A. Program History

1. The department has experienced strong, fairly steady growth

since the college opened (Fall 1987 showed a particularly large

surge but this has since been corrected). On the negative side,

since resources were always in short supply, this was usually

achieved by overloading night sections with students to prove a

need for additional sections in the future. On the positive side,

there has been a real awareness of balancing the curriculum

needs of the college and we have always grown more slowly than

student demand would have dictated.

2. Growth in number of students and number of sections has of

course been paralleled by growth in faculty numbers. We have

always employed a high number of part-time instructors, and

despite many excellent teachers, turn over is alarmingly high.

Part-time hires are conducted every year, and often every

semester. This is because there are many full-time math

positions available around the bay and because our part-time

instructor salaries are considerably below many of our

neighboring districts. The ratio of full-time to part-time has

varied over the years. In the mid-eighties, part-time faculty

number increased dramatically to around thirty (compared to

five full-time). More recently the number of full-time faculty

has grown to nine and the number of part-time faculty remains

in the twenty to thirty range. For example, statistics from

opening in Fall 75 to current Spring 89, shows:

# of class # of F-T # of P-T

units Instructors Instructors

Fall 1975 46 2 5

Spring 1989 225 9 23

% of increase 389 350 360

3. In recent years, state competency requirements in mathematics

have increased, requiring more students to take intermediate

algebra and one math course beyond that for transfer. This has

caused an increase in the number of unprepared students and a

major problem with attrition/retention. There is a generally high

attrition rate (although this is true in general of math

departments) and a particularly high drop rate in beginning and

intermediate algebra. It has also meant that students are faced

with a choice of which course to take after intermediate algebra.

This choice is often made inappropriately, with many students

taking trigonometry, when Finite Math, Statistics, or Liberal Arts

Math would be more useful.

4. One of the strongest features of the department has been an

unusually cohesive group of full-time faculty, which has grown

slowly enough over the years, to maintain excellent communi-

cation and coordinated planning. We meet together at least once

a week for both day to day business and long range planning (for

example, Title V Review or Program Review). Our department's

electronic mail network assists this as we continue to grow. This

cohesiveness has occasionally produced surprise in other

segments of the college when confronted with a united group of

faculty.

5. During this growth and the repeated hirings, the department has

experienced many of the district's attempts at affirmative action.

We probably have the greatest departmental diversity in the

district. Currently, over 50% of the faculty are women, and over

50% are minorities. These ratios are significantly better than

other colleges in the area, and of course, complement the

diversity of our student population.

6. In contrast to the cohesive, stable faculty group, administrative

support has been in constant flux. There have been six different

Deans in the last ten years, and considerable time has been spent

familiarizing them with the mathematics program. Relocation of

the Deans from the second floor faculty areas, to the first floor

administrative area, did not help.

7. The loss of department release time has, in general, made

operation of the department more difficult. Administrative work

has always been shared with different full-timers, responsible for

specific areas, in order to provide continuity. Scheduling and

hiring take up a particularly large amount of time and are not

suitable for delegation to an outside coordinator. At present, the

Operating Unit Coordinator is assisting greatly with part-time

faculty evaluation. This ever expanding number of administra-

tive tasks seriously impinges on class preparation time since time

is "borrowed" from class preparation to carry out other tasks.

8. Mathematics is a totally service oriented department. Students

who consider themselves math majors, are almost non-existent.

But all transfer students and most degree and vocational

programs, require a considerable number of our courses. We

have contact with faculty in all these areas through the dispersal

of math faculty offices throughout the college.

9. The biggest difficulty facing our students seems to be the desire

to finish their programs as soon as possible, and rush through

courses without acquiring the necessary prerequisite skills. This

might be corrected by better placement, but, it is the professional

opinion of the math faculty that diagnostic tests are not an

effective tool for placing our unique mix of students. Factors

which most affect their performance in class are mainly lifestyle

conditions such as time, work, and family. Their level of

commitment can produce drastic changes in performance, not

predicted by a pre-entry test, where they tend to perform much

worse than they do in a subsequent class). Any effective

placement system will have to be much more elaborate and

hence, much more expensive, than a simple are not an

effective tool for placing our unique mix of students. Factors

which most affect their performance in class are mainly lifestyle

conditions such as time, work, and family. Their level of

commitment can produce drastic changes in performance, not

predicted by a pre-entry test, where they tend to perform much

worse than they do in a subsequent class). Any effective

placement system will have to be much more elaborate and

hence, much more expensive, than a simple test.

