| Mukasa E. Ssemakula, Ph.D. ssemakul@et1.eng.wayne.edu Div. of Engineering Technology Wayne State University Detroit, MI 48202 | Chorng S. Houh, Ph.D. houh@math.wayne.edu Dept. of Mathematics Wayne State University Detroit, MI 48202 |
Mary L. Mayer, Ph.D. GelmanSciences 600 South Wagner Road Ann Arbor, MI 48103 (formerly with Dept. of Chemistry, WSU) | Vladimir Sheyman, Ph.D. sheyman@et1.eng.wayne.edu Div. of Engineering Technology Wayne State University Detroit, MI 48202 |
This paper describes an integrated Algebra
and Chemistry course that has been developed as part of the
requirements
for a Manufacturing Engineering education curriculum being
implemented
by the NSF funded Greenfield Coalition for New Manufacturing
Education.
The philosophy behind the development of the course was the need
to teach basic mathematics and chemistry to students pursuing
degrees in the manufacturing engineering area, with the
manufacturing
shop floor serving as the motivating force for the instruction.
The goal was to teach the fundamentals of algebra and chemistry
in a manufacturing context. The need to understand the chemistry
of the various processes served as the backdrop to motivate the
teaching of the basic algebra relevant to the analysis. The student
body addressed by this project was mainly inner city minority
students, and they were mostly first generation college students.
They were all working full time in the manufacturing facility
at Focus:Hope and this working experience was integrated into
the educational curriculum being developed.
The Greenfield Coalition for New Manufacturing
Education, also called the Greenfield Coalition; is made up of
Focus:Hope's Center for Advanced Technologies (CAT); academic
partners University of Detroit-Mercy, Central State University,
Lawrence Technological University, Lehigh University, University
of Michigan, and Wayne State University; as well as industrial
partners Chrysler, Ford, General Motors, Detroit Diesel, and
Cincinnati
Milacron; and the Society of Manufacturing Engineers. The CAT
serves as the primary implementation platform for the Coalition's
curricula, enabling integration of hands-on manufacturing
experiences
with an interdisciplinary engineering education within an
applications
context. The degree candidates are full-time employees at the
CAT, and the educational goal is to provide these candidates with
a diverse technological education utilizing the manufacturing
resources available on the shop floor.
The Coalition's educational model entails hands-on
training in the programming, operation, maintenance, and repair
of manufacturing equipment; interdisciplinary study of pertinent
mathematics, science, engineering, business, and general education
courses; as well as structuring and delivery of knowledge within
a production environment to provide context. The curriculum is
being developed in a modular fashion, with each module being
delivered
in an innovative instructional process. Modularization makes it
possible to use a mix of sub-discipline experts to design and
deliver modules within a given knowledge area, thus enhancing
overall learning.
The Coalition has identified desirable competencies
for the manufacturing engineer of the future that would enable
the engineer to achieve leadership in the field. Working with
the industrial partners, competencies appropriate to various stages
of the manufacturing engineer's career have been specified. A
person meeting with these competencies has been named the
Renaissance
Manufacturing Engineer. The competencies are then related
to individual knowledge areas requiring mastery, which are in
turn developed into individual modules. In implementing the
modules,
developers in general begin with practice and end in theory in
order to instill an intuitive sense of physical phenomena to which
candidates can then turn their attention.
The development and implementation of the Algebra/Chemistry
curriculum described in this paper involved team teaching by
faculty
from the disciplines of chemistry, mathematics and engineering
technology; all working to demonstrate the practical relevance
and applications of the theoretical material covered. Out of class
assignments were given and group projects were used to encourage
collaborative learning. There was also a wide range of
computer-based
experimentation utilizing commercially available software to
motivate
learning.
