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Statistics Can Be Sweet

By Bill Pride
Printed in Practical Homeschooling #83, 2008.

Everything you need to learn about homeschooling your kids in statistics.

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Bill Pride

When I was in grade school and junior high, my math books didn’t include anything about probability and statistics. When I moved up to high school, the college-prep sequence didn’t include a statistics course, even as an option.

Today, parents who have been focused solely on the Algebra 1-Geometry-Algebra 2-Precalculus-Calculus sequence may be surprised to learn that AP Statistics has become more popular than the more rigorous version of AP Calculus. If the trend continues, enrollment in AP Statistics may soon surpass that of both AP Calculus courses combined.

In 1997, when the AP Statistics exam was first offered, 7,500 students took the exam. Four years later in 2001, 43,000 exams were graded. Six years later, in 2007, this number almost doubled again, as 82,307 students took the AP Statistics test. Compare that to 166,986 who took Calculus AB and 51,693 who took the tougher Calculus BC that year. In fact, more kids took the AP Statistics exam last year than took Chemistry, Computer Science, Economics (even when you add Macro and Micro together), Environmental Science, European History, World History, or any of the Art, Foreign Language, and Music exams. Statistics is currently the eighth most popular AP exam.

In the meantime, some elementary statistics and probability has been added to each level of the K-12 math curriculum, ensuring students are at least slightly comfortable with the idea of statistics before high school. (There has been no such introduction of calculus and trigonometry concepts into early and middle grades.)

How did statistics become such a large part of the math curriculum?

AP Statistics grew out of a movement during the 1970s called “Quantitative Literacy.” Quantitative Literacy’s purpose was to improve the numeric and quantitative abilities of high-school and college graduates. In the 1980s the American Statistical Association (ASA) developed a workshop for teachers to educate them in how to get data analysis and quantitative reasoning into the K-12 curriculum. Probability and data analysis became part of the 1989 NCTM Math Standards. The Advanced Placement Statistics program in high schools was a direct result of this.

Why have statistics courses blossomed? Christine Franklin and Robert Gould give a succinct and somewhat self-revealing answer in a session they gave at the National Summit on the Mathematical Education of Teachers. They said, “Statistics in K-12 is a great background for college work in statistics, both for disciplines which require some statistical training and for providing departments that teach statistics more opportunities.”

According to The College Board’s booklet Statistics: Course Description:

In colleges and universities, the number of students who take a statistics course is almost as large as the number of students who take a calculus course. . . . An introductory statistics course, similar to the AP Statistics course, is typically required for majors such as social sciences, health sciences, and business. Every semester about 236,000 college and university students enroll in an introductory statistics course offered by a mathematics or statistics department. In addition, a large number of students enroll in an introductory statistics course offered by other departments. Science, engineering, and mathematics majors usually take an upper-level calculus-based course in statistics, for which the AP Statistics course is effective preparation.

Statistics is required in college for such varied courses of study as economics, biology, psychology, optometry, business, nursing, social work, sociology, engineering, anthropology, and, of course, mathematics. I am sure there are more, but these were drawn from the first 40 of the 700+ entries that came up when I searched for “statistics course” on umsl.edu.

AP Statistics or Just Plain Statistics?

The value of doing well on one or more AP exams is well known. According to The College Board’s press release regarding its 2007 “AP Report to the Nation”:

    Of the estimated 2.8 million students who graduated from U.S. public schools in 2007, almost 426,000 (15.2 percent) earned an AP Exam grade of at least a 3 on one or more AP Exams during their high school tenure, the report documents. This is up from 14.7 percent in 2006 and 11.7 percent in 2002.

Why the huge upsurge in kids taking AP exams . . . and doing well on them? Because college admissions officials are convinced that AP scores really, really matter. As the press release goes on to state:

    Earning a 3 or higher on an AP Exam is one of “the very best predictors of college performance,” with AP students earning higher college grades and graduating from college at higher rates than otherwise similar peers in control groups, according to recent reports from researchers at the University of California at Berkeley, the National Center for Educational Accountability, and the University of Texas at Austin.