11. Budget constraints over the years have resulted in a steady

increase in the size of math classes. This is partly a response to

efforts to add sections (1) above, and partly it is due to an

increase of the maximum class size from 35 to 45 as stated in the

ACE-WVMJCCD Contract. Large sizes particularly hurt our poorer

students, who need individual attention to succeed in class. Since

large initial class sizes also correlate significantly with high drop

rates, they are probably not even cost effective in the short term.

12. These same high risk students have been hurt by the recent

administrative policy of canceling the first week of classes

whenever an instructor is sick. This can mean up to five hours of

lost time for a Calculus class. While it is often difficulty to obtain

substitute instructors, funds should be made available so that

cancellation is not the first standard option.

13. Scheduling naturally becomes more difficult as the department

size increases. On the faculty side, almost all full-time faculty

members have a part of their regular load at night and this can

only get worse as more full-time faculty are hired in response to

AB 1725. On the student side, there is still unsatisfied demand in

the evenings when rooms are unavailable. Several years ago the

Math Department expanded into off hours scheduling, such as

mid-afternoon, very early morning, and Friday afternoon. The

advent of WSCH/FTE goals has curtailed this, since although we

can attract students at these hours, classes are undoubtedly

larger at more conventional times. This poses a problem for

expansion. There is already a problem for students in that we do

them a disservice by offering no choice of classes in the afternoon

(because they would be small) and by sending them to the Wilcox

site in the evening (because they are deprived of the use of the

math and computer lab facilities).

14. Since the earliest years the concept of the Math Lab and its

tutoring operation has been an integral, vital part of the

department's success. Significant support is provided by using

the math instructional aides to run the lab, rather than to provide

the more traditional support of faculty. The change of location of

the math lab, away from math classroom and faculty areas,

caused great difficulties in creating an atmosphere of "the place

where everyone goes to do math". This character seems to be

returning with the hiring of new permanent staff. However,

there is a growth in overcrowding, since in the move, our area

was reduced by 30%. In a Spring 89 survey the two

greatest complaints by students using the math lab were that it

was overcrowded and overheated.

Thought needs to be given to the upcoming administrative

difficulty produced by operating unit reorganization and the

hiring of two new deans. The math lab is not part of LATC

although much of the tutor funding comes from that budget. It is

a math department operation with the two instructional aides

reporting to the math department faculty. Without support

provided by the math lab, many more of our weaker students

would be unable to complete their courses.

15. Computer facilities for integration of computers with mathematics

courses are inadequate. Historically the CIS program at Mission

was funded from math department faculty time and money. It

was anticipated that this would allow us to develop a computer

component in math courses. Since the forcible separation of the

math and CIS departments, we are seriously under-equipped

(compare West Valley's math department computer lab). This

means courses like computer supplement to Calculus or Stat-

istics are just not offered.

B. Intent and Focus

The intent and focus of the Mathematics department to a large

extent mirrors that of the college:

1. We prepare students for transfer to four year colleges and

universities by providing lower division classes required for their

major or general education pattern classes for their transfer

certification.

2. Many of these same classes also satisfy requirements for those

students who choose to obtain their associate degree at Mission

College.

3. Some of these classes also serve as skills courses to meet the

needs of other academic disciplines or vocational programs in the

college.

More specific features are to meet the needs of the community by

offering specialty classes upon request (for example, the current

program with Intel) or diagnostic testing and recommendations for

local companies (in the past, General Electric and Intel). These pro-

grams increase specific skills and provide career advancement. We

also aid other programs in the college to assess the math skills of

their students and prescribe suitable action (eg: diagnostic testing

for Electronics Programs and for Nursing Programs). In addition,

we provide the option of a Math proficiency test to satisfy grad-

uation requirements and challenge exams for suitable students.

The department also tries to participate in all major college and

district committee activities by making sure that it has a full-time

faculty member serving on each committee.

