concern. While this may indicate that some of our students are indeed in the
lowest percentile nationally it may also be a reflection of the relative unimportance that students
place on this exam. They take the exam in the second half of their last semester and there is no
incentive or accountability to encourage them to perform well (or even try). Some possible ideas
that have been considered would be to include the MFT as one factor in determining the
‘Mathematics and Physics Award’ recipient, present a separate award at the KME induction to the
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highest scorer on the MFT or give the exam earlier in the senior year when students are not
experiencing ‘senioritis’ or are not under as much pressure. Another reason for such low
performance may be that 10-20% of the material that the MFT exam covers is not taught in our
major (e.g. topics in discrete mathematics, dynamical systems, and point-set topology).
The MFT results also included individual assessment indicators which are shown in Table 2.
Based on this data, there are some indications that we are showing improvements institutionally in
MFT results, compared to the two previous years, both overall and in the Calculus, Nonroutine, and
Applied assessment indicators. However, since we have only used this assessment for 3 years we
are hesitant to over-interpret the results and view improvements with a degree of cautious optimism.
Institutionally we have improved from the 10th percentile to the 25th percentile. The largest
improvements in individual assessments have been in the Calculus area (going from the 5th to the
40th percentile) and the Nonroutine area (going from the 1st to the 20th percentile). Our results in the
Algebra and Routine assessment indicators have shown a slight but statistically insignificant decline
over the same period. While still not up to national means, our students seem to be relatively more
adept at Nonroutine and Applied problems than at Routine problems. Students are able to correctly
answer a higher percentage of Routine problems than Nonroutine problems (which would be
expected since Routine problems should be more straightforward) but relative to other institutions
they did rather poor.
Table 2: MFT results over the past 3 years showing average overall scores and percent of correct
responses in each of 5 assessment indicators. Percentiles (xth) showing the percentage (x) of results below our
results are also shown.
Year
2002-03
2003-04
2004-05
Overall
average
138.7
(10th)
139.1
(10th)
146.1
(25th)
Calculus
Algebra
Routine
Nonroutine
Applied
24.5%
(15th)
21.4%
(5th)
32.8%
(40th)
36.8%
(15th)
33.4%
(5th)
32.2%
(5th)
31.8%
(10th)
30.6%
(5th)
29.5%
(5th)
17.7%
(1st)
16.2%
(1st)
22.7%
(20th)
31.2%
(20th)
30.8%
(15th)
32.7%
(20th)
With the goal of refining our comparison to institutions that are more similar to CBU, during
the 2004-2005 academic year Dr. Alan Fossett requested that ETS prepare a report of consolidated
comparative data for 18 institutions (Table 3) that he felt were most similar to CBU in being small,
private, Christian-affiliated institutions. [NOTE: This list is slightly different from the list in the
2004-2005 final assessment report which incorrectly listed institutions chosen for the Biology MFT
comparison]. In the years 1999-2002 there were 224 students from these 18 institutions who took
the mathematics MFT, as compared to 3877 students from all institutions (218 total).
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Table 3: Comparable institutions for which ETS generated a report of consolidated comparative data.
Campbell University, NC
Master’s Coll. and Sem., CA
Shorter College, GA
East Texas Baptist Univ., TX
Mercer University, GA
Southern Nazarene Univ., OK
Eastern Nazarene College, MA
Missouri Baptist Univ., MO
Southwest Baptist Univ., MO
Georgetown College, KY
Mt. Vernon Nazarene College, OH
Union University, TN
Houston Baptist Univ., TX
Oklahoma Baptist Univ., OK
Wayland Baptist Univ., TX
Howard Payne Univ., TX
Samford University, AL
William Carey College, MS
In a one sense, students from these two groups of schools had rather similar means and
scores required to attain the 50th percentile were identical (Table 4) but the ‘curve’ seems narrower
as indicated by the higher scores required for the 10th percentile and lower scores required for the
90th percentile for the comparable institutions subset.
Table 4: Comparison of MFT results between institutions that were determined to be similar to CBU and all
institutions that utilized the MTF mathematics exam.
comparable
institutions (18)
total institutions
(218)
Mean
150.6
10th percentile
135-136
50th percentile
150-152
90th percentile
174-178
152.4
132-134
150-152
176-183
Therefore, it is not surprising that when we compare our results to these ‘comparable
institutions’ (Table 5) our students did almost the same as when compared to all institutions.
