A recent visit to my sonâ€™s family in North Carolina produced some robust discussions with our grandchildren on mathematics education in our public schools. This prompted me to review some earlier research on this topic, from which I present excerpts here.
When I first read that Georgia state legislators had voted to decrease the number of credits students needed to graduate from high school (to lower the dropout rate), I laughed out loud. But I realized that this was one of those things (as my Pop used to say) that â€œwasnâ€™t funny enough to laugh at, but weâ€™re too big to cry.â€
Then, mirth gave way to anger. Really, I wondered, are the people who govern and educate us playing with a full deck? (Do their elevators go all the way to the top?) It seemed unbelievable that those posing as serious leaders could have so little understanding that they think making a diploma easier to get does anything positive for either those students or society in general. Later, I read that other states are moving similarly to raise graduation rates by lowering requirements. (Hello! Is anyone in there?)
My siblings say Iâ€™m sounding more and more like my grandfather. â€œWhen I was your age,â€ he used to say (as he thumped his cane), â€œI got up at 4 AM, peeled 20 lbs. of potatoes, walked 5 miles to school, barefoot, and was scolded by the teacher for being late.â€ I have always been skeptical of all those tales of hardship, although the potato part was probably true. Grandpopâ€™s people were potato farmers; they ate potatoes three times a day.
For all I know, maybe all of it was true. Things were different in the 1880s and â€˜90s â€“ especially in school. I know this not because of movies Iâ€™ve seen, or because of Grandpopâ€™s stories, but because I actually have his old textbook, Milneâ€™s High School Algebra, published by The Eclectic Press, Cincinnati, in 1892. (Grandpop graduated in 1901.)
I began to work some of the problems in that book when I was in junior high school, and Grandpop was still around to talk about them. Iâ€™m amazed by the sophisticated material a high school graduateÂ had to master then. Here is an example (from page 164 of Milne):
There are two fractions which have the same denominator. If 1 be subtracted from the numerator of the smaller, its value will be 1/3 of the larger fraction; but if 1 be subtracted from the numerator of the larger, its value will be twice that of the smaller. The difference between the fractions is 1/3. What are the fractions?1
When I show that problem â€“ actually, a fairly trivial one from Milneâ€™s section on Simultaneous Equations â€“ to high school (or even college) students, most of them get a glassy-eyed look and shrug. Other sections in Milne include: Quadratic Equations; Progressions; Imaginary Quantities; and a lengthy chapter on the Binomial Theorem, a topic I studied in college math.
Contrast this with Rain Forest Algebra â€“ the moniker that author, college professor and parent Marianne M. Jennings hung on a textbook she found her daughter using. Here are excerpts from an article she wrote about it for the Christian Science Monitor on April 2, 1996. (Please pardon this lengthy verbatim passage, but Mrs. Jenningsâ€™ account is so expressive that I didnâ€™t want to attempt a summary.)
â€œI am a college professor who has algebra homework every night. My teenage daughter is studying algebra using a book that includes Maya Angelou’s poetry, pictures of President Clinton, and lectures on what environmental sinners we are.
â€œIt has photos of students with names such as Tatuk and Esteban, who offer my daughter thoughts on life. It includes icons for fine arts, industry and science. The book is full of color pictures and graphics. About the only things you can’t find are explanations about how algebra is done and actual algebra problems.
â€œWelcome to rain-forest math. My daughter is studying algebra under a newly adopted, district-wide curriculum that includes an integrative textbook and cooperative/group learning. Students measure their wing spans for a class period. They toss coins for another class period just to be certain we aren’t lying to them about probability. For all I know, they’re joining hands and singing â€˜Kum By Yah.â€™
â€œWhat’s certain is they are not learning algebra. Though my daughter has an â€˜Aâ€™ in beginning Algebra, she has yet to grasp the idea that what you do to one side of the equation, you must do to the other.