More generally, we have some philosophical goals which affect the

whole program:

4. We try to provide an atmosphere and opportunity for students to

feel less anxious with mathematics so that they can be challenged

to meet their potential in a non-threatening environment; we aim

to bolster the student's self image and build self confidence so

that they may enjoy and appreciate mathematics. All courses are

offered with a credit/non credit option.

5. We teach deductive reasoning and encourage critical thinking as

tools in problem solving rather than rote memorization of

formulas. This is very much in keeping with state Title V

requirements. Unfortunately, this approach is often at odds with

requests from industry for skills courses and with the desire

of students to transfer or graduate as fast as possible.

6. We do all this in a culturally pluralistic way that recognizes the

universality of mathematics as a common language with roots in

all cultures. This is made easier by our diverse student and

faculty groups.

7. We help students to become generally mathematics literate so

that they may understand and communicate ideas and relation-

ships in a mathematical way appropriate to our technological

society; we relate abstract concepts to concrete examples.

8. We provide both in the classroom and through the math lab, for

students to gain learning and study skills which can be applied

to areas inside and outside of mathematics.

9. We create classroom situations where students can become

familiar with computer technology and the solution of problems

with mathematically sophisticated software. (This is hampered

by lack of equipment, see A:14 and A:15 above.)

10. The Math Lab learning center, which offers a helpful, friendly

atmosphere, where students may obtain free, regularly scheduled

tutoring or drop-in tutoring, during day and evening hours.

Many of the full-time faculty spend a portion of their office hours

in the math lab. Books, audio visual materials, and computer

software, are also available there to create a space where every

type of student can go to do mathematics. It is important that

the math lab is not just a place where weaker students go to get

help and which is avoided by the rest of the program.

11. A friendly full-time math faculty who are unusually student

oriented and willing to help students, individually or in small

groups, in their offices or in the math lab.

12. A program where both the students and the faculty show a wide

diversity of cultural backgrounds.

13. Our unusual location as a mathematics program located in the

middle of high technology companies in Silicon Valley, where

competency in mathematics is vital to advancement.

C. Program Needs

1. Classrooms

Many classrooms are currently unsuitable for math classes.

Recommendation: All classrooms in which math classes are

scheduled should be equipped with at least three, side by side

chalk boards of good quality. In addition, the general problem

of noise from center space activities and neighboring classrooms

needs to be remedied. (estimate $2500)

2. Math Lab

Now that the Math Lab is finally back to its full staffing level,

planning is needed for its long term operation and expansion to

meet continuing student needs:

a. As mentioned elsewhere, the current space allocation is too

small, having been cut by 30% compared to the original east

wing location. At times students are spilling into the adjacent

tutoring area. It is important to maintain a separate space to

develop the concept of an all purpose math activities center,

rather than just remedial tutoring. More space is needed for

additional students, for computer facilities listed above and

for the storage of enrichment materials. Current students are

complaining about the lack of space.

b. Storage files are required for current and new materials.

(estimate $800)

c. Funds are needed to purchase enrichment materials to serve

our entire curriculum and student population. (estimate

$2000 initial, then $1000/year)

d. Over the years, there has been frequent difficulty in having

adequate funding to provide students with sufficient tutoring.

The amount of tutoring per student has been severely re-

stricted on several occasions. This is destructive to the long

term health of the entire math program and a better planning

mechanism is needed to avoid similar unforeseen crises in the

future.

e. Thought needs to be given to administrative structure since

a new dean will be taking over LATC. The Math Lab is not a

part of LATC, although there is regular contact between them,

and tutor funds come from that budget. The Math Lab is a

math department operation, with two instructional aides

reporting to the math faculty. It would be senseless to have

them further report to a dean different from the department's

dean.

Recommendation: A plan and timetable for implementation of

the above resource and structure needs.

3 Computer Resources

The mathematics faculty, after holding back for several years

a. Two MacIntosh computers and printer for use in the Math Lab

c. Funds for software purchases and site licenses for use in class-

rooms and by students in the Math Lab and Computer Lab.

(estimate $5000 initial, then $2000/year)

d. Two MacIntosh computers and DataShow projectors for use by

faculty in classroom demonstrations. (estimate $10,000)

e. Computers for faculty offices. Faculty will never totally

realize integration of computers unless they are available

right on their desks. (estimate $30,000)

Recommendation: A plan and timetable for purchase of the

above equipment.

