This semester, I decided it was time for a new first project. In earlier semesters, I have used the Medical Insurance project or the Gas Prices project as the first project. Each of these projects covers linear equations in some form. However, I wanted a more basic project to start the semester. Something I can use to apply linear equations and teach Excel.

The College Costs 2 project accomplishes these goals. In this project, each student is assigned average college cost data from a state. Students are either assigned data for the average cost of four-year public and two-year institutions or four-year private and two-year institutions. Using the data, students construct a linear model of the data and use it to calculate how much is saved by attending the two-year college during a four-year college career.

To do this, student complete several technology assignments. In Make a Scatter Plot of College Costs, they use Excel to make appropriate scatter pllots of the data. They learn how to select columns and format the graphs they create. Once they have created the scatter plots, they complete the technology assignment Find a Linear Function for College Costs to find the line that passes through to of the data points in the scatter plot. Finally, they put their graphs and functions into a Word document in the technology assignment Paste Equations and Graphs. These technology assignments are located on the College Costs 2 project page.

These technology assignments put them in a position to use the functions to determine the costs savings of spending two years at a community college and then another two years at a four-year college compared to four years at a four-year college. How you get the documentation for the rest of the solution is up to you. I have them write a technical memo for the project. However, you could have them complete a much shorter assignment to assess the solution. This part is up to you. The number of students in your class, the amount of time you have to grade, and the overall importance of projects and real world problems all influence how you assess the solution.

I gave a talk earlier today on how to develop a student project. In this session, I discussed the Medical Insurance 2 project and the associated technology assignments.

In the video above, I also discuss some of the logistics of administering a project like the Medical Insurance 2. It is a quick (25 minute) trip through the slides in my session at ICTCM.

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.

The Medical Insurance Project now has a web page with all of the resources for it in one place. You can click on the link above or access it the the Projects page on the menu at the top of this page. In the notes for this project there is a link to an example of a technical memo for this project. You’ll need to contact me to be able to access this PDF since the file is password protected.

My next conference presentation will be at the AMATYC Conference in Austin, Texas. I’ll be presenting on “A Different Strategy for Solving Optimization Problems in Calculus” on Thursday, November 10 from 11:20AM to 12:10PM. Hope to see you there! If you are not able to make it, I’ll post a Flash video of the session immediately afterward.

Once the students have an appropriate table, they need to graph the data.

Excel Table for Basic Plus Plan

In the next technology assignment, student learn how to  make a line graph of the total medical charges versus the total annual charges.

Technology Assignment: Graph the Total Annual Cost   DOC | PDF

Upon completing this assignment, students will have a graph for each health insurance plan like the ones below.

Total cost as a function of medical charges.

To compare these graphs, it is convenient to have them on the same graph. In the next technology assignment, students put these two graphs together and find the piecewise linear functions corresponding to each health plan.

Technology Assignment: Find Piecewise Linear Models   DOC | PDF

With the graphs together, it is much easier to compare the total costs.

Both graphs for the health plans on the same axes.

Once students have put these graphs together, hopefully they will make the next logical step which is to find the point of intersection using the piecewise functions.

If the students get to this point successfully, they are over the major hurdles of this project. Next they need to document their solution strategy. I’ll describe the document they turn in for this project in my next blog post.

For 17 and 18 year old students, this is a daunting task. Not only are they struggling with using Excel, they are also struggling with the terminology. In the technology assignment handout, I take great pains to spell out exactly how to use Excel to create the table.

Technology Assignment: Calculate the Total Annual Cost DOC | PDF

As you can see, each step is carefully outlined. You would think that it would be a very simple task for students to create the table for each plan.

Oh how wrong I was about that! Students focus on the steps of using Excel and completely shut down thinking about where the numbers come from. Here are a few of the glaring errors I saw the first time I used this assignment.

• Students do not understand the difference between a medical charge and the cost they pay. Often I found the copay in the medical charges column and vice versa. In an aha moment, I realized that most of them had never seen a bill from a dentist or hospital or received a statement from their insurance company…their parents always got these!
• On the first page of the handout, it describes the assumptions for the table…two office visits, one specialist visit, and one generic prescription. Most student glossed right over the bulleted list and the statment that in the handout I would assume the office visits incur a charge of $100 each, the specialist visits incurs a charge of $150, and the generic prescription incurs a charge of $30 per month.
• There is a lot of confusion over the fact that one must pay the deductible before the charges are split with the insurance company. And once the coinsurance kicks in, they pay a percentage of all charges beyond the deductible and any charges for the visits. While this is not exactly true with all plans (in some you pay the deductible before the copays kick in on the visits), almost every plan my students chose worked that way.
• Some companies report their out of pocket maximum including the deductible and others report it without the deductible. For instance, Blue Cross / Blue Shield reported a deductible of $10000 on one plan with a $4000 out of pocket maximum. This confused students greatly until they noticed that the max did not include the deduictible. In effect, the most that a person might pay in a year under the plan was $10,000 + $4000.
• Students assumed that their first plan was like the Basic Plus Plan (coinsurrance but no copays for visits) and their second plan was like the Premier Plan (copays and coinsurance for visits). In actuality, almost every student chose plans with copays for visits (at least for the first three visits). I had to focus them on the Premier Plan so that they could fill out the tables for both plans.

After giving this assignment for the first time, I had to clean up the carnage so that they could continue working on the project successfully. I created another handout for them on the specific entries in the Premier Plan.

