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% The class was developed by  Marc Frantz with suggestions of the 
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\documentclass{simiode}

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% With this version of the tex file and the associated SIMIODE.cls file you can produce BOTH a Student Version and a Teacher Version of your modeling scenario or technique narrative.
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% Basically the Student Version contains the title STUDENT VERSION along with the NAME OF SCENARIO, with no abstract, no keywords, no tags, no author identifiers, and no COMMENTS section. The Student Version contains only the STATEMENT of the modeling scenario with appropriate figures, data, instructions, and perhaps a bibliography appropriate for student resourcing, but nothing in the bibliography which would "give away" the nature of the modeling scenario, etc.
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%The Teacher Version contains the material in the Student Version, namely the title NAME OF SCENARIO, now headed with   TEACHER VERSION, but also full author  identification, abstract, key words, tag words, and, following the STATEMENT, a section of COMMENTS which can be discussion of presentation  ideas, "solutions," techniques, etc.
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% Authors can prepare a full Teacher Version using the notions immediately below  to create a pdf for review (but in review please eliminate all information about the author as we use a double-blind referee system. Such information will be restored when accepted and published in SIMIODE at www.simiode.org.
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%***********   Toggle the following line to turn the teacher version on (1) or off (0). ***********
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\def\TeacherEdition{0} % Toggle this line's value.
\newcommand{\teacher}[1]{\ifnum\TeacherEdition=1 #1 \fi}
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% The \teacher{ } command wraps any text that will appear only in the teacher version of
% the document. See this file for examples. This has been done for you in the document below.   
% Rename the pdf after you compile each final version.
% This option was created  by Eric Sullivan, Carroll College, Helena MT.
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\usepackage{amsmath,amssymb}
\usepackage{color}
\usepackage{graphicx}
\usepackage{hyperref}

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\begin{document}

\newpage
% You only need to change the NAME OF SCENARIO in the next line and delete the footnote. See above for instructions on toggling from Teacher Version to Student Version.
\title{\ifnum\TeacherEdition=1 TEACHER VERSION  \else STUDENT VERSION \fi\\SAVING FOR A CHILD'S COLLEGE EDUCATION}



\markboth{Saving for a Child's College Education}{Saving for a First Child's College Education}






\author{Brian Winkel,
Director SIMIODE\\
Chardon OH 44024 USA\\
BrianWinkel@simiode.org}


\makeStitlePDFLaTex
 


\begin{abstract}
 We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.
\end{abstract}



\section*{SCENARIO DESCRIPTION}

Model what you will do to completely pay for a child's first year of college education. It is most important that you 

\begin{enumerate}
  \item make clear your assumptions,
  \item build a mathematical model,  
  \item perform a complete analysis, summarize your actions, and 
  \item perform a sensitivity analysis, i.e. address the question, ``What would slight changes in your assumptions or parameters do to your plan?'' 
\end{enumerate}

\noindent Consider a full four year (or more) college education, possibly for more than one child.



\teacher{
\section*{NOTES FOR TEACHERS}



One major aim of this assignment is to have students blend mathematical analysis with exposition and personal interest. We believe that this blend helps students develop more technical communication skills. Some students will try to make things very complicated, e.g., using random numbers to vary the interest rate. The idea is to keep this simple and so we discourage too much complexity for, as we discuss with them, some changes might not offer much in return for our investment of time.



We include an example  Mathematica notebook both in Mathematica notebook format (1-003-T-Mma-CollegeSavings-TeacherVersion.nb)  and universally readable pdf (1-003-T-Mma-CollegeSavings-TeacherVersion.pdf) format in which we offer up a typical write-up that students produce after about 10-15 minutes of class discussion and time at home to do the mathematics and writing.  We have given students about 2-3 days of homework time to complete this assignment. 

We have used the assignment in many classes and students have written up their work in a variety of formats:  text documents,  computer algebra files, and spreadsheets. We have even begun the semester on the first day of class - without any preparation - just out of the chute, in class. We have used it in a differential equations course, a modeling with differential equations course, and first year course in which we will be studying discrete dynamical system models as a prelude to studying the calculus.

Working with a spreadsheet requires students  to develop slightly different strategies, for a spreadsheet does not usually possess the symbol manipulation and equation solving capabilities that a CAS will offer. However, it is exceptionally good at iteration in which students can see the successive balances on their savings year after year.

Students are often intrigued with this problem, albeit the topic  is remote from their current thinking for many students. Sometimes, they will find a calculator at some site on the web which will permit them to enter their parameters, e.g., current tuition, interest rates, amount they plan to contribute, etc. and the calculator page will ``do the math'' for them. I encourage them to cite such resources, but each student has to construct a set of assumptions, build a mathematical model, offer up a solution with analysis, and a write a complete summary.


There are many variations and considerations which students will produce.   The main point is to get students to make their own assumptions and live with them and point to them in their model building (or modify them) as they go through their analysis and write-up. Thus, grading is about process and reasonableness of assumptions, not conformity to one set of assumptions.  For example, the analysis offered in the example notebook we provide assumes savings will begin while the student provider is still in college. Most students  assume that their  saving will begin upon graduation from college and the attainment of the first paying job. This makes the accounting different and they will obviously have to save more per year in this scenario. Often, we compare assumptions - even in the formative stage of our first and only class discussion - and our results to see why they are different.

In our experience  this problem has never failed to grab the attention of the students and to get them thinking about and doing assumptions, modeling, analysis, and communication. Try it, you will like it - and so will your students.
}


\end{document}