4. Miscellaneous Needs

a. Funds for substitute instructors.

Currently, unless another instructor is willing to teach for no

compensation, classes are cancelled for the first week of an

instructor's absence. This seriously affects weaker students,

who may lose up to five hours of class time. The district

needs to develop a policy to compensate all substitutes. Then

the department needs to develop a plan to cover as many

classes as possible, rather than cancel them.

b. Funds for Readers/Graders.

Most of our students need the feedback of having large

amounts of homework assigned and corrected. With current

class sizes, this is impossible in most classes. Many colleges,

including West Valley's math department, have funds to hire

student readers for papers. (estimate $10,000/year)

c. Copiers.

Current copier facilities are totally inadequate with much

faculty time being wasted on copiers that are too few, too far

away, and too often broken. A department copier should be

purchased as is already the case for most departments at West

Valley. (estimate $10,000)

d. Faculty Offices.

Many of the current faculty office spaces are simply in-

adequate. Once filled with a faculty member, books and

computers, there is space for perhaps one student. Small

groups of students, working at an office chalk board, is a very

effective technique that we are unable to use because of that

lack of space.

sider office needs in college facility planning.

5. Library

Traditionally, mathematics students at our level do not use many

library resources, preferring to stick mainly to their assigned

textbooks. This is reflected in the basic library holdings, which

are very small compared to the number of students enrolled in

math classes.

This is changing, somewhat, as more courses require writing and

term papers (for example, Liberal Arts Math). Many of the

librarians have become experts at assisting with the location of

topics for such papers and the collection of general interest math-

ematics books is growing.

There is now a large selection of commercially available audio

visual material for mathematics courses, but we have not pur-

chased much as yet. We have internally-developed series for

beginning and intermediate algebra and a purchased series for

liberal arts. Various other single topic items are not heavily used.

Students seem to be more likely to use a complete series. A

series is needed for the arithmetic level.

Other books and A.V. material are kept in the Math Lab, along

with the latest in high technology interactive video tape and disc

systems. We also have a growing collection of mathematics

computer software but no comprehensive system for getting it

into the classroom (one full-time faculty member is currently

studying this on sabbatical).

Recommendation: A larger part of the library budget should

be used to purchase books and audiovisual material for the math-

ematics program.

6. Counselors

Counselors provide considerable advice to students on which

math classes are necessary for their programs and what is an

appropriate level to start. This will presumably become more

complicated as matriculation is implemented. Recall from Part

One, section 9, that the math faculty do not believe that any

diagnostic test is an appropriate placement vehicle for our

students. They are willing to provide one if it is required, but

feel that the results will be unpredictable and inconsistent. The

natural tendency to take as few classes as fast as possible, often

leads to frustration for unprepared students. This is perhaps

best described by a student comment on the Spring 89 surveys:

"Math classes have too many prerequisites. My teacher

expects me to know things from previous classes that I

don't know"

A placement test, administered before the semester, is not

appropriate for most of our students, since they have not studied

math recently and are almost certain to do poorly (despite the

availability of sample tests). Their subsequent success is deter-

mined mainly by previous classes, attitudes and current deter-

mination. This requires individual assessment and counseling

which is of course expensive.

Recommendation: More information and closer work with

counselors may be necessary to ensure correct placement of

students as required by matriculation. Consider hiring a math

instructor or instructional aide to be available during registration

to give individual placement consultations in math.

7. Educational Transition Program

This program has provided support for various mathematics

activities over the years, mainly concerned with re-entering

women students and math anxiety at the lower course levels.

Last year it funded a successful faculty workshop. Future

possibilities include similar workshops for part-time faculty,

additional tutoring facilities or some means of providing students

with additional study time.

Recommendation: Continued cooperation would seem to be

appropriate since it can benefit the students at the lower end of

our curriculum. One of our faculty members has been planning

activities for next year.

D. Curricular Scope

The current course list is a very standard community college math

course offering with few variations or surprises. It was basically

inherited from West Valley College. A survey of the offerings of

surrounding colleges shows a bewildering variety of individual

approaches (for example, Math Lab, computer assisted instruction,

self-paced, fast and slow courses) to courses that we already teach.

