Syris Learning Modules 2001-2002: The Power of the Exponent

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2000-2001

2001-2002
* The Power of the Exponent
* A Treasure Lost
* Breathless
* Evolution: The Only Constant is Change
* Enzyme Activity and Computer Modeling
* Earth Fissures
* Aerobic Metabolism
* The Science of Survival
* Tailpipe Emissions

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2001-2002 SyRIS Science Module Collection

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Module Title:

The Power of the Exponent

Faculty Team Members (Discipline):

Pushpa Ramakrishna (Biology), Scott Adamson (Mathematics), Tom Foster (Instructional Technology), and Trey Cox (Mathematics)

College:

Chandler-Gilbert Community College

Student Group Targeted:

100 and 200 level courses in Biology, Chemistry, Mathematics and Computers.

How Will the SyRIS Goals Be Met?

Interdisciplinary Component: An interdisciplinary unit was developed with concepts related to exponents. For example, biology students studied the exponential growth of bacteria; math students and physics students used the Newton's Law of Cooling to explore the concept of exponents. Math students explored this concept through application problems such as a rumor mill. The module is built around a case study of a professor dying due to food poisoning; the data collected and analyzed is used to solve a mystery in a wholistic manner.

Active Learning Strategies:

Hands on activities
Collaborative learning groups share ideas, explain methods, and summarize results
Case study, problem-centered learning
Discussion related to a real life application
Use technology to solve problems

Module Overview:

Background: The topic of exponents is critical to all science and math disciplines. Students find it hard to fathom the complex concept of exponents. To better comprehend the matter, a case study was developed. This real life scenario helps the students grapple with the complex issue and meaningfully apply their knowledge in various subject areas. The learning outcome of this project is that students piece together the clues obtained in different disciplines, analyze the results and independently solve the case.

Intended Use:

Students explore the module using scientific methodology and mathematical models.
Learning centers where students of different disciplines facilitate discussions to aid the transfer of knowledge.
A common blackboard site was developed for the purpose of sharing the results of the different experiments and discussing the perspectives from various disciplines. Physical limitations of space were avoided and a classroom beyond walls was created.

Potential Significance: Students must analyze results from various disciplines in order to solve a case. This case study mimics a real life situation where there are in essence no boundaries between disciplines. This wholistic learning approach creates a learning environment where students are welcomed, respected and are a community of learners. The students walk away with a sense of what science really is because they have solved a case just like real scientists and mathematicians.

Module Objectives

Mathematics -- Students will be able to:

Model Newton's Law of Cooling as a differential equation.
Create a slope field from a differential equation and explain its appearance in words.
Solve numerically a differential equation using Euler's Method.
Solve symbolically a variable separable differential equation.
Analyze numerically, graphically, and symbolically a situation involving Newton's Law of Cooling and use the results to predict an outcome.
Collect temperature data from a cup of cooling water, represent the data as a solution to a differential equation, and apply this knowledge to determine the time of death of person.
Model mathematically the spread of a rumor with an appropriate function.
Interpret the rate of change of an exponential function in the setting of the spread of a rumor.
Interpret the initial value of an exponential function in the setting of the spread of a rumor.
Determine the validity of an exponential model for the spread of a rumor.
Alter the model to most accurately portray the spreading rumor.
Use technology to find how long it takes for the vast majority of people to hear the rumor.

Biology -- Students will be able to:

Explain the patterns of the growth of bacteria.
Analyze the growth curve and describe the underlying phenomena by interpreting the graphs.
Distinguish between the different regions of the growth curve.
Analyze factors that maintain exponential growth for longer periods.
Explain the basis of bacterial population growth.

Module Materials:

see full record from Maricopa Learning eXchange (MLX)

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This project is supported, in part, by the National Science Foundation
www.nsf.org