The combined Algebra and Chemistry curriculum
was developed within the context of the guiding principles
discussed
above. The knowledge area was divided into four modules designed
to link mathematics to chemistry, together with applications and
case studies, using the manufacturing experiences in the CAT to
provide context. The focus was on the study of Chemistry and
Algebra
through experimentation, with particular attention to chemical
processes that candidates witness on the manufacturing floor on
a regular basis. The material covered in this knowledge area was
equivalent to four semester credits in a traditional setting,
with two credits assigned to Algebra and two credits assigned
to Chemistry. Table 1 below shows the structure of the four
modules.
| Gauging and inspection | Manipulations with real numbers | Scope of Chemistry |
| Precision and accuracy | Algebraic manipulations | States of matter |
| Preferred numbers | Exponential expressions | Solutions, compounds, mixtures |
| Standard sizes | Use of scientific notation | Scientific numbers |
| Mass production | SI and English systems of units | Basic Chemistry measurements |
| . | Significant digits | Chemical reactions |
| . | Series of numbers | Oxidation states |
| Graphing applications | Relationships between sets | A history of chemistry |
| Mechanical properties of metals | Graphing functions | Moles as a measure of matter |
| Metals vs. plastics | Manipulating functions | Mass - mole - mass conversions |
| Comparison of various metals | Equations and function values | The periodic table |
| . | Linear functions | Chemical nomenclature |
| . | Equation of a line | Oxidation states |
| . | .Exponential functions | . | .
| . | .Significance of the exponent | . | .
| Estimating answers | Recognize graph of f(x) = k/x | Aqueous solutions |
| Solving manufacturing problems | Polynomial functions | Chemical equations |
| Verifying solutions | Shapes of curves of polynomials | Balancing chemical equations |
| Corrosion | Relate length, area and volume | Limiting reagents |
| Rusting | Solving mathematical problems | Stoichiometry |
| . | . | Acid-base solutions |
| . | . | Oxidation and Reduction |
| Turning diameters | Perform algebraic manipulations | Atomic and molecular shapes |
| Bolt-circle diameters | Recognize shapes | Orbits and electron shells |
| Tool positioning | Know properties of polygons | Heat and enthalpy |
| Geometry calculations for CNC | Law of sines and Law of cosines | Heat of reaction |
| Crystalline structure | Parametric equations | Molecular bonding |
| . | Trigonometric identities | The octet rule |
| . | . | Crystallization |
The following discussion will focus on the
content of the first module. We will describe how the content
was designed to satisfy the development goals and how course
delivery
was implemented. This same model was followed in the development
of all the other modules.
Module Integration
The students that are targeted for all Coalition
courses are experienced machinists. They are familiar with the
measurement and inspection of machined parts. This module was
designed to introduce formerly the concepts of tolerances, accuracy
and precision in part inspection. Since this was an activity that
the students are involved with daily, they could see the
significance
right away. Topics in systems of units, scientific notation and
significant numbers were then introduced from the mathematical
standpoint. But keeping applications in measurement in mind, the
practical applications could be easily demonstrated. The
measurement
that candidates do in the manufacturing context was used as a
bridge to introduce measurements that are relevant in Chemistry.
Since Chemistry was a new science to the students, the opportunity
was taken to introduce its scope but with particular attention
to its relevance in a discrete parts manufacturing environment.
This entailed discussion of what matter is, the various possible
states of matter and introduction of the concept of a chemical
reaction. Within the module, the mathematical topics were developed
to include the manipulation of real numbers as well as algebraic
manipulations. The treatment of mathematical series was anchored
on the use of preferred sizes in manufacturing, which are
themselves
derived from geometric series. Finally, standardization of parts
which makes mass production possible was detailed. Below, we
describe
how this helps to round out the module content.
Module Contextualization
The basic property about a series of numbers
is that there is a fixed relationship between the members of the
series. If one member of the series is known as well as the
functional
relationship between the members of the series, then all other
members of the series can be determined easily. This fact in
algebra
can be used to illustrate the meaning of functions. For this course
however, we go beyond the simple illustration to actual
applications.
The use of preferred numbers in product standardization serves
as a basis to illustrate series in a way that manufacturing
engineers
and technologists can readily associate with.
Preferred Numbers and Standard Sizes:
Many mass produced articles such as bolts,
and semi-finished products such as steel bars, can be made in
a wide range of sizes. In most cases, it is technically feasible
to make an infinite range of sizes for these products. From a
practical consideration however, it would be too difficult and
costly to manufacture, distribute, and stock all the different
possible sizes. It is therefore preferable to make only a select
set of sizes chosen so as to serve the needs of the majority of
customers. A good range of sizes for any product should start
with small increments at the bottom of the range, with gradually
increasing step sizes towards the top of the range. The range
of sizes normally made is referred to as standard. By standardizing
on a small select set of sizes, it is possible to take advantage
of economies of scale and make large quantities at a relatively
low cost and avoid frequent changes of setup that would otherwise
be required. The range of sizes typically used in manufacturing
involve a geometric series. A geometric series has the
important property that the ratio of any one number to the previous
(or next) number in the series, called the common ratio,
is always constant.
