I recently finished reading the first two books of the three-book series The Hunger Games, by Suzanne Collins.  The series, and the movie currently in theaters, seem to be extremely popular with a lot of teens right now.  Last week I asked a group of students if they had read the books; every one of them had read at least the first book, and most of them had read all three.

Lately, the story seems to be popular with math teachers, too.  A frequently referenced recent Wired post comments on the probability and game theory involved in the lottery-like selection of “tributes” and their strategy during battle in the arena.  When students are already interested in the story, it can be a great opportunity to motivate discussion of related interesting mathematics.

Frankly, I do not think these are great books.  Good, yes, with an interesting and thought-provoking premise.  But at times they feel like fast-food writing, with quite a few gods in the machine to keep the plot stitched together.  In a 2008 review, Stephen King points out some examples in the first book of what he calls “authorial laziness.”  The motivation for this post is one particular episode in the second book, Catching Fire, that arguably also fits that bill… but which can also be viewed more optimistically as an opportunity to discuss the non-intuitive nature of probability with students.

Spoiler Alert: The following may give away important plot points in Catching Fire.  You have been warned.

The story takes place in post-apocalyptic North America, where the country has been divided into a controlling Capitol and 12 Districts.  As punishment for a long-ago rebellion, every year each district must send one boy and one girl, called tributes, to take part in the Hunger Games, where the 24 tributes fight each other to the death in an arena until one victor remains.  That victor is rewarded with a life of wealth, luxury… and freedom from participation in future Games.

However, on the 75th anniversary of the rebellion, the evil Capitol decides to add a twist to that year’s Hunger Games: instead of selecting tributes from their young boys and girls, each of the 12 districts must instead send one male and one female from its pool of past victors, some of which might now be old men or women.  As described in the book:

In the history of the Games, there have been seventy-five victors.  Fifty-nine are still alive… As one would expect, the pools of Career tributes from Districts 1, 2, and 4 are the largest.  But every district has managed to scrape up at least one female and one male victor.

Let’s re-state the setup, just to be clear: among the 59 living victors of past Hunger Games, each of which could be male or female, and from any of the 12 Districts, there is fortunately at least one female and one male from each district, to make up the 24 contestants for the 75th Games.

ObPuzzle: Making any necessary assumptions, how unlikely is this scenario?  That is, what is the probability that, among 59 victors emerging from the male and female populations of 12 Districts, at least one male and at least one female from each district is represented?

I like this problem for several reasons.  First, at first glance it may not look like a problem at all.  When considering situations involving some element of randomness, our intuition is notoriously unreliable.  This particular example highlights our tendency to equate “random” with “evenly distributed.”  Second, the problem may be attacked in several different ways: computer simulation, exact analysis, etc.

As usual, solutions/discussion are welcome in the comments.

Education has turned out to be a less frequent topic in this blog than I thought it might be when I first started.  But as with the previous post on home schooling, here again I think it is worth calling attention to some recent interesting developments.

A Tennessee bill made its way through the state House and Senate and will soon become law.  The intent of the law is “to create an environment within public elementary and secondary schools that encourages students to explore scientific questions, learn about scientific evidence, develop critical thinking skills, and respond appropriately and respectfully to differences of opinion about controversial issues.”  (Read the entire text of the House version of the bill here.)

Sounds great, right?  The problem is that many scientists, educators, and parents are concerned that the law will effectively open the door to teaching creationism, intelligent design, or other religiously motivated ideas, presenting them as scientifically credible alternatives to the “controversial” theory of evolution.

The text of the bill insists, however, that religion has nothing to do with it (Section 1e):

This section only protects the teaching of scientific information, and shall not be construed to promote any religious or non-religious doctrine, promote discrimination for or against a particular set of religious beliefs or non-beliefs, or promote discrimination for or against religion or non-religion.

Sounds pretty defensive to me.  We’ll see.  I want to be optimistic, and agree with Tennessee governor Bill Haslam, who says he does not believe that the law “changes the scientific standards that are taught in our schools.”  That is, it is possible that the law will have essentially no impact on the quality of education received by students in Tennessee.  It will be interesting to look at the situation, say, a year from now, to see if there will be any real effect.

But the cynic in me suspects that this law has succeeded in furthering simple religious denial, in the clever disguise of “scientific objectivity.”  The mistake that proponents of creationism, intelligent design, etc., repeatedly make is claiming that science demands that all ideas deserve equal time… when in fact they do not.

I’m originally from Kansas, so unfortunately this is not a new story.  But it will be interesting to watch how this one unfolds.

This month’s issue of the Notices of the AMS contains an interesting article on “Mathematics and Home Schooling” (see reference below).  I think the title is slightly misleading, as the article deals more generally with the past and current state of home schooling in the United States, with only a minor focus on science in general, as opposed to mathematics in particular.  But no matter– the article is still a great informative read.  The following are merely highlights, reactions, and rants.

I found particularly interesting the survey of legal precedent and various interpretations of the states’ assumed responsibility for childrens’ education.  For example, the “Amish exemption” resulting from Wisconsin v. Yoder (1972) allowed the Amish community in Wisconsin to sidestep the state’s compulsory school attendance law, “because [the court] believed that the very nature of the religion would be undermined with exposure of its young people to the worldly culture of education beyond the eighth-grade level.”  But this allowance seems to be unique; “attempts by other religious groups to claim an “Amish exemption” for their educational practices or lack thereof have not been well received by the courts.”  It is not clear to me how these differences of treatment of different religions are justified or reconciled.

One rather disturbing feature of religiously motivated home schooling addressed in the article is the potential lack of gender equity.  For example, quoting guidance from Stacy McDonald (who a quick web search suggests is associated with FamilyReformation.org):

A girl’s education “should be focused on assisting her future husband as his valuable helpmate, not on becoming her ‘own person’.” Girls are counseled to “[r]emember that a strong desire to be a doctor or a seeming by-God-given talent in mathematics is not an indication of God’s will for you to have a career in medicine or engineering. Sometimes God gives us talents and strengths for the specific purpose of helping our future husbands in their calling.”

Sigh.  Of course, at the end of the day I suppose it is necessary to consider whether any of this matters– that is, it’s nonsense, but can anything be done about it?  Should anything be done about it?  Getting between parents and their children can be a pretty nasty subject.  To answer these questions, I think you have to consider the extent to which you think that withholding education– or providing absurdly inaccurate education– is harmful or abusive to a child.

For my part, I think education is as critical to quality of life as medical care.  If a child grows up without learning what the rest of the modern world is learning, then that child has been denied the chance to be great, to possibly make the next ground-breaking advance in astronomy, biology, physics, etc.

Reference: Acker, Gray, Jalali, and Pascal, Mathematics and Home Schooling. Notices of the AMS, 59(4) (April 2012): 513-521. [PDF]