Table 5: MFT results over the past 3 years compared to ‘Comparable institutions’ showing average overall
scores and percent of correct responses in each of 5 assessment indicators. Percentiles (xth) showing the
percentage (x) of results below our results are also shown.
Year
2002-03
2003-04
2004-05
Overall
average
138.7
(5th)
139.1
(5th)
146.1
(25th)
Calculus
Algebra
Routine
Nonroutine
Applied
24.5%
(10th)
21.4%
(1st)
32.8%
(55th)
36.8%
(20th)
33.4%
(10th)
32.2%
(1st)
31.8%
(10th)
30.6%
(5th)
29.5%
(1st)
17.7%
(1st)
16.2%
(1st)
22.7%
(20th)
31.2%
(10th)
30.8%
(10th)
32.7%
(20th)
One other area that I would like to address is the great improvement in the Calculus
indicator. Compared to all institutions we went from the 5th percentile in 2004 to the 40th percentile
in 2005 in this area (and going from the 1st to the 55th percentile when comparing us to ‘comparable
institutions’). This indicator covers topics that students unusually see in their 1st three semesters so
by the time they take the MFT exam they are over two years removed from it. Dr. Pankowski
decided to do a series of three review sessions this past year to help review the calculus material (not
all students participated) and it is possible that this small amount of review helped the students to
7
recall the information more clearly and, as a result, perform better on the MFT in this area. In the
future we will propose a more formal course in ‘problem solving’ that hopefully will help students
perform better on GREs and other exams in addition to the MFT.
A final factor to be considered is the timing of courses. Since most upper-level courses are
only offered every-other year there will likely be different levels of ‘freshness’ (if a course was taken
recently or not) and coverage (if a student is currently enrolled in a course or has not taken a course
yet) that need to be accounted for.
Program Student Outcome #2
The second PSO that was evaluated during the 2003-2004 and 2004-2005 academic years
was the ability of Math majors to apply their mathematical knowledge in other fields and to real
world models. To accomplish this we entered a team of 2 students (in 2003-2004) and 3 students (in
2004-2005) in the Mathematical Modeling Contest which is sponsored annually by the Consortium
for Mathematics and its Applications. In both years our team was recognized as a ‘Successful
Participant’.
In 2005 there were 664 teams entered in this contest. Out of these, 37% were US teams and
63% were from other countries including Canada, China, Finland, Germany, Hong Kong, Indonesia,
Ireland, South Africa, and South Korea. Out of all entered teams only a combined 44% in 20042005 and 38% in 2003-2004 were given a designation above ‘Successful Participant’ (Table 6).
Table 6: Mathematical Modeling Contest results for all teams entered.
Designation
Outstanding Winner
Meritorious
Honorable Mention
Successful Participant
2003-2004
1%
10%
27%
62%
2004-2005
2%
13%
29%
56%
While we originally set the goal of being recognized at the level of ‘Honorable Mention’ or
above, we now recognize that this is a rather lofty goal given both the caliber of institutions that
enter this competition and also considering that we have very little experience in this contest and we
only enter one team each year. We have re-set this goal to having 1/3 of CBU teams be recognized
as Horonable Mention or above on an on-going basis and all teams be recognized as ‘Successful
Participants’ but it will take several years to determine if this goal is realistic.
Even if we continue to only be recognized as’ Successful Participants’, the sheer experience
of participating in a competition such as this pays enormous dividends for our students. In a related
matter, we had one student (Daniel Majcherek) present a paper on his work at the KME convention
in April, 2005. This was a good first step in getting our students to the level where they feel
comfortable in presenting their work at seminars directed at undergraduate-level students.
8
Comparative Curricular Review
For this part of our self-study we chose to compare the curriculum of CBU’s mathematics
major to 5 other institutions of higher education. The two of these which we consider to be most
comparable to CBU (Biola University and Azusa Pacific University) are Christian Universities in
Southern California. One (Westmont College) is a Christian College in Southern California which
we consider to be dissimilar to CBU based on their relatively higher academic stature. The final two
(University of California Riverside and California State University San Bernardino) are considered
to be dissimilar because of their larger size and secular status but are geographically close to CBU.
