The following are sample ILAPs (Interdisciplinary Lively Application Projects)
developed at CU-DHSC. Each project involves collecting data, building a model
based either on physical principles and/or biological concepts, comparing the
results of the data with the model and then performing some analysis. For the
longer ILAPs, students are required to write up a 10-20
page typed report (or sequence of smaller reports) summarizing their results.
Students at the beginning of the sequence (Calculus 1) have ILAPs
which are much more structured than those developed for Calculus 3 or Ordinary
Differential Equations.
The difficult aspect of
incorporating ILAPs into a course is time; once class
time is used to go through an ILAP, modifications to the traditional schedule
must be made. Typically students are required to do either one major ILAP per
course, which requires about 1.5 hours of net classroom time (usually spread
out over a period of 2 to 4 weeks) to go through the background necessary for a
successful ILAP, or 3 to 4 smaller ILAPs. We feel we
have managed to be more efficient in covering topics by using technology in a
manner which allows discovery of new topics or exposure to old topics from more
directions than the traditional lecture mode allows. This allows us to reach
students with a wide array of diverse learning styles. This continues to be a
challenge and we are continuously evolving how we incorporate the ILAPs into a course.
When many different
instructors are using an ILAP it is important to have an instructors
guidance manual to accompany an ILAP. This is the primary reason why we
developed these ILAPs in-house: ILAPs
which we found available from other institutions only provided what the
students received and did not provide resources for instructors. We found that
unless we had someone who had actually been through an ILAP with an experienced
instructor, we did not know how to proceed. For our major ILAPs
we have some instructor guidance pages. These are not included on this page
since students should not have access to them, but if you would like a copy of
the instructor guidance pages please e-mail me at Lynn.Bennethum@cudenver.edu. Please
note that I will require evidence that you are an instructor.
Calculus 1:
Pendulum Project: This is a long-term project which takes students more than a couple of
weeks to complete (working about an hour in class and then 4-6 hours outside of
class). This project involves using a real pendulum (string and washer),
measuring data (such as length of pendulum arm, period), and fitting a curve to
determine the horizontal and vertical displacement. The second part of the
project involves deriving the governing equations using
Pendulum ILAP version 1 (using vector decomposition)
Pendulum ILAP version 2 (not using vector
decomposition)
How close are the expressions from the two parts of
version two?
Heat it then Cool it! This is a short term project which takes about 20
minutes of class time and will take students 1-3 hours outside of class. This
project is given when introducing derivatives, after introducing basic
differentiation rules but before introducing the chain rule. It uses
exponential functions to model temperature as a function of time, and then
explores the relationship between the function and its derivatives.
Around the Corner: This is a short term project which takes about 15 minutes of class
time and will take students 1-3 hours outside of class. The project involves
finding the maximum length pipe that can be carried around a corner (if not
tilted) using three methods two of which uses optimization techniques.
Walk This Way:
This is a short-term project which takes about 30 minutes of class time and
will take students 1-3 hours outside of class. The project involves taking data
of a person walking away from a motion detector at various speeds and then
using the velocity data to approximate the distance (using Reimann
sums) and then explores the relationships using the mean value theorem.
Calculus 2:
Disease ILAP:
This project models the spread of the disease in a closed system. Students
first do an activity modeling the spread of a disease by rolling die and noting
the resulting curve representing the number of students infected over times of
encounters. Then the governing differential equation is ‘derived’, and the
students analyze and interpret the meaning of the coefficients. It takes about
60 minutes of class time and then another 4-6 hours outside of class.
Fuel it Up: This
project looks at an airplane’s fuel consumption versus speed, and then explores
the relationship between the rate of fuel consumption and its integral using
the trapezoidal rule, average fuel consumption, and the mean value theorem for
integrals. This takes about 20 minutes of class time and 1-3 hours outside of
class.
Fill it Up: Calculate
the volume of a cup by modeling the cup as a “solid of revolution” and then
also by using geometry (volume of a cone). Find the surface area as well. This
takes about 20 minutes of class time and 1-3 hours outside of class.
Let it Hang: Hang
a chain by two fixed points. The shape of the chain is in the form of a catenary function. This involves comparing the real shape
with the centenary function, then exploring the hyperbolic cosine and hyperbolic
sine functions for their derivatives and series expansions. Compare the actual
length of the chain with the calculated version (line integral) . This takes about 40 minutes in class and 1-3 hours
outside of class.