Some of the most common courses which we do not offer include:

Discrete Math, Technical Math, Math for Elementary Teachers, Test

Preparation (CBEST or ELM) and Math Anxiety.

Current WSCH/FTE goals discourage expansion into new areas or

experimental courses since the FTE must be taken from already full

courses. For this reason, previous experiments (one unit arithmetic

topic classes) have been dropped from the catalog and current

experiments (MCTV interactive classes) continue only because they

are funded from another source.

It would be appropriate to expand into new areas but only if this

can be done by the gradual addition of FTE. It should not be done by

cutting existing course sections.

Possibilities for future experiments include:

1. Collection and integration of culturally pluralistic material into

existing math courses.

2. Math Anxiety course or workshop (possibly in conjunction with

Educational Transition).

3. Computer supplements to Calculus, Finite Math and Statistics

(dependent on hardware availability).

4. Addition of a discrete math course. We have recently received a

letter from the Computer Science department at San Jose State

University requesting that we make this course available so that

their students may complete all their lower division require-

ments at Mission.

5. Creation of special combined differential equations and linear

algebra course for Engineers.

6. Short topic review courses in algebra.

7. Short course in algorithms and problem solving, logic and proofs.

8. Substantial modification of the geometry course.

9. Integration of current computer software into math courses, both

for faculty and for students.

Course Unit Revisions

With the existing curriculum structure, there is a high drop out rate

in beginning and intermediate algebra. Most of these students have

attempted algebra elsewhere in the past and are repeating it for

some requirement. They are particularly at risk in large fast moving

classes. We are proposing that both these courses be increased to

five units to allow the slower moving students time to succeed.

Intermediate Algebra, in particular, is our critical filter to all the

more advanced science and business math courses.

The problem begins with lack of time in beginning algebra so that

students arrive in intermediate algebra with a weak background.

They then cannot keep up with the accelerated pace there and are

forced to drop out. We proposed, several years ago, that one

possible solution to this, was to allow and encourage course repeti-

tion in Math 102, A and C, thereby ensuring that students do not

move on until they are really prepared. However, this was rejected

by the Curriculum Review Committee.

As an alternative, we now propose increasing units in A and C to

provide extra class time. This is already done at many surrounding

colleges and seems to be successful at West Valley. With the pro-

spect of a flex calendar and diminishing teaching calendars, it is

even more important. This of course will require additional FTE

since increasing the number of units, while reducing the number of

sections, would be counter productive.

Other courses which experience problems in covering all the

required material, are Business Calculus and third semester Calculus.

Business Calculus essentially covers two semesters of regular

calculus by omitting much of the mathematical rigor and condensing

it into one semester. Poor algebra background is again a problem.

Third semester Calculus frequently omits the important concepts of

Stokes, Gauss and Divergence Theorems from the end of the course.

There is a conflict here between the desires of Engineering majors

to have as few units as possible and yet to be fully prepared for

transfer.

Recommendation: Revision of the course units should be the top

curriculum priority. Other changes should be tried gradually but a

mechanism needs to be found to alleviate the current cumbersome

curriculum and FTE funding processes. We have no surplus sections

that can be removed to offer new courses.

See the attached Appendix A part Three and the results of the

Some of the more interesting results are noted below:

Several responses vary considerably from level to level, for

example, from remedial to Calculus level we see:

decrease in percentage of women from 52% to 30%;

increase in percentage of students concurrently attending San Jose

State;

decrease in students working over 38 hours per week.

Overall gender distribution is becoming fairly close to an even split.

Age distribution is becoming more evenly spread with the 21-25

category declining and others growing slowly. The 18-20 group

shows the most growth.

Ethnic distribution shows almost equal numbers in the white and

asian groups with small numbers of many other minorities.

The unit load distribution is hard to interpret because of the strange

categories chosen by district computer services. However, most

math students appear to be taking at least one other class, even in

the evening.

In future program reviews, it would be useful to have data, possibly

from Matriculation, studies on preparation levels for different

courses and the subsequent success rate.