However, mathematics is a discipline in which secular vs. non-secular standing should have little
bearing on the number of courses required for a major and the foundational content of those courses.
A comparison of degree programs at the 5 institutions including a breakdown of units is
shown in Table 7. In comparing the mathematics major at CBU to majors at the other 5 universities
several observations can be made:




The required number of units at CBU (52) compares very well with the average number
of units required in all other programs (52), which range from 43 to 70 semester units.
CBU requires the least number of lower-division units and a higher than average number
of upper division units. This is most likely a result of variations in numbering systems.
CBU offers very few elective options for students with their only choice being 6 upperlevel math elective units (2 courses). For students pursuing the Single Subject Matter
Competence the options are even less since these students must take 2 courses (MAT 353
and MAT 363) as part of their major. This effectively removes any electives from their
major.
Likewise, CBU only offers one type of degree (a Bachelor of Science in Mathematics)
while other institutions offer up to 4 different types of degrees. While it is
understandable for a much larger university, such as UCR, to offer more options it is also
apparent that even smaller institutions, such as Westmont which has an enrollment of ½
of CBU’s, offer a variety of options. APU is the only other institution that offers one
type of mathematics degree.
9
Table 7. Units required for Mathematics Majors at 6 institutions.
Science†
Computer
Science
8 PHY
3
3
52
47
12
53
8
6+9
(may be CS)
18
3
47
18
20
6
3
16
16
13
11
9
20
21
21
4
(may be CS)
16
20
16
10
24 [16]
24 [16]
36 [24]
24 [16]
Inst.
Degree
Emphasis
Lower-level
math units
10
18
Upper-level
required
math units
25
20
Upper-level
elective
math units†
6
6
CBU
Biola
BS
BS
18
8
18
Other†
Total
Applied Mathematics
BS
Computer Science
BS
Mathematics
BS
16 ED
63
Math. Second. Teach.
APU
Westm.
BS
BS
4
16
10 PHY
9 PHY or
8 CHE
9 PHY or
8 CHE
9 PHY or
8 CHE
4
36 [24]
20 [13]
12 [8]
12 [8]
4 [3]
4 [3]
76 [51]
86 [57]
20 [13]
16 –20
[11-13]
20-44
[13-29]
4 [3]
24 [16]
24 [16]
24 [16]
(may be CS)
12 [8]
20 [13]
64-80
[4353]
104
[69]
22 [15]
28 [19]
46 [31]
5 [3]
PHY
4 [3]
Grad. School Prep.
BS
Secondary Education
BS
Applied and Comput.
BA
52
55-56
3 ED
61-62
56-57
4 AST
50
General
UCR‡
BA
BS
Pure
BS
Applied*
BS
Computational
Math.
CSUSB‡
BS
BA
22 [15]
28 [19]
20 [13]
4 [3]
* Options include Biology, Chemistry, Economics, Environmental Science, Physics, and Statistics
†
PHY = Physics, CHE = Chemistry, CS = Computer Science, ED = Education, AST = Astronomy
‡
UCR and CSUSB are on the quarter system so equivalent numbers of semester units are shown in brackets
next to each set of quarter units.
105
[70]
74 [49]
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A similar comparison of mathematics minors is shown in Table 8. While there is less variation in
minors several relevant observations can be made:


As with the major, the number of units required at CBU (26) compares very well to the
average of the average of other institutions (25.8).
CBU requires many more required upper-level units (13) than other institutions, of which
the maximum is 7 units at APU. As a result CBU students have fewer than average
elective options.
Table 8. Units required for Mathematics minors at 6 institutions.
University Lower-level Lower-level Upper-level Upperrequired
elective
required
level math
math units math units math units electives
CBU
10
13
3
Biola
18
6
APU
9
7
6
Westmont
16
8
UCR*
20 [13]
24 [16]
CSUSB*
20 [13]
2 [1]
4 [3]
4 [3]
Computer
Science
3
4
4 [3]
Total
26
27
26
24
44 [29]
34 [23]
* UCR and CSUSB are on the quarter system so equivalent numbers of semester units are shown in brackets next to each
set of quarter units.
