Category Archives: Survey of Calculus

Alternate Technology Assignment for Medical Insurance Project

I get more interest in the medical insurance projects than any other project on this website. I use two different versions of the project in my classes. In College Algebra, I use the Medical Insurance 2 Project. I have student compare two different plans to decide which is cheaper. In Business Calculus, I use the Medical Insurance 3 Project where students model an insurance plan and prove it is continuous. These project share a number of technology assignments. The second one that students complete is Technology Assignment: Calculate the Total Annual Cost (DOC | PDF). For my students, this is usually the hardest assignment of the semester. It is a collision between insurance terminology (which they have no clue about) and Excel (which they also have no clue about). To find a model more efficiently, I needed to tone down the Excel component and ramp up the insurance component. Continue reading Alternate Technology Assignment for Medical Insurance Project

Average Rates of Change and Verizon

SmartPhoneOver the past few years, I have worked to keep the attention of my students in class (and online). This is no small task. In his book, Brain Rules, 12 Principles for Surviving and Thriving at Work, Home and School, John Medina writes that “information is remembered best when it is elaborate, meaningful, and contextual.” This may seem obvious at first, but how does it play out in practice?
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Tax Rates in NC and LA

The activity I describe in the post on Continuous Tax Functions may be linked to real data to make an extended class activity. In this extension, students need to come up with the piecewise continuous function for a state. Once they have the function, they prove that it is continuous using the definition of a continuous function.
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Continuous Tax Functions

One of the disadvantages of using projects in a course is the time it takes to administer and grade. For many faculty members with large class sizes or large amounts of content to cover, it is not feasible to do a project over several weeks. Fear not! You can still incorporate realistic applications in your classes as activities.
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Updates to the Medical Insurance Project

I have been absent from this page for a while. Over the winter break and throughout the beginning of the semester I have been updating the Medical Insurance Project and adapting it for my calculus class. In addition, I have a new project for college algebra on college costs. In this post I want to outline the changes I have made to the Medical Insurance Project.

Last semester, my students struggled with taking their plan details and creating a table of charges and costs. It seemed like they needed an intermediate step between entering the plan details in Excel and creating the table in Excel. In addition, creating models for two plans was quite a bit of work. To help mitigate these troubles, I have rewritten the project and named it Medical Insurance 2. This project includes a new technology assignment, Find and Understand Costs, where they fill out a table of charges and costs by hand. This forces them to confront the unfamiliar terms before they ever begin their cost calculations in Excel. Instead of finding two insurance plans to model, they only find one plan and compare it to the Basic Plus Plan. They should simplify the project a bit, but still preserve the same solution strategy.

In Medical Insurance 3, calculus students choose a health plan and model it with a piecewise linear function. Using three technology assignments, they complete the same strategy as college algebra students complete in Medical Insurance 2. Once they have their model, they use the definition of continuity to prove that it is continuous. This amounts to proving that the function is continuous at the charge where the deductible is met and the charge where the out of pocket maximum is reached. Great example of continuity in a real world context.

Both of these project utilize similar technology assignments. Since these assignments take some effort to create, reusing them makes better use of my time. My college algebra students are currently completing Medical Insurance 2. My business calculus students completed Medical Insurance 3 as their first project of the Spring semester. All of the students are frustrated with the non-mathematical content. This keeps me very busy in office hours and answering many emails each day. However, I get a lot of feedback about how important they think it is to understand all of this. After all, the debate over health care in the US and how to pay for it is far from over. Maybe these projects can do a small part to contribute to better understanding of the issues for my students.