In 1879, a Frenchman by the name of Renard
proposed a set of geometric series that could be used as the basis
for determining sizes for use in a wide variety of applications.
There is a total of five of these geometric series, also called
R-series, represented by the codes R5, R10, R20, R40 and R80.
For each series designated Rn, the common ratio n
is given by 101/n. Thus the R5 series has a common
ratio 101/5, the R10 series has a common ratio
101/10,
and so on. The raw numbers in this set of series have been rounded
to convenient values that have since been accepted internationally
as a basis for determining sizes for a wide variety of
applications.
These resulting rounded values are used in preference to other
numbers and they are referred to as preferred numbers.
The values of the preferred numbers are given in the US national
standard ANSI Z17.1-1973 as well as the international
standard ISO R286. Table 2 shows the members of the R5, R10 and
R20 Renard series and the corresponding preferred numbers in the
range 1 - 10. These values can be used to derive other members
of the series by multiplying by an a power of 10.
In all cases where one has a choice of sizes
to use, the preferred numbers should be used provided they meet
functional requirements. The R5 series of numbers are referred
to as the first choice preferred numbers and where possible, these
should be used in preference to all other numbers. The R10 series
are second choice preferred numbers, R20 are third choice preferred
numbers and so on. It is left as an exercise to the students to
derive all the members of the R40 and R80 series.
The derivation of preferred sizes from the
raw Renard series numbers is a perfect example of the application
of significant figures, rounding-off of numbers and standardization
- all important issues in today's global manufacturing environment.
Looking at the preferred numbers and comparing them to the raw
members of the Renard series, students can see how approximation
and rounding of numbers are applied in this case. Students can
also see that in the interest of standardization, some of the
rules of rounding are not used in generating the preferred numbers.
Indeed some values are rounded up while others are rounded down.
Application of preferred numbers in Chemistry are also included
in the course for completeness.
The complete curriculum developed for the candidates
at Focus:Hope was first offered to the candidates in Spring of
1995. The material was delivered primarily as stand up delivery
with provisions for videotaping all lectures and demonstrations.
The class typically met once a week for three hours per session.
Course delivery entailed team teaching of the course by faculty
in the three areas of Chemistry, Mathematics and Engineering
Technology.
Each session was planned to provide an integrated experience
involving
each of these three areas. In-class demonstrations were utilized
to showcase the principles being covered in the lectures, while
discussions of shop floor experiences that students were familiar
with served to ground the material in an applications context.
Student learning was evaluated through traditional written tests.
Due to the non-traditional approach used to
deliver the course, a number of challenges had to be faced. The
students were not used to the idea of team teaching and it took
them a while to adjust to a course being taught by multiple
instructors.
There are inevitable differences in teaching styles. For an
approach
such as this to be successful, careful attention has to be given
to the need to coordinate not only course content, but also
teaching
styles overall pedagogy.
It was found that whereas the students had
a very good understanding of the principles of manufacturing,
their level of preparation in mathematics varied widely. Although
they had all passed pre-tests, applying the mathematical concepts
in unusual (non-canned type) settings was a major leap. Some could
not overcome this hurdle and they ended up dropping out of the
course. This might have been exacerbated by the fact that this
was a not a campus setting and accessibility of faculty to the
students was limited. Other than the weekly meetings, students
relied primarily on using the telephone and e-mail which did not
work quite as well as personal contact. Those who were able to
complete the course however were very positive and enthusiastic
about the course design.
Finally, one practical problem peculiar to
the setting was the need to accommodate changing production
schedules
that would sometimes lead to students missing learning sessions.
This is an issue that is still being grappled with in the delivery
of courses in other knowledge areas.
Acknowledgment:
This work was funded by the National Science Foundation through a subcontract under the Greenfield Coalition, cooperative agreement number EEC-9221542.