Practical Math Lesson Teaches Critical Thinking and Problem Solving

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By Ed Lott, Math Teacher at Falmouth Academy

I have been asked many times why I do a project about retirement with high schoolers. They should not be worrying about retirement yet – right? Since the decline of the pension and the advent of the 401k retirement plan, thinking about and planning for retirement has become a much more serious part of life – and the building of a retirement plan as a class project brings math into the real world and therefore makes it much easier for students to understand.

An Insured Retirement Institute survey done in 2015 for CNBC showed that over half of people age 40-55 have less than $60,000 saved for retirement and 16% have not saved anything for this life phase. My project shows students how a theoretical concept works in reality; it demands smart uses of technology; and it is personal, which means it is more likely to stick with them later in life.

As a teacher, much of my core philosophy about teaching math can be traced back to two courses I took in college, Differential Equations and Application of Mathematics. The first class was a 14-week lesson in how I did not want to teach. The professor focused almost solely on the abstract nature of the material and never gave the material any concrete context. When I walked into Application of Mathematics, I found my footing again. Each theoretical concept was put into a real-world context. The questions had tangible, meaningful answers. I looked forward to every lecture, and that stuck with me as I moved into my teaching career._dsc3770Fast forward to 1997 when I taught Algebra II at Falmouth Academy for the first time. The unit that caused my students the greatest frustration was exponential growth and logarithms. Seeing their frustration sent me right back to that classroom for Differential Equations. I had to find a way to contextualize the material that would help students see it as something truly useful.

It was the beginning of the dot.com boom and so I asked students to look at how investments in companies changed people’s lives. As the class investigated doubling times of different investments and potential return in the future, students began using these theoretical concepts effortlessly. I knew I was onto something.best_dsc0559-copyExpanding these lessons and giving students more ownership of how we explored these topics is how the individual retirement project came about. I created a basic outline—I gave them some ideas on where to put their money and how much they should put away each year. I allowed for flexibility so that each student could incorporate life goals into the plan. Did a student want go to grad school, retire early, work into their seventies, travel when they retired, or just sit at home and enjoy the grandkids? Was the student a risky investor, conservative investor, early investor or late in life investor?

Students research mutual funds and try to find better returns. They research salaries, mid-career earnings, and even the costs of raising kids to try and make their plans as real as possible. At the end of the assignment, almost every student is happy with his or her plan and feels a sense of accomplishment. Additionally, they understand the significance of exponential growth and compounding.  They are almost always amazed how much money they have when it comes time to retire, even with investing two to three thousand dollars a year at the start, and the importance of starting early, an equally important life lesson that I hope to get across.

When this project first began, students created tables and graphs by hand, using calculators and repeating the same mathematical operation hundreds of times. I showed students the advantages of using a spreadsheet, and expanding their skills with Excel, because they knew 40 minutes of computer work was certainly better than hours of plugging numbers into a calculator.  random16With spreadsheets, students can test their plans with many different variables and I can broaden the scope of the project. Every year somebody finds a new mutual fund that has spectacular returns. On more than one occasion, I have wished I had put money in some of those funds, as they have continued to do quite well! With each new use of technology and information by the students, this project has evolved and grown even more effective.

I have been doing the retirement project for over fifteen years. Though it has changed, the goals of the assignment remain the same.  I want students to understand the significance of exponential functions, see how technology can help attack a problem more efficiently, and learn that saving for retirement is possible and not as daunting as it might seem, as long as you have a plan. I love watching students drag their first formula down a column in a spreadsheet and see that final dollar value. Their eyes almost always light up, not just because of the dollar amount but also because they realize how easy it is to figure out.

Still, if the only thing my students remember from my class is that you can effectively save for retirement, then I have succeeded, as that is the one lesson that may help them most in life.

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