When comparing individual courses that are either required or offered as electives between
CBU and the 3 programs that are most similar to ours (APU’s B.S., Biola’s B.S. with a concentration
in ‘Mathematics’, and Westmont’s B.S. ‘Graduate School Preparation Track’) several distinctives
are evident (Table 9):


CBU is the only university that requires a separate ‘computer laboratory’ course for
calculus and we require a 1-unit course each semester
CBU requires two courses - Complex Variables and Geometry – which the other 3
universities offer as electives but do not require.
Prerequisites for upper-level courses also vary widely between the universities. Considering
those courses that are viewed as ‘bridge courses’ or those that are required for an extensive number
(3+) of other courses:

CBU requires MAT 313 “Mathematical Proofs and Structures” as a pre-requisite for 5
upper-level courses (Modern Algebra, Complex Variables, Linear Algebra, Advanced
Calculus, and Fundamental Concepts of Geometry). This is identified as a ‘bridge
course’ in its description.

Biola is most similar in this aspect by requiring “Discrete Structures” – a course whose
content is very similar to MAT313 – as a prerequisite for 4 upper-level courses
(Advanced Calculus, Modern Algebra, Probability, and Number Theory and History of
Mathematics). Biola also requires “Calculus III” as a prerequisite for 4 courses
(Advanced Calculus, Probability, Differential Equations, and Complex Variables) and
“Linear Algebra” as a prerequisite for 3 courses (Modern Algebra, Numerical Analysis,
and Differential Equations).
11


Westmont requires “Calculus II” as a pre-requisite for 6 courses (Multivariable Calculus,
Linear Algebra, Differential Equations, Introduction to Numerical Analysis,
Combintorics, and Probability and Statistics) and “Linear Algebra” as a prerequisite for 6
courses (Mathematical Analysis, Modern Algebra, Geometry, Number Theory, Topics,
and History of Mathematics); Multivariable Calculus also suffices as a prerequisite for 3
of these.
APU requires Calculus 1 as a pre-requisite for 3 courses (Calculus II, Discrete
Mathematics, and Linear Algebra), and Calculus II as a prerequisite for 5 courses
(Advanced Multivariate Calculus, Differential Equations, Probability and Statistics,
Introduction to Real Analysis, and Complex Variables).
Table 9 – Coursework required for similar mathematics majors at 4 institutions.
Coursework
CBU – APU – Biola – B.S.
Westmont –
B.S.
B.S.
Mathematics B.S. Grad
School Prep
Calculus 1
R
R
R
R
Calculus 2
R
R
R
R
Calculus lab
R–2
Proof and Structures (Discrete
R
R
R
E
Mathematics, Combintorics)
Modern (Abstract) Algebra
R
R
R, E
R, O2
Complex Variables
R
E
E
E
Multivariable Calculus
R
R
R
R
Linear Algebra
R
R
R
R
Differential Equations
R
R
E
Advanced Calculus (Real Analysis)
R
R
R
R, O2
Geometry
R
E
E–2
E
Logic
E
Probability and Statistics
E
E
E–2
E
History of Math and Number Theory
E
E
E
E–2
Numerical Analysis†
E
E
E
†
Mathematical Modeling
E
E
Explorations in Teaching†
E
Special Topics
E
E
O2
Mathematical Physics
E
Reading, Writing and Presentations
E
Readings
E
R–2
Research, Thesis or Senior Project
E–2
E
Problem Solving
R–3
Physics
R–2
R–2
O1
Chemistry
O1
Computer Science
R
R
R
†
Not in catalog but a regularly offered Special Topics Course
R = Required, E = Elective, OX = Optional choice from a limited set (X) of courses, -X = X courses offered in area
12
Report from on-site visit by Dr. Wil Clarke, Professor of Mathematics at La Sierra University
Report of a Visit with the Mathematics Faculty at
California Baptist University
April 13, 2005
The Visit
I arrived on campus at 8:00 a.m. and left about 12:30 p.m. During my time there, I had individual visits with Dr
Catherine Kong, Dr James Buchholz, Dr Frank Pankowski, and Ms Elizabeth Morris. I also attended parts of three
classes, MAT 255 Calculus II, MAT 135 Precalculus, and MAT 127 Mathematical Concepts and Applications II. All
four professors and I lunched together with Dr Thomas Ferko. I also spent about a 20 minutes visiting with a group of 6
students.