B. Statistical Trends

See attached Appendix A - Part One and Two

Enrollment trends show the daytime figures holding almost constant

and the evening ones steadily growing. There was a one time large

increase in Fall 87. This corresponds to the change to the late calen-

dar but since all our neighboring districts experienced a similar

growth spurt without a corresponding change in calendar, the reason

is unclear.

Attrition/retention is a problem area for the math department.

Attrition from week two to the end of the semester is approximately

30% compared to about 20% for the college average. From week four

through week eleven, it is approximately 10%. Curiously, the rate

seems to increase and decrease along with the college average. Math

programs, by nature, probably have higher drop rates than the

college average. In future program reviews, it would be interesting

to obtain comparable figures for math departments at other colleges.

Many of our recommendations in this review are aimed at reducing

the drop rate, since this is an area where we should be able to have

a real effect.

Department WSCH figures represent a significant portion of the total

(approximately 10%) and generally meet the college WSCH/FTE

Fall figures are normally larger than Spring. There is still a problem

with unrealistically high goals which were based on the one time

enrollment surge in Fall 87. This severely restricts the flexibility to

offer small and large sections under the performance unit section of

the contract.

The program still uses a large number of part-time instructors,

between twenty and thirty in any given semester, but the number

of full-time faculty is slowly rising. There are not enough day time

sections to provide all full-time faculty with a complete load. Almost

all full-time faculty teach at least one course in the evening or on

Saturday.

C. Employment and Transfer

As a totally service-oriented department, we do not have relevant

employment and graduation data. The number of majors and

associate degrees is minimal. Future reviews might find it possible

to obtain data from other Mission College programs on the level of

preparedness of their students who have math prerequisites. Some

data might also be obtained from universities to which our students

transfer, but this requires long term tracking at another institution.

The college has never attempted this.

III. Analysis and Interpretation

A. Trends

The mathematics program is experiencing slow, steady growth with

no particularly unusual trends apparent at this time. There are

many interesting small features and problems which have been

examined in detail in part one of this review. In the future, more

data from mathematics programs at neighboring colleges might

provide useful insight.

B. Trend Interpretation

The mathematics department is in a strong position. Enrollment is

steady and no crisis planning is necessary. There is a large choice

of future expansion possibilities related to new classes and integra-

tion of computers into the existing curriculum. A significant problem

which can be addressed is attrition.

IV. Summary and Recommendations

A. Summary

Program review has provided a valuable picture of the current state

of the mathematics program. Owing to the lack of consistent statis-

tics from the past, it is hard to see a clear long term trend in many

areas. In future reviews comparable data should continue to be

available and should make comparisons easier.

Various problems and opportunities have been identified and with

the newly improved financial situation of the California Community

Colleges, funds should be available to address many of these.

There seem to be three major areas which need to be addressed:

1. Make program enhancements to reduce the current high attrition

rate. These can include improvements to the Math Lab program,

a decrease in maximum class sizes and the increase of units being

proposed to Curriculum Committee. Faculty development work-

shops that include part and full-time faculty, and seminars on

teaching styles would be appropriate.

2. Add new courses.

3. Obtain sufficient computer resources to integrate computers into

the regular curriculum and enhance the Math Lab program.

B. Recommendations in order of importance:

Highest importance:

1. Offer new courses without reducing current sections: Discrete

Math, Math Anxiety, etc. Modify courses for math or cultural

pluralism content where necessary.

2. Expand space for the Math Lab. Obtain more storage space.

Obtain audio visual and computer enhancement material. Expand

the amount of individual tutoring available and put the funding

on a long term stable basis.

3. Increase units in Math A, C, 12, and 4A.

Next highest importance:

4. Obtain department release time for administrative duties.

5. Reduce maximum class size to the 35 level that was standard

prior to the current contract.

6. Obtain sufficient computers and software to integrate into regular

curriculum. Computers to be available in the Math Lab for tutor

training and initial student use. Software to be available in the

Computer Lab for subsequent student use.

Lower importance:

7. Obtain funds for readers to allow more attention to individual

student papers.

8. Obtain a department copier.

9. Improve faculty offices and obtain computers for each faculty

member.

10. Improve counseling and placement in math classes.

11. Improve library materials in math.

12. Install chalkboards and soundproof classrooms.

13. Math department faculty seminars on teaching.