MAT120/MAT122 Intermediate Algebra MAT151 College Algebra Faculty Member: Keith Worth Phone Number: (480) 423-6425 College: Scottsdale Community College Credits: 3
OFFICIAL COURSE DESCRIPTION ABSTRACT OF DIVERSITY INFUSION WITHIN COURSE TEXTBOOK PRESENTATION OF DIVERSITY-RELATED MATERIALS CLASS SCHEDULE OF DIVERSITY-RELATED SEGMENTS SUCCESSES AND DIFFICULTIES STUDENT EVALUATIONS OF COURSES INFUSED WITH DIVERSITY RECOMMENDED RESOURCES

 OFFICIAL COURSE DESCRIPTION: TOP
Intermediate Algebra (MAT120 & MAT122)
Quadratic, rational, radical, exponential, and logarithmic functions and equations; graphs of quadratic, exponential, and logarithmic functions; equations quadratic in form; operations on rational expressions, radical expressions, and complex numbers; rational exponents; applications. Prerequisites: Grade of "C" or better in MAT090, MAT091, MAT092, MAT093, or equivalent, or a satisfactory score on the District placement exam.
Course Note: May receive credit for only one of the following: MAT120, MAT121, or MAT122.
College Algebra (MAT151)
Relations and functions; polynomial functions; exponential and logarithmic functions; systems of equations and inequalities; matrices; sequences and series. Course Note: May receive credit for only one of the following: MAT150, MAT151, MAT152, or MAT187. Prerequisites: Grades of "C" or better in MAT120 or MAT121 or MAT122 or equivalent, or satisfactory score on District placement exam.
Course Note: May receive credit for only one of the following: MAT150, MAT151, MAT152, or MAT187.

ABSTRACT OF DIVERSITY INFUSION WITHIN COURSE:TOP
I implemented a mathematics project at the intermediate/college algebra level that infuses diversity of world views. This project asked students to model world population growth, density of population in terms of arable surface area, and depletion of non-renewable resources, using exponential and logarithmic functions. A total of 50+ students in three different classes were assigned this project during the Fall semester of 2002. As a starting point for the investigation, this project uses materials from the Maricopa Mathematics Modules which I co-author with seven others. The Maricopa Mathematics Modules are published by Houghton-Mifflin.

COURSE TEXTBOOK:TOP
Intermediate Algebra MAT122 Intermediate Algebra Tussy2ND Edition

College Algebra MAT151Functions Modeling Change Connally 2ND Edition

PRESENTATION OF DIVERSITY-RELATED MATERIAL:TOP
Students were asked to analyze geographical data for 8 different countries of the world with widely varying physical geographies, cultures, and political, socio-economic, and technological conditions. The eight countries were Bangledesh, Brazil, China, Germany, Indonesia, Mexico, Nigeria, and the United States. For each country students computed values for each of the empty cells (?) shown in the sample table below. The sample is for the country Brazil.

Country Total
Land (km2) %
Arable
Land Total
Arable
Land (km2)
Brazil 8,456,510 7% ?
Country Population
(in 1000’s) Total
Land
Per 1000
People (km2/1000) Total
Arable
Land
Per 1000
People (km2/1000)
Brazil 162,661 ? ?

Results for the 8 countries ranged from 0.71 km2 of arable land per 1000 people in Indonesia to 6.88 km2 of arable land per 1000 people in the United States. Arable land was defined in this project as land currently available for any human use (living needs, agriculture, urban activities, etc.). When I first discussed the meaning of the given data in this project with my class I used Brazil to illustrate that much of its total land is currently uninhabitable and unusable for any human purpose (only 7% is arable). The class then discussed why this is the case in Brazil. Conclusions were that most of Brazil’s population lives along its South Atlantic seaboard with much of its interior too mountainous and forested to be arable. The class also discussed why there might be pressure in a country like Brazil to clear cut and burn rain forest areas to create more arable land. As a class we also discussed how different societies might use arable land, for example, a technologically primitive, agrarian society versus a modern, industrial, high-tech society.

Next, students were asked to find an exponential growth model (J-curve) based on world population data using the data regression capabilities of the TI-83 graphing calculator. This model was then graphed and used later to estimate the year when world population grows to its maximum “crowding” point based on an upper limit for average acceptable population density worldwide (actually expressed in reciprocal form in the data table in km2 of arable land per 1000 people). Students were asked to use one of the eight countries as a standard for the upper limit for average acceptable population density worldwide.

At this point, we discussed as a class the two countries in the list that come closest to the current world average for square kilometers of arable land per 1000 people, Mexico and Nigeria. We also discussed what the entire world might be like if it was like the societies in Mexico or Nigeria. Would every family have autos, computers, cell phones, televisions, and VCRs or DVD players? In what kind of place would most people live? What would a typical day be like for them?

To answer these questions for what the world would be like in the future, the students had to search for the answers to these questions for countries in the list where the population density was greater than the current world average. This really limited their research to Bangladesh, China, Germany, and Indonesia. They were asked to find out about qualities for these countries such as physical geography, culture, and socio-economic and technological conditions.

Only countries with greater population density were researched because the growth in world population could not continue without crowding more people into the world’s current amount of arable land. The students were asked to consider that world population would continue to grow by crowding more people into the world’s existing arable land until a different maximum world population limit is achieved.

