How Financially Literate Are Our Students?

The answer, according to a recent study conducted by Annamaria Lusardi, Olivia S. Mitchell, and Vilsa Curto (you can download the full paper here) is "not very."

In the most recent wave of the National Longitudinal Survey of Youth, three basic financial literacy questions were asked of a representative sample of 23-28 year olds (N = 7138). Here are the three questions:

1. Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow: more than $102, exactly $102, or less than $102? (Do not know; refuse to answer).

2. Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year. After 1 year, would you be able to buy more than, exactly the same as, or less than today with the money in this account? (Do not know; refuse to answer).

3. Do you think that the following statement is true or false? "Buying a single company stock usually provides a safer return than a stock mutual fund." (Do not know; refuse to answer).

The bad news: less than half of the respondents (46.8%) could answer question 3 correctly; slightly over half (54%) could answer 2 correctly, and four out of five (79.5%) could answer question 1 correctly. As a whole, only 27% of respondents could answer all three questions correctly.

There are serious implications to financial illiteracy among young people - excessive debt, credit card misuse, lower levels of investment, etc. (for an expanded discussion of the issues, go here and here). As mathematics instructors, we are in a position where we could make some contribution, however small, to improve the situation. What could we do?

I personally intend to expand the coverage of financial mathematics in Chapter 10 of Excursions the next time I teach the course, but I haven't yet decided what form this expansion will take. For the time being, I would like to hear other people's ideas, suggestions, and experiences teaching financial mathematics topics.

While mulling over how to expand my coverage of financial matters in my classes, I came across some resources and tools on the web that students and instructors might find useful. Below is a short list of ones I like and have the added virtue that they are free.

• Money Smart. Ten modules on basic financial literacy sponsored by the FDIC. Available either in computer-based or instructor-led formats.

• National Endowment for Financial Education. A financial planning program aimed primarily at young adults. The focus is in developing personal money management skills (budgeting, saving, goal-setting) but some lower level financial mathematics is included.

• Kanjoh. An extensive library of short videos covering an extensive array of topics on financial matters. The videos cover topics in personal finance, investing, and much more.

• WeSeed. A site focusing primarily on learning about the stock market. Students can play the market with fake money. It includes an educational component with lesson plans and study guides.

• BrokePiggy. A forum for sharing informatin on everyday financial matters, aimed primarily at young people. Funky, but well organized.

• Mint. A superb online tool for managing personal finances, it includes a blog with educational features and resources. Mint is incredibly useful, well designed, and definitely worth a look. I like it so much I'm thinking of offering extra credit to my students just for signing up.
  

On Being a Good Host

Imagine the following: You live in a small country. You think your country is interesting, exciting and beautiful, and so do most of your fellow citizens. Outsiders, however, have a completely different opinion. They often know little about your country and when they have an opinion they mostly think it is dull, mysterious and intimidating. This bugs you and your countrymen to no end.

Now imagine that you have the opportunity to host a group of young visitors from abroad. If you are like most people, you will do your best to be a good and gracious host, but in fact, you will want to do more: take them to visit some of the more interesting and beautiful sights, show them a good time and share your excitement and love for your country. The ultimate goal is not necessarily to get the visitors to move to your country but simply to change their opinions about it. Hopefully they will go home and tell others that your country is pretty rad.

I'm sure that by now you know where this metaphor is going. I just wanted to share my perspective when writing and why after all these years I still get excited every time I teach the Liberal Arts Mathematics course to a bunch of fresh faces.

Gimmick: How to Rig a Non-Gimmicky Class Election

The Fall term is here, and as usual, I'm optimistic. If you are like me and like a good gimmick to kick-off the course (and are planning to cover Chapter 1: The Mathematics of Voting) then I highly recommend getting things started with a "non-gimmicky" class election. Over they years I have tried this many times with varying degrees of success (less success in my first few attempts, better luck lately) and in this blog I would like to share some of my experiences and if I may, offer some suggestions. But before I start, let me first explain in a little more detail what I mean by "a non-gimmicky class election."

The point of having a class election where the students are voting on some particular issue is to motivate the students and generate some excitement about Chapter 1. If you can start the semester with some motivational capital, with a little nurturing and a dose of good luck it can carry you a long way.