Initial Impressions
From the self-study report and looking at the university website, I had the following initial impressions.
 CBU has no general education mathematics component. I found this rather strange and questioned whether
CBU was a serious liberal arts institution or a glorified Bible college.
 CBU has two instructors with PhD’s in mathematics, one instructor with a PhD in Physics and one
instructor with an M.S. in Education. I found myself questioning whether a viable mathematics program
could exist with such limited resources. I wondered if, by reshuffling personnel, another mathematician
could join the department.
 The courses for a B.S. in mathematics seem adequate for a major, especially if the student intends to earn a
teaching credential in mathematics; they might not be as adequate for those proceeding on to a graduate
degree in mathematics.
 The courses MAT 343 Multivariable Calculus (which seems to correspond with UCR MATH 010A & B,
and LSU MATH 233) and MAT 413 Differential Equations (which seems to correspond with UCR MATH
046, and LSU MATH 232) might be better classified as lower division.
 The courses MAT 323 Modern Algebra, and MAT 443 Advanced Calculus really should be expanded to 2
semesters each in order to give enough time for sufficient coverage of the basics of these fields.
Impressions gained during my visit
CBU should reevaluate its decision to have no college level mathematics in its general education program. After all,
we are living in the 21st century when technology has become vital to our very survival. Allowing MAT 115
Intermediate Algebra, a high school sophomore level class, to count towards graduation seems unconscionable.
When I visited the classes, I found them well run. They were all rather small, which should make a great selling
point to prospective students. The students participated actively in the instruction and were paying attention. One class
had trouble with students coming in late; however, I have had trouble with students doing the same thing in the
comparable class at LSU. The teachers were not only professional but also obviously knew their material and presented
it clearly and well. CBU can be proud of their math teachers!
The classrooms I sat in were light and well ventilated. They had barely adequate marker boards. I would prefer more
area, personally. They were furnished with tables and comfortable chairs. They had TV-monitors with a VCR or
VCR/DVD player in each. One teacher used an overhead projector to display slides. The projector shone directly on the
marker board, which left a bright spot limiting visibility. A day light screen would have really helped solve this problem.
None was built into the classroom. The full room lights were kept on during the projection. This made me squint to see
the slide. I missed the availability of a digital projector and screen so that computer output could be used in the
classroom. One teacher did use the monitor to present the output of a graphing calculator.
Concern was expressed that MAT 313 (Mathematical Proof and Structures) served no real purpose. It was admitted
that the teaching of calculus would need to include a strong theorem-proof component to actually eliminate MAT 313.
Another option, in my opinion, might be to focus the course on only a few of the topics listed in the catalog, rather than
trying to cover too much. For example, one might study various methods of proof in the context of set theory, then,
13
possibly, lead into the properties of real numbers that are used in advanced courses such as MAT 323 and MAT 443.
Certainly, a student needs to learn how to reason mathematically, and this might well be a good place to start.
Another concern that was expressed was that some teachers might be passing students who have not mastered the
material of the class. This, then, jeopardizes the quality of all classes that require that class as a prerequisite. Such a
situation can, of course, be very frustrating to the teacher of the later class. Interestingly, in my discussion with students,
they raised the same issue. They raised it in the context of respect and popularity amongst other teachers at CBU.
Concern was raised over the use of the Calculus lab. I didn’t have the opportunity to observe a calculus lab. With the
huge quantity of material that has been compressed into the calculus sequence, the average teacher despairs of covering
everything that really needs to be covered. He or she then looks on something like a lab as an extra unit that they might
use to cover a bit more of the material. If the calculus lab is carefully correlated with the calculus class, it might indeed
help alleviate the pressure to some degree.
One of the teachers mentioned in class that they had material on-line. I searched in vain for this material. Maybe the
webmaster needs to provide links to these pages so they can be found easily.
Visit with students
When I visited with the students, they were very positive about their experiences at CBU. They were especially
positive about their teachers. They felt that the math teachers were consistently excellent academically. They really
appreciated the fact that the teachers were available outside of class both early and late. They told me that they felt their
teachers really cared about each student individually. They expressed an appreciation that it was full time teachers who
taught their classes and not graduate assistants. They valued the low student-to-teacher ratio.
They were a little concerned that they really had only two teachers who taught their major subjects. They felt that
they were missing out on a greater variety of teaching styles that they might have if the number of teachers were greater.