Once each student picked a crowding limit for the future based on one of the four allowable countries, their research helped them describe what the world will be like when this limit is reached. Also, by using the value for square kilometers of arable land per 1000 people for their country, they computed the world population limit by dividing the value of the world’s total arable land in km2 by their country’s arable land per 1000 people (see example below).
Example: Bangladesh has 0.73 km2/1000 people. The total arable land in the entire world is 14,894,000 km2. Dividing the latter by the former gives a limiting world population of 20.4 Billion people (the current world population is 6 billion).

Finally, the students imposed this limiting population level on the graph of world population growth (which they produced using their exponential growth regression model). The intersection of these two plots described the time in years after 1950 that this limiting population would reached (see example below).

For the earlier example using Bangladesh, the exponential growth model intersects the 20.4 billion people limit 116 years after 1950 or in the year 2066. My students were shocked to realize that this is certainly within their childrens’ lifetime (if not their own).

Each student was asked to submit their mathematical analysis including their regression model and graph and the completed table for the eight countries. Each student was also asked to submit a paper in which they discussed what a future world at its world population crowding limit would be like and in what future year this would occur based on their chosen country’s current population density and the resulting world population limit computed from total arable land on the earth and this population limit as described in the example discussed earlier.

Description of Supplemental Material and How Integrated in Course:
On the day I handed out the project, I showed the one hour video entitled “Six Billion and Beyond” which was originally produced for PBS television. This video was available through our Biology Department and our Environmental Biology professor, Dr. Roy Barnes, suggested it as good introduction to students regarding population growth issues. This video worked very well setting the stage for discussing the goals of the project.
Special Assignments and Activities:
Projects are a normal part of my mathematics courses so I do not consider this project to be outside of the normal course requirements for my students.

OUTLINE OF CLASS SCHEDULE SHOWING DIVERSITY RELATED SEGMENTS: TOP
How I structured this project into my course syllabus (Grading Criteria portion of syllabus is shown below):
VI. COURSE GRADING:
Ranges:
A: 100 - 90
B: 89 - 80
C: 79 - 70
D: 69 - 60
F: below 60

i. 40% of grade:
Classroom Quizzes
ii. 20% of grade:
Midterm Exam
iii. 20% of grade:
Final Exam
iv. 20% of grade:
Three Projects

Actual Project Description:
MAT120/122/151 PROJECT#3:
The Earth Viewed as a Petri Dish.
This project will explore "how many people can live on the earth". You will complete the activities in your book for Lessons 11-13 of EGD (pages119-138) as described below. After reading and doing the described activities you must write no less than three hundred words that answer the following three questions:
I. How does the amount of land limit the total population that the earth can support?
II. What is the upper limit of human population that the earth can support based on your findings in Lessons 11 & 12?
III. How does mathematics help a person understand issues related to world population and limits on resources (Use Julian Simon's wager as an example...did Julian Simon win his bet with Paul Ehrlich?)?
Here are the Activities with page numbers that you must do to answer the questions above:

Lesson
in EGD Activity
or
Problem Pages in
text Remarks
11 Activity 1 P 119 Use world
population
data on page
78 of Lesson 7.
11 Activity 2 P 120-121
11 Homework
Problem 5 P 123 Modify problem
as follows:
do web research
to find the
appropriate data
on another important
world commodity.
12 Reading P 125-127 Analyzes copper as
a nonrenewable
commodity.
12 Activity 1 P 128-129 Analyze the commodity
you researched in this
Activity.
13 Reading P 133-134
13 Activity 1 P 135-137
13 Activity 2 P 138 Stop after question2.

Your report must be typewritten and contain your graph of the regression model for world population using data from 1950-1999. The Math/Science Center is a good place to produce word processed reports and the people in there can assist you in copying your regression graph from your calculator screen into your report using a program called GRAPHLINK.

SUCCESSES AND DIFFICULTIES ENCOUNTERED: TOP
I am planning for students to do this project in spring of 2004. Listed below are areas I wish to refine and improve before I assign the project again as a result of this first effort.

• I will give my students much more direction about where and how to research the physical geographies, cultures, and socio-economic and technological conditions of the various countries.

• I will ask them to write a longer length paper because it was difficult for them to organize their research and integrate it with their mathematical analysis.

• I will consider asking them to do oral presentations of their project results to the entire class.

I believe that the time and effort required of me and my students in this diversity infusion project was well worth it. Students gained an appreciation for how their assumptions about the world’s population growth and the way different people’s of the world live, affect how we all view our capacity to live and grow on this earth as a global community. I recently ran into one of my former students who did this diversity infusion project in the fall of 2002. His first name is Brian and he has gone on to take higher-level math requirements for his business transfer program since then. Without any prompting from me (I hadn’t recalled that he had been in the project classes), he stated that doing this project was the first time that his eyes had been opened to how mathematics could be used to understand important world issues.

STUDENT EVALUATION OF COURSE INFUSED WITH DIVERSITY: TOP

RECOMMENDED RESOURCES:TOP
I would recommend the Maricopa Mathematics Module entitled “Exponential Growth and Decay” published by Houghton-Mifflin for historical data on world population and the baseline data on the eight countries described in this project.