For a class election to be motivating, the issue behind the election must be both meaningful (i.e. relevant to the student's experience) and consequential (i.e. students must have something at stake in the outcome). A third criterion (this applies to all elections) is that voters should know enough about the issue to be able make informed choices. (For example, having the students vote on the topics to be covered in the course is not a good idea—the content of the course might be meaningful and consequential to them, but at the start of the semester students are hardly in a position to make informed choices about it.)

It seems to me that as instructors, there are only two broad areas that we can control, that are meaningful and consequential to our students, and where students can make reasonably informed choices: the grading scheme for the course and the timing and deadlines for the assignments. So far, I have only experimented with in-class elections involving the former, as I have no good ideas yet for how to incorporate the latter into an in-class election. (I would very much like to hear some suggestions for an election dealing with timing and deadlines.)

So, that leaves the grading scheme for the course as my default election issue. Clearly, this issue is both meaningful and consequential. Democracy at its best—the students get to choose the grading scheme for themselves! (Warning: If you are going to do this you might want to discuss it with your Dean first.)

As an instructor, there are many variables that you can use to manipulate a grading scheme: the number of homework assignments, the number of tests/midterms, do you have projects/papers?, and the percentages allocated to the various elements. I have found that the two variables that work best for me are the number of midterms (between 2 and 4) and the relative percentage allocated to midterms and final. (Note: I leave the total value of the homework constant because I have found from past experience that it dominates all other variables—students will overwhelmingly choose the option where the homework is worth the most.)

It goes without saying that whatever the outcome of the election is, you should live with it (you are going to lose all your motivational capital if you end up invalidating the election because you didn't like the results). It follows, that all the options should be pedagogically sound so that your learning outcomes are never compromised. (For example, I would not recommend an option where 80% of the grade is based on the homework and only 20% of the grade is based on midterms and final—you are not going to be happy with the learning outcomes.)

I usually stick to three options (I recommend at least three and not more than five) and in my latest election they were:

• Option A: HW = 20%; Four midterms @ 15% each; Final = 20%

• Option B: HW = 20%; Three midterms @ 15% each; Final = 35%

• Option C: HW = 20%; Two midterms @ 25% each; Final = 30%

One of the reasons I like these options is that there seems to be no clear-cut favorite among the three, and the preferences are reasonably well balanced. (I will disclose the outcome of my last election in a later post ... maybe. In the meanwhile, you are welcome to guess.)

One of benefits of having an in-class election is that as you move through the chapter and apply the various concepts to "the" election (which option is the winner under each of the methods?, are any of the fairness criteria violated?, etc.) the students really pay attention. With a little bit of luck you may get different winners under different methods (what do you do then?).

Finally, a couple of suggestions about implementation details.

I introduce the options the first day of class, after handing out the syllabus (with the disclaimer "The grading scheme will be decided by popular vote and will be announced the second week of the semester.") and a brief introduction to preference ballots. The student are then instructed to turn in their ballots on-line (they drop them in my Blackboard dropbox—good practice, since that is how they will turn in all of their assignments). The deadline is midnight of the next day, and as a sweetener I give them a token number of points for turning in their ballots on time . If I have a small class (small for my school means under 60 students) then I collect the ballots and create the preference schedule for the election myself. If I have a large lecture (about 200 plus students) I let my TA have the honors. In either case, by the second class meeting I have a slide with the results of the election and a great segue to the topic of preference schedules.

Implementing a meaningful and consequential class election is a bit of a hassle, but in my opinion, well worth it. I highly recommend that you give it a try (and come back and post a comment telling us how it went.)

EMM FAQs

By far, the most common type of query I get from instructors who use, will use, or might use Excursions in Modern Mathematics has to do with matters of implementation—how to organize and structure a course using the topics in the book.

In this post I will try to address some of these issues using an FAQ format. For starters, I will throw out my own ideas (based on my experiences, opinions, and prejudices) and hope that others will throw out their own ideas. Hopefully, we can get a meaningful thread going.

So, here we go.

Q: How many chapters should be covered in a semester (quarter) course?

A: My general rule of thumb is 3-4 class periods per chapter (I am assuming fifty minute class periods). Thus, in a 3-credit semester course (about 45 class meetings) I try to cover 12 chapters. In the past I have taught as few as 9 chapters, never more than 12. I don't think that covering all 16 chapters in the book is reasonable (the only reason the book has 16 chapters is to give instructors some choice).

Q: What are the precedence relations among the parts and among the chapters in each part?