They suggested, in particular, that they would like to see some kind of group learning used once in a while. They
expressed appreciation that one of the teachers required them to find specific applications for the material they were
learning. They felt that faculty, in general, at CBU were overly critical of teachers who enforced excellence in their
students. Teachers who were too “easy” had become popular amongst the rest of the faculty, thereby hurting the
reputation of those who were classified as “hard teachers.” They wanted to learn as much as they could and felt that
teachers who were too easy were cheating them out of the learning experience they required. Needless to say, I was
really impressed with their attitude in this regard!
The students wished the science department were bigger. This would provide a greater variety of electives for them.
Additionally, there was concern expressed that at least one teacher had the reputation that students could cheat (and did
cheat) freely in his/her class without the danger of being caught.
Several students expressed real appreciation for the math club and the KME groups on campus. One student was
really looking forward to going to a KME meeting later this week. They enjoyed the service learning experiences they
got in KME, such as working to create a math day in a local elementary school.
I asked them whether, knowing what they know now, if they had it to do all over again they would come to CBU.
The clear majority indicated they would. Those who indicated they probably wouldn’t hastened to add that they really
valued their experience at CBU. The reasons they gave for valuing their CBU experience were both academic and faith
based.
Conclusion
I was very favorably impressed by what you are accomplishing at CBU, especially with the limited resources you
have available. I found a really supportive spirit amongst both the faculty and students. You have people who are willing
to go the extra mile to make your program a success, and I applaud you.
Respectfully submitted by
Wil Clarke, Ph.D.
La Sierra University
951-785-2548
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The State of the Mathematics Program
The Mathematics program at CBU is housed within the Department of Natural and
Mathematical Sciences (NMS). Both a major in mathematics, which leads to a Bachelor of Science
degree, and a minor in mathematics are offered. The department also offers a California-approved
Mathematics Subject Matter Competence program for students who plan to become secondary
school mathematics teachers and hosts a very active ‘math club’ and chapter of Kappa Mu Epsilon –
a national undergraduate mathematics honor society.
In addition to courses offered for the mathematics major and minor there are several courses
offered as part of the General Education (GenEd) curriculum or for students who plan to become
elementary school teachers and are pursuing a Liberal Studies/Elementary Subject Matter degree.
For the GenEd ‘Competency Requirements’ students can meet mathematics competency in one of 3
ways: 1) Score 550 or above on the SAT II math exam, 2) take MAT 115 (Intermediate Algebra) or
higher, or 3) attain a passing score on a MAT 115-level exam which is administered by the NMS
department. Students who are not prepared to enter MAT 115, based on SAT or AC T scores, must
pass MAT 095 first. Recommended SAT/ACT scores for enrollment into entry-level mathematics
courses are shown in Table 1. For liberal studies students a two-courses sequence (MAT 125/127) is
required.
Table 1: SAT/ACT cutoff scores and other pre-requisites for entry level math
courses as of March 2005:
Course
required
required
additional prerequisites
ACT
SAT
MAT 095
<18
<450
MAT 115
18-20
450-500
and H.S.: Alg. 1; Alg. 2 “B” or better
MAT 125,
21-22
500-550
135, and 144
and H.S.: a full year of Trig/Precalc
MAT 145 and >22
>500
“B” or better
245
Faculty
NMS is a hybrid math/science department containing programs and faculty in a variety of
disciplined including biology, chemistry, mathematics, and physics. Out of a total of eight full-time
faculty in the department, four have backgrounds in and teach mathematics courses. A listing of
mathematics faculty along with courses taught in the last 2 full years (Fall 2003-Summer 2005) are
as follows:
James Buchholz, Ph.D. Professor of Mathematics and Physics
courses taught: MAT 145, 400 (Explorations in Teaching)
Catherine Kong, Ph.D. Associate Professor of Mathematics
courses taught: MAT 127, 135, 144, 245L, 255L, 313, 323, 353, 363, 400
(Mathematical Modeling), 403, 443, 463
Elizabeth Morris, M.S. Assistant Professor of Mathematics
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courses taught: MAT 095, 115, 125, 127, 400 (Explorations in Teaching)
Frank Pankowski, Ph.D. Professor of Mathematics
courses taught: MAT 115, 135, 245, 255, 333, 343, 400 (Numerical
Analysis), 413
In addition to the full-time faculty listed above, the NMS department employed 9 individual
adjunct faculty to teach math courses (exclusively MAT 095 and 115) over this same 2-year period.