Handout: Deconstructing the Premier Plan DOC | PDF

In this handout I tried to link the formulas in the cells with the assumptions in the plan. Using this, they could modify the formulas to fit their own plans. It is not uncommon that an assignment does not work as anticipated. Sometimes it is just too much too handle in one assignment or your assumptions about your students is way off base. For this assignment, my students had no idea how insurance worked so assuming they could track the numbers through the handout easily was doomed. However, next semester this might work just fine for a group of older, more experienced, students.

Even after I had posted the Deconstructing the Premier Plan Handout, there were a few stragglers still fighting with their Excel spreadsheets. I decided to make a short video on putting together the table of values for total annual cost as a function fo the total medical charges.

Video Constructing the Table for an Insurance Plan

Next semester I plan to put together a short worksheet which the students can complete in class and a corresponding video for online students. This worksheet will give them three different charges (one from each of the three regions on the model) and ask them to caclulate the corresponding charge by hand. This way they will have some familiarity with the concepts and numbers before they start putting the formulas into Excel. I’ll post that worksheet once it is complete.

To present the components of the project, let me explain my thought process in developing the project. The goal of the project is to have students develop models for two medical insurance plans of their choosing and to compare them. The models should give the total annual cost of each plan to the insured as the total medical charges increase. With these models they construct a graph to compare the plans like the one below.

Based on the graph, students can make a choice of the two insurance plans based on their own lives. As a template, I lead them through a potential solution using the information from my two health plans, the Basic Plus Plan and the Premier Plan. They will need to follow the same strategy with two plans of their own choosing.

This means the first task they need to accomplish is selecting two health plans. The technology assignment

Technology Assignment : Collect and Organize Data DOC | PDF

is customized to their unique data (state, age, dependents). This accomplishes one of my requirements of projects. Each student does a unique project based on the theme of comparing health plans.

Once they have this information in hand, they use Excel to document their plan. The primary goal of using Excel in this assignment is to get them familiar with the interface and to demonstrate how to format cells. Later assignments utilize Excel’s capabilities more fully.

A sample submission for the technology assignment

When I grade the assignment, I make sure that they have at least given me the most basic information about their plans such as copays, coinsurance, deductibles and out of pocket maximums.

I used this assignments this semester and students had little trouble completing it. There were many comments in class about why some plans are cheaper than others. I was surprised at how many students were completely ignorant about how insurance works. I guess I should not be too surprised since my classes are mainly 17 to 21 year olds with a handful of older students. Opening their eyes to the important issues and terms regarding healthcare was very satisfying.

In my next blog post I’ll talk about the second technology assignment I give students. In this assignment they make a table of increasing medical charges and the corresponding costs to the insured.

Normally this would not be a big deal except many students are beginning to purchase Word 2010 as a part of Office 2010. I could certainly recommend that the college purchase a new site license for the latest version of Mathype, but in these trying economic times such purchases are not likely to go through. Instead, I decided to reevaluate the equation editor that is provided in Word 2007 and 2010 to see if it would be a reasonable substitute for Mathtype.

After several weeks of using the equation editor in Word 2007 and 2010, I decided that it was easy for students to use and produced professional looking equations. It certainly does not produce equations as well as Mathtype, but for College Algebra, Finite Math and Calculus students, it is good enough.

I have been adding new material in the Technology Assignments to cover the usage of the Word equation editor in addition to the existing Mathtype instructions. The affected technology assigments are

• Technology Assignment: Row Operations on the Ti-83  DOC | PDF in the project Arsenic Removal from Drinking Water
• Technology Assignment: Rational Model DOC | PDF in the Doctors and Nurses Project

Future projects with Mathtype components will also include a corresponding Word equation editor component also.

The two plans are described in the summary plan (PDF). Examining the two plans you’ll see that there are several differences for family coverage.

• The out of pocket maximum for the Premier Plan is $6000 per year versus $12,000 per year for the Basic Plus Plan.
• The annual deductible for the Premier Plan is $600 per family versus $1200 per family for the Basic Plus Plan.
• In general, the Premier Plan covers 80% of medical charges and the Basic Plus Plan covers 60% of medical charges.

The plans differ in cost too. Family coverage under the Premier Plan is $514 per month compared to $46 per month under the Basic Plus Plan. There are other difference regarding in network and out of network, but these facts are what I used to make my coverage decision.

Under a number of assumptions (which I’ll detail in later posts), I came up with the following graph.

This graph shows the total annual cost for each plan as a function of the medical charges incurred by the insured. As you can see, each plan is described by a piecewise linear function. If my family incurs less than $26,880 in medical charges during the year, the Basic Plus Plan is cheaper. For more than $26,880 in medical charges, the Premier Plan is cheaper.

In this project, I want students to create a graph and accompanying mathematics for other insurance plans. Luckily, it is easy to get health insurance quotes online. Humana One will give you an instance quote when you click on the Get Quote link on their webpage. Although they ask for a lot of personal information, only the state, zip code and birthday information about the insured are required. For a family coverage of a 46 year old in Arizona, this PDF demonstrates that a number of plans are available with different levels of coverage, different out of pocket maximums, and different deductibles. Another great source for health insurance quotes from many different companies is eHealthInsurance. I want my students in College Algebra to enter in their pertinent information and compare two plans like I did in the graph above.

Over the next week, I’ll post the assignments I create to help point students in the proper direction as well as the project letter I come up with.