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## Lower Division Math Courses

## Syllabi for UH Manoa Calculus Courses

215 syllabus

241 syllabus

242 syllabus

243 syllabus

244 syllabus

251A syllabus

252A syllabus

253A syllabus

##
System-wide Math Course Coordination Meeting

Representatives of the various Math Departments in the UH System met at

Kapiolani CC to discuss the coordination of our programs. There were

- 7 faculty members from UH Manoa
- 2 from the UH office of the Vice Chancellor for Academic Affairs,
- 1 from UH Hilo,
- 1 from UH West Oahu,
- 5 from Kapiolani CC,
- 0 from Honolulu CC,
- 4 from Leeward CC,
- 2 from Windward CC,
- 1 from Kauai CC,
- 1 from Maui CC,
- 1 from Hawaii CC,
- for a total of 25.

This report is an informal summary of the discussion.

**I. Calculus**

Overall we are in fairly good

shape with respect to calculus. The course syllabi are similar at the

different campuses, and articulate smoothly. We will obtain the course

descriptions/syllabi and make them available for comparison. These should

be sent to J. B. Nation (email address listed at the bottom).

UH Manoa has revised its numbering scheme for calculus (241-242-243-244),

while the other campuses have kept the traditional scheme (205-206-231-232).

The system would like us to eventually adopt a uniform scheme.

The use of computers was discussed. Most campuses use computers in

calculus, and most instructors feel that it is an effective tool for

illustrating calculus concepts. The way in which the computer is used

varies some with the instructor, but this was not thought to be a major

issue. A few campuses still do not have adequate facilities to do this

effectively.

There are two minor differences in the curriculum. Following requests

from the Engineering College, Manoa now has vectors in Calculus I and

an introduction to differential equations in Calculus II. Both of these

seem to fit rather well, and we would like to suggest that other schools

consider it.

The importance of completing the syllabus in all calculus courses

was noted.

Standards in calculus has not been a major problem, with the exception

of the usual anecdotal reports. (None of us wants to be held responsible

for our worst C student.) It is important that we keep it this way.

The applied calculus course, Math 215 at Manoa, was discussed as a

viable alternative for calculus I. Currently, roughly 40% of the first

semester calculus students at Manoa are in 215. While the course is

slightly more applied and less theoretical than 205/241, it is intended

to be a substantial calculus course. While having two (or more) options

might be difficult for the smaller schools, other campuses have a large

enough calculus enrollment to justify the option. Smaller campuses could

consider alternating the courses.

Business calculus, Math 203 at UHM, is a less substantial alternative.

It remains true, however, that we can offer a better business calculus

course than business or agriculture departments. If there is enough

demand, offering a “better business calculus” would be a service to

our students.

**II. Math 100**

There was a major discussion

about the spirit and topics of Math 100. There was general agreement with

the principle that Math 100 should introduce students to the beauty and

precision of mathematics, including mathematical reasoning as well as

counting and algebra. The argument as to which topics best serve that

purpose was more vocal. One side argued that financial math and probability/statistics

did not serve this purpose well. The response was that these topics have

meaning for the students because of their applicability, and that they

illustrate the use of important ideas such as geometric series. It was

emphasized that, the memo of 15 years ago notwithstanding, no one should

dictate the topics for Math 100. Rather, we should insist that a variety

of topics and approaches be covered, and that these be done in a non-cookbook

fashion.

It was noted that teaching Math 100 in a reasonably-sized class can

be much more effective than a large class, but this is a matter over

which we have little control.

With respect to the problem of the Manoa Gen Ed requirements, see

below.

**III. Articulation**

According to Executive policy

E5.209 the AA degree at any UH community college satisfies the Manoa Gen

Ed requirements, and any 100 level non-technical course transfers to any

other UH institution. The say of the “receiving institution” in this situation

is somewhat cloudy, but it is clear that the administration would prefer

that they say “yes.” However, the various colleges may (and do) have additional

core requirements in addition to the Manoa Gen Ed requirements, and the

transferred credits may not apply to these additional requirements.

Problems with non-Fast Track approval were due to the fact that we

were to approve equivalencies only, and did not have the authority to

approve courses per se.

The Manoa Symbolic Reasoning requirement (FS) is not a math requirement.

It was not written by or for math people, nor specifically approved

by them. The broadly written hallmarks are hard to satisfy with the

broad class of our elementary courses. Nonetheless, that is the objective.

In particular, Math 100 is no longer a quantitative reasoning course,

it is a logic course (!).

A more minor problem: Math 103 – “College Algebra” – is designed for

students transfering to HPU, Chaminade and UNLV (etc). Nonetheless,

it transfers to UHM for credit, though the same course at other schools

probably does not.

**IV. Elementary Education**

History: Manoa’s old Math

111 failed because we didn’t give high enough grades. This left us in

the undesirable position of having no role in the education of primary

teachers, while those students took Math 100, an inappropriate substitute.

Some folks in the College of Education were concerned about this situation,

and joined us in attempting to revive a math course for elementary education

majors. UHM has added Math 111 and 112, and the Big Island schools have

107-108.

Supposedly at least the first course will be required starting in

2006 (!). It is good for the state and education for us to be involved

in this, if it flies.

The problem solving (constructivist approach) is crucial, but too

limiting to be used exclusively. More experience should help find a

balance. Standards can be a problem, but again experience will help

us adjust this.

**MATH 100 satisfies the general education requirement for quantitative reasoning.**

For details, see Topics

in Mathematics (Math 100)

MATH 100 should include:

Proofs. The student should be able to follow and present some basic

proofs. The goal is to develop critical thinking skills.

Topics which illustrate the beauty and power of mathematics. Topics

should include at least a few topics from advanced math courses and

their applications such as topology, group theory, network theory, etc.

The goal should be an appreciation of what mathematicians do.

Algorithms should not be used without developing their derivations.

The goal should be to develop the logic behind formulae.

Topics may include the history of number systems to illustrate the

universality of mathematics, as well as the cultural differences. The

goal should be to illustrate the advantage of and encourage the appreciation

of different perspectives.

Topics may involve the mathematics behind popular “logic” puzzles.

The goal is to illustrate what “common sense” is expected by society.

## Participants

To foil email harvesters, addresses in the above binary image can

not be cut and pasted.

## Calculus Courses

UHM | UHH | HCC | KCC | LCC | WCC | Hawaii | Kauai | Maui | |

Computer Lab | 241 | 205 | 206 | 206 | 206 | 205 thru 232 | |||

242 | 206 | ||||||||

ODE’s | 242 | 206 | 232 | 232 | 205 | 206 | 232 | ||

232 | 232 | ||||||||

Polar | 244 | 231 | 231 | 231 | 231 | 231 | 231 | ||

Vectors | 241 | 231 | 231 | 231 | 231 | 231 | 231 | ||

243 | |||||||||

Series | 242 | 206 | 206 | 206 | 206 | 206 | 206 | 206 | 206 |