â€œWhen I spoke to her teacher about the book and how class time was being used, she responded: â€˜We don’t plug and chug anymore. We’re teaching them to think.â€™ It’s odd, however, that the students are never required to show their work on homework papers or tests. â€˜How do we know what they’re thinking if all we’re checking is answers,â€™ I asked. The teacher assured me that five years from now these kids would be great in math.
â€œI did some research and found an integrative, group-learning math experiment in California. Now in its fifth year, the program’s first graduates are in college. Not surprisingly, they can’t even pass remedial math at that level.
â€œOther parents and I joined forces and went one-by-one to the school to discuss our concerns. First, we sent in an engineer. She questioned the use of application problems before the students have been taught the basics. Our engineer mother was told that she did not understand the education process or what was needed in the business world.
â€œWe sent in a lawyer. He returned having been told that universities had guided and approved the curriculum and textbook. Next it was my turn. I was given the worst blow of all: â€˜You may have to face the fact, Mrs. Jennings, that your child may not get algebra.â€™ I had tried to explain that my daughter is studying Captain Nemo and South American languages, but can’t find rise over run explained anywhere.
â€œI made an offer to the assistant principal and the head of the math department: Give the students a standard algebra test covering the areas mentioned in the book so far; if they do well, I’ll go away. â€˜We don’t do that,â€™ they sniffed. They directed me to the central administration. I tried a friend on the school board. She offered the â€˜she may never get algebraâ€™ defense of the curriculum, but set up a meeting with district officials. I met with assistant superintendents in charge of instruction, curriculum, and math.
â€œI took in pages from the book. Find the problems, I challenged them. I even took along another mother. â€˜Find an explanation of order of operationsâ€™, she said. We asked about showing work. I mentioned the California program. Two of the three told me, â€˜You may just have to face the fact that your daughter won’t get algebra.â€™
My child and thousands of others are being sacrificed on the altar of theory. I am told of studies that confirm this instructional approach works, but no copies of the studies have been forthcoming.â€2
With cutting-edge training like this, is it any wonder that American students score near the bottom among students from the top twenty countries in the world, yet feel best about their level of learning? Talk about believing your own press clippings. It’s an advertising triumph.
I am embarrassed for a store clerk who gets confused when I give him 20 dollars and 2 cents, after his register has calculated my change from $20. I wanted to eliminate the pennies from the change for a bill of $18.47, but he still gave me $1.53 in change. I shook my head and pushed the coins back. His face clouded. Then, comprehension dawned. He confidently gave me 51 cents. Again I shook my head. Finally â€“ desperate now â€“ he gave me $1, two quarters, and five pennies. I gave up. Those change-calculating machines have saved modern merchants from complete ruin.
Of course, our degraded education levels affect us far beyond wooly-headed clerks who canâ€™t figure change. One of the more ruinous effects of Rain Forest Algebra and its ilk is that, increasingly, students graduating with mathematics and engineering degrees from American universities are from foreign countries, where the benefits of RFA have not yet been bestowed. Know-nothing math â€œeducatorsâ€ (who probably flunked math) are re-making us into a third-world country of young Dummkopfs hanging out at the mall in $300 sneakers, smoking weed, and texting on cell-phones produced in foreign countries.
As Mrs. Jennings noted, many indigenous American students can’t qualify for higher levels of mathematical study because they lack the required foundations. But finally the states (God bless â€˜em!) are addressingÂ this serious situation by taking decisive action. One by one they are paring back the requirements for a high school diploma so more students can get a piece of paper that says they are educated. Itâ€™s a political miracle â€“ almost a rapture! (Really, I donâ€™t know how we can be expected to go about our normal workâ€¦)
As Yakob Smirnoff used to say, â€œWhat a country!â€
 The fractions are 4/15 and 9/15. (No, I didnâ€™t cheat by looking at the answers.) See if you can work the problem. Solution in a later column.
 See Dr. Jenningsâ€™ article in its entirety at http://www.csmonitor.com/1996/0402/02182.html