A: Each of the four parts is independent, so the parts can be taught in any order. Within each part, the relations between chapters are more complicated. The following table summarizes my suggestions for each part. The columns show the suggested choices depending on whether you want to cover only two chapters, three chapters, or all four chapters.




Q: How do chapters (and parts) compare in their level of difficulty?

A: I feel that the most relevant source of information to answer this question is the aggregate opinion of the students in the course. At the end of each semester I give an exit questionnaire that includes several questions on the relative difficulty of the chapters–over the years, I have collected thousands of students' opinions on this matter. Here is a crude summary of what my students think (keep in mind that my students may be very different from your students):

(1) In ranking the difficulty of the chapters, Chapter 16 is considered the most difficult, followed by Chapters 4 and 15. The opinions on the easiest chapter are all over the place.

(2) Within each part, the last chapter in the part is consistently ranked as more difficult than the first chapter. This is true for all parts but the different is most significant in Part 4. (If you think of each part as a hike, each hike represents a slight uphill climb with Part 4 being the steepest climb.)

(3) When ranking the overall level of difficulty of the parts, my students rank Parts 1 and 3 as slightly more difficult than Parts 2 and 4, but the differences are not significant.

Q: Is there some significance to the fact that the book is organized into 4 independent parts with 4 chapters each?

A: While there is no compelling reason for a 4 by 4 organization, I like the flexibility that this format offers. In particular, I like the symmetry of having the same number of chapters in each part and the modularity of having four independent parts. For example, an instructor that wants to cover 12 chapters in a semester course can choose a 3 by 4 format (three chapters from each of the four parts) or a 4 by 3 format (full coverage of three of the four parts). The former approach offers a little more breadth, the latter a little more depth. I think that both approaches are consistent with the goals of a Liberal Arts mathematics survey course.

Welcome to the EMM blog

Welcome to the first post of the Excursions in Modern Mathematics blog. Why, you may wonder, a blog for a mathematics textbook? At the moment, I can think of three good reasons. One of my measures of the blog's success is how many other good reasons will surface after others have a chance to add their input.

Here are my three reasons:

(1) Once a book goes to the printer the contents of the book are set in concrete, at least until the next edition or, in the case of minor errors and typos, until the second printing. This is a problem for a book that places a premium on currency and relevance. I will illustrate how I will use this blog to get around this problem later in this post.

(2) In addition to updating information already in the book, I plan to use the blog to introduce facts, tidbits and resources that fall under the umbrella of "enrichment" of core concepts in the book. Typically these resources will be websites, videos or articles that I will introduce and, when appropriate, briefly discuss. In my second post I plan to start the ball rolling on this one.

(3) A blog can be a good place for networking– not as good as a social networking site but good enough for people to interact productively and share comments and ideas. As the book's author I have had some opportunities to hear from and interact with users of the book, but I would welcome much more sharing. The success of this aspect of the blog depends on you. I am hopeful that this blog will eventually take a life of its own and become a shared "meeting place" for all users of the book.

As promised, in this post I want to discuss a couple of substantive updates to information that went to press with the 7th edition and soon become dated. In one case the circumstances were foreseeable, in the other they were a bit of a shock.

Much to my regret, I had to submit the final manuscript for Chapters 1 and 2 in July 2008. Thus, by an accident of bad timing I was unable to discuss or even mention one of the most exciting presidential elections in U.S. history. My biggest regret is that I had to use the 2004 presidential election for the cartogram that illustrates the "real" Electoral College in the opening image for Chapter 2. Thanks to Mark Newman of the University of Michigan, a new cartogram with the 2008 Electoral College results (shown below) is readily available for anyone to use under the Creative Commons License (text and images may be freely distributed). I definitely plan to use it in my introduction to weighted voting and the Electoral College. To download the cartogram,
click here. In a later post I plan to discuss some of the other amazing cartograms produced by Mark and his team.
















The second piece of real-world data badly in need of updating is Example 10.4 on the ups and down of the Dow Jones Industrial Average. When I wrote the example the Dow Jones was at around 12,800. As I write this post, the Dow Jones is at 8,300. Had I known the stock market was going to tank I would have done Example 10.4 (plus a lot of other things) differently. When I cover Example 10.4 in class I plan to change the numbers to reflect current values for the Dow. And who knows, maybe by then 12,800 will be a current number again. That's a cheery thought!