So you can offer a regular statistics course, or even an Honors Statistics course, but it won’t have the cachet of AP Statistics.

Which Colleges Give Credit for AP Statistics?

Though colleges are hot for AP exams, for some reason the AP Statistics exam still is the poor cousin in the math department. While Calculus BC will at least get you out of freshman calculus almost anywhere, top engineering and some Ivies tend not to give credit or advanced standing for those who have done well on the AP Statistics exam. Examples: MIT, Caltech, and Yale.

Some other top schools allow students to take more advanced courses if they have an AP. Harvard will accept a “4” or “5” for a half credit (out of four needed) to receive “Advanced Standing.”

Statistics doesn’t always even count for math credit. Some top schools only give economics or business department credit (for their required stats courses in those majors), for an AP Statistics score of “4” or “5.” Examples: For a “5” score, Princeton allows 3 credits for Economics 202. For a “4” or “5” score, Rensselaer will grant 3 credits for MGMT 2100, Statistical Methods.

Most state schools allow one semester of credit for a “3” score or better. Examples: University of Missouri-St. Louis, Texas A& M.

Calculus or Statistics?

Which course is best for your student?

Once your student has completed Algebra 2, this becomes a serious question.

The best way to answer it is by asking:

(1) Is my student a hands-on, concrete person or an abstract thinker?

(2) Does my student intend to pursue a career in math, physics, chemistry, or engineering?

Abstract thinkers and future mathematicians, physicists, chemists, and engineers are best served by a calculus course in high school. Those aiming for “soft” sciences, humanisties, or health career fields will find high-school statistics more useful.

Fun Things You Can Do with Statistics

Analyzing statistical relationships can be a fascinating passtime.

For example, in my summer Applied Statistics course I got to play with actual data on SAT scores by state vs. the amount of money spent per child for education.

Some people have observed that the more money is spent on each child’s education, the lower the SAT scores, and the data shows this is true. There is a significant negative correlation between the amount spent and scores. But a correlation does not necessarily mean there is a cause and effect.

To see this consider that in St. Louis city the number of murders tends to rise with the amount of ice cream consumed, yet I doubt there is a cause and effect relationship between ice cream and murder.

In the case of SAT scores, the strongest relationship was between the percentage of students taking the SAT and the SAT scores. The higher the percentage of students taking the SAT in a given state, the lower the average SAT score. This makes sense, since if a greater percentage of students take the SAT, a greater number of less-gifted students take the test.

The question then becomes: Does spending more cause more students to take the SAT? Maybe higher expenditures means more guidance counsellors. More counsellors means more students are advised to take the SAT.

Another possibility is that the cause and effect is the other way around. Lower SAT scores lead some states to spend more on education.

Statistics raises questions. You propose the answers.

Where Homeschoolers Can Find Statistics Courses

Creating Your Own Statistics Course

Jan Olson’s article in this issue on page 52 explains how to create a course and pass the AP audit. For a web page with links to syllabi others have created that were certified for AP, go Here.

For a regular statistics course (not AP), your options are much more flexible. They can run the gamut from a Dummies book, to software, to video-based courses, to a selection of books about statistics that you find by searching for “statistics” on Amazon. If extra report writing or research is involved, it could qualify for an Honors course. If your student completes it more quickly than normal, it could be an Accelerated course.

  • Teaching Company. Meaning from Data: Statistics Made Clear (4 DVDs). www.teaching12.com.
  • Annenberg Media. Against All Odds: Inside Statistics (26 programs on 7 discs.) Click Here!

Where Are the Christian Courses?

While writing this article, I checked out the books offered by major Christian publishers.

Guess what? Neither A Beka, Alpha Omega, nor BJU Press had a statistics textbook.

It’s possible there may be some statistics coverage in their Business Math courses. However, for college-prep purposes, an actual statistics course would be great to have.

Bill Pride has a B.S. in mathematics from MIT and a M.A. in mathematics from University of Missouri-St. Louis. He is currently studying toward his Ph.D. in mathematics.

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