An overview of hours taught by adjuncts during this time is shown in Table 2.
Combining hours taught by adjunct faculty with overload hours taught by full-time faculty
we find that during the 04-05 academic year 40.5% of all hours are adjunct/overload. During the 0506 academic year this ratio is expected to rise to 43.1%.
Note: According to university policy, once this ratio reaches the 40% level on a consistent basis
we should propose to add an additional faculty member. However, this was not done in the
current budget cycle because for biology courses in 04-05 this ratio is at 39.2% but is expected to
rise to 49.5% in 05-06 with the addition of a Nursing major. The Department Chair presumed
that a proposal to add two new faculty members in the same budget cycle in the NMS department
would not be seen with favor and our greater perceived need is in Biology since adjunct faculty
are being used to teach upper-level majors courses in that major.
Table 2. Hours and percent of total hours of CBU math courses taught by adjunct
faculty from Fall 2003 through Summer 2005.
semester
MAT course hours total MAT course % taught
taught by adjuncts hours offered
by adjuncts
Fall 2003
15
54
28%
Spring 2004
6
44
14%
Summer 2004
6
6
100%
Fall 2004
21
66
32%
Spring 2005
21
62
34%
Summer 2005
6
6
100%
TOTAL
75
238
32%
Students
A comparison of mathematics-related majors over a 4-year period (Fall 2001 – Fall 2004) is
shown in Table 3. From this data, a measured but consistent increase in the number of students
majoring in mathematics is evident. Of students who were majoring in mathematics in the Fall of
2004 (the last period for which data were available), 5 were identified as Freshmen, 5 were
Sophomores, 8 were Juniors, and 13 were Seniors. While this trend seems on the surface to indicate
that the number of majors is decreasing, it is inconsistent with the overall increase in majors seen
over the last 4 years. Instead, an increase of majors in later years is more likely because of one or a
combination of the following factors:


A considerable number of students transfer to CBU.
Some students do not declare a major until required to do so, usually in their junior year.
16


Some students who enroll in MAT 115 or MAT 135 change their majors to Mathematics.
Because of changing to a mathematics during or after the Sophomore year, failure to pass
a course, and the irregular offering of math courses, some students take 5 years or more
to complete their major in mathematics.
Table 3. Comparison of numbers of students majoring in mathematics over a 4year period.
Major
Fall 01 Fall 02 Fall 03
Fall 04
AMAT – Applied Mathematics 1
0
0
0
MAT – Mathematics
19
25
29
31
PMAT – Pure Mathematics
3
0
0
0
TOTAL: 23
25
29
31
Recommendations
Based on the report of our outside reviewer, Dr. Wil Clarke, and my own analysis of this the current
state of our mathematics program, I (Dr. Tom Ferko) propose the following 8 changes to our
mathematics program. In the Fall of 2005 these will be discussed with the mathematics faculty and
formal changes will be instituted, as needed.
1. Our current California-approved ‘Mathematics Subject Matter Competence’ program (waiver) in
mathematics has expired and students entering CBU this Fall (2005) will not be covered by the
old waiver. Dr. Dawn Ellen Jacobs, Assistant Provost at CBU, has taken the lead in getting all of
CBU’s Single Subject Matter Competence programs re-written and Dr. Jim Buchholz will be the
principle Faculty in mathematics charged with re-writing this document. Submitting a revised
Single Subject competency programs in Mathematics is essential but we also need to develop
and submit a competency program in ‘Foundational Mathematics’, a new waiver that focuses on
teaching mathematics up through calculus. This will also require the development of a new
major since it will be fundamentally different from the traditional mathematics major. Prof.
Betsy Morris will be the principal author of this document.
2. We need to include separate entries in the catalog for Single Subject Matter Competency
programs. While this will be essential for the Foundational Mathematics, even for the traditional
Mathematics waiver a separate catalog entry is warranted since there are several courses that
these students must take as part of their major which are different from requirements for
mathematics majors who do not desire the waiver.
