The Mathematical Adventures of Alexandria Jones

“Using mathematics to tell stories and using stories to explain mathematics are two sides of the same coin. They join what should never have separated: the scientist’s and the artist’s ways of uncovering truths about the world.”
—William Frucht

It began with some 4th-8th grade friends who met in my dining room to work math puzzles and play games. At first, a few of the kids wondered how anyone could have fun with math. But we did enjoy ourselves, and Math Club grew until we couldn’t fit anyone else around the table.

When one girl had to move away, I thought, “Why not send Math Club with her?” Thus was born Math Club by Mail newsletter (later renamed Mathematical Adventures), a 4-year snail-mail newsletter that brought puzzles, strategy games, art projects, historical tidbits, and more to readers as far away as Hawaii.

Never very many readers, I admit—certainly never enough to make a profit—but it was a blast while it lasted.

So I thought you might like to read Alex’s story from the beginning, as my original math club kids did. The stories will appear sporadically, scattered between my more typical math-activity and teaching tip posts.

I hope you will have as much fun reading these adventures as I had writing them.

Introducing Alexandria Jones

My newsletter stories followed the adventures of homeschooler Alexandria Jones, her archaeologist father, and the rest of their family as they discovered a triangular treasure from Ancient Egypt, puzzled over patterns in Pythagorean pebbles, or explored the applications of math in daily life.

We learned about hieroglyphic math, fractals and chaos theory, logarithms, geometric algebra, and how to multiply any numbers using only the times-two table.

As I attempt to resurrect Alexandria Jones and her family here, the stories will appear sporadically, along with snippets from history and a side dish of math puzzles.

The first story, down below, actually appeared later in the original newsletters, but it makes a nice introduction.

Alexandria’s Dog is Now a Teacher

From the beginning, Alex’s dog supported her adventures with eager energy. In the original stories, Rammy was named after a famous Indian mathematician, but a reader of Indian descent was kind enough to write to me about a difference in our cultures.

In the US, or at least in the parts with which I am familiar, it is common to name one’s pet after a famous person. In India, however, to name a dog after a human is a very deep insult.

Therefore, I have re-named Alexandria Jones‘s dog after a Westerner. I would like to keep the tradition of naming the characters in my Alex stories after people in math history, so I am hoping this one will not offend anyone.

Peter Ramus: Homeschooler, Teacher, Magnet for Trouble

Peter Ramus is also known as Petrus Ramus or as Pierre de la Ramée. Born in France in 1515, he was educated at home until the age of twelve, when he entered the Collège de Navarre in Paris. He worked his way through college, graduated with a master’s degree at the age of 21, and began teaching philosophy—until his attacks on the dominant Aristotelian curriculum of his day got him banned.

Ramus switched to the study of mathematics, was reinstated, and rose to become the head of the the Collège de Presles. Always involved in controversy, however, he converted to Calvinism and spent several years in exile due to religious wars.

In addition to being a popular lecturer and author, Ramus was determined to reform educational philosophy. He had no patience for mnemonic tricks or rote learning. Instead, he thought it was the teacher’s job to break each of the liberal arts down into its most basic principles and organize these into a systematic and practical method of study. Above all else, education should be useful.

Due to his growing conviction about the fundamental importance of mathematics, he proposed a chair of mathematics at the University of Paris. Putting his money where is mouth was, Ramus endowed the chair in his will.

In 1572, he was killed in a massacre of French Huguenots.

A New Style of Teaching

“By emphasising the central importance of mathematics and by insisting on the application of scientific theory to practical problem solving, Ramus helped to formulate the quest for operational knowledge of nature that marks the Scientific Revolution.”
—M. S. Mahoney

Peter Ramus promoted many educational reforms, including:

• the simplification of knowledge, using his “laws of method”
• attention to pedagogy, the science of effective teaching
• increased attention to teaching physics and other sciences
• an emphasis on experimentation and practical application
• a de-emphasis of theoretical speculation (including abstract geometry proofs)

Ramus had great respect for Aristotle and other ancient philosophers, but fought repeatedly with the Aristotelians of his day. For at least a century after he died, Ramists and Aristotelians continued to argue about what logic really was and how we should teach students.

Enough Background! Here’s a Story: The Mysterious Temporal Freeze

Alexandria Jones stepped into the huge tent that protected her father’s excavation site from the desert winds. She laughed to herself. It was like walking into a circus.

She knelt down to whisper in the ear of her faithful dog Ramus.

“In this ring, grad students carefully brush away another layer of sand. In the next ring, the artist sketches every piece as it is found.” She waved her arm. “And over there, our flashiest attraction—drum roll, please—the photographers shoot each shard of pottery from every possible angle. But where is the Master of Ceremonies?”

Alex and Rammy found Professor Jones near the back of the tent, talking to another student. While she waited for her dad, she looked through an assortment of numbered artifacts that were ready to be packed and sent to the museum.

Fibonacci Jones had discovered the tomb of a scribe, an ancient Egyptian secretary and bookkeeper. It didn’t look like much—merely a hole in the ground, way different from a pharaoh’s hoard—but Alex knew her father. To him, a roll of papyrus was a treasure more precious than jewels.

She picked up the scribe’s palette, a carved wooden block about the size of a box of watercolors. This palette had three bowl-shaped pits for ink. Two of these held dried-out remains of the scribe’s black ink, and in the