The first two projects in the College Costs series focus on linear and quadratic models. In this post, we’ll look at exponential models of the college cost data and use it to answer the question: If you spend your first two years of college in a two-year college instead of a four-year college, how much would you save? We will demonstrate the process by modeling the national costs y as a function of the number of years after 2000 t with
y = Pert
This allows us to incorporate exponential function into the College Algebra curriculum as well as logarithms.
No discussion of passive learning can begin without a reference to Ben Stein’s portrayal of an economic teacher in “Ferris Bueller’s Day Off” in 1986.
I think most of us could argue quite persuasively that there is no learning going on in this classroom. Although the teacher attempts to interact with the students with the infamous “Anyone, anyone?” question, there is no response from his audience. One might note that he is facing the class and attempting to gauge the student’s understanding of voodoo economics. Is he practicing active retrieval to help his students consolidate the information in memory? Continue reading →
In the College Algebra course taught at Yavapai College, modeling data with different types of functions is a key focus. So the projects I use in my class utilize the same data and question. As noted in Part 1 of this post, the goal of this series of project is easy to understand.
If you spend your first two years of college in a two-year college instead of a four-year college, how much would you save?
Over the past several semesters, I have developed a series of student projects that I use in College Algebra and Finite Mathematics. These projects incorporate a large number of the learning objectives in these courses. They require students to apply these learning objectives to a real world problem over a significant portion of the semester. My use of projects like these are based on research coming out of the field of neuroscience. Many of these results are summarized nicely in the book Making It Stick: The Science of Successful Learning by Peter Brown, Henry Roediger, and Mark McDaniel. In this book, the authors point out that many of the strategies students use to study, like rereading a text or massed practice, are not very productive. They give the illusion of mastery and result in learning that is not very durable. As the authors put it,
Learning is deeper and more durable when it’s effortful. Learning that’s easy is like writing in sand, here today and gone tomorrow.
Using student projects is definitely effortful since it requires students to apply basic mathematical concepts to a problem with no unique solution. It helps them to distill the key parts of a problem and to put it into a mathematical framework. Since this framework is sustained over several projects, additional knowledge is acquired and organized in the brain so that new information is consistent with prior information. Continue reading →
Populations are often described by their doubling times. The doubling time is the amount of time it takes a population to double. We can calculate the doubling time of an increasing exponential model by examining its graph carefully. Since students seem to enjoy themodel for population growth on Gilligan’s Island, I like to use it to illustrate doubling in an exponential function. Continue reading →