3. In addition to the waiver programs we should explore ways of offering more variations in the
math major. One way would be to offer an ‘Applied Mathematics’ major as most other
universities do. This could be done with a minimum of new courses if we develop a program
such as UCR has where students combine mathematics courses along with those of another
major (biology, business, etc.) to form a major. Some courses that are electives or special topics
courses in the current Mathematics major (Probability and Statistics, Numerical Analysis,
Mathematical Modeling) could be also be required elements of an applied math major.
Another way would be to change some of the required courses to electives. Two possibilities
would be to make Complex Variables and Fundamentals of Geometry elective courses, as they
17
are at the other universities that we compared our program to. Additionally, we should decrease
number of required upper-division units in the math minor from 13 (to 7 or 10) to give the
student more options.
4. There are several courses that are regularly offered as MAT400 ‘Special Topics in Mathematics’
courses which should be officially added to the university catalog. These include:
Numerical Analysis
Mathematical Modeling
Explorations in Teaching
Additionally, we should explore the possibility of additional courses in ‘Problem Solving’ such
as Westmont has (which could include a review for GRE/MFT exams) and a ‘Senior Project’
capstone course. We should also evaluate the content of certain courses (such as Modern
Algebra and Advanced Calculus) and divide them into 2 courses, if needed.
5. For every course, we need to re-evaluate content, prerequisites and offerings. Would Calculus II
be a sufficient prerequisite for some courses instead of Proofs and Structures? Are we covering
the content that is being evaluated by the MFT? (Should we be particularly concerned with
this?) We also need to re-evaluate the semesters in which some courses are offered to ensure the
courses are distributed throughout the program as evenly as possible.
6. Building on Dr. Clarke’s observation that CBU really does not have a college-level mathematics
general education requirement, we as a math/science faculty are in agreement that CBU should
have a mathematics aspect of the general education requirements above that of a high school
sophomore-level course (e.g. MAT115). Being realists, however, we realize that the ‘math
phobia’ that was evident on behalf of most of the majority of the faculty when the current Gen
Ed was instituted makes this unlikely. However, this does not mean that we should be limit
ourselves to offering MAT115 ‘college algebra’ or traditional mathematics courses (pre-calculus,
statistics, etc.) as the main/only way to meet this competency. Other universities offer various
course that are designed for liberal arts students and not math majors (eg. ‘The Nature of
Mathematics’ at Biola, ‘Analytical Inquiry’ and ‘Contemporary Mathematics’ at APU,
‘Mathematics in Western Culture’ at Westmont). A course of this type would be appealing to
the student who surpasses the SAT/ACT requirement for MAT 115 but who does not wish to
take a ‘traditional’ math course.
7. Given the level of overload/adjunct hours that we have in mathematics (>40%) we will propose
the addition of another mathematics faculty member in the 2006-2007 budget cycle. Not only
will this help in meeting the demands for lower-level course, it will also help to spread around
the load of upper-level courses. One of Dr. Clarke’s principle criticisms was the small size of
our math faculty and the fact that we have only 2 faculty members with mathematics Ph.D.s.
These 2 prefessors (Kong an Pankowski) essentially teach all of the math major courses. With
an additional faculty member the students could be exposed to a greater variety of teaching
styles.
8. As a related issue, I will encourage our mathematics faculty to teach more of a mixture of lower
and upper level courses while concentrating on the same courses for several years. A major area
of concern is that Dr. Kong has taught 11 different mathematics lecture courses in addition to the
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2 Calculus lab courses. Since Dr. Kong teaches most of the upper-level courses that are offered
every-other year she has had very few opportunities to teach the same course repeatedly. It
would be preferable if she could teach a course such as Calculus I or Calculus II every year to
lighten the required prep time.
For some (Kong and Pankowski) this will involve teaching at least one lower-level course each
semester. For Prof. Morris this will involve a plan to move towards including more upper-level
courses in her schedules [Note: Professor Morris is currently completing a Ph.D. in Mathematics
Education and, when finished, plans to pursue a Masters in Mathematics to prepare her to teach a
wider variety of courses.] For Professor Buchholz, this will include teaching one mathematics
majors course every year. This may require that we have some adjunct instructors teach
mathematics majors courses (they normally only teach MAT095 and MAT115 presently) but,
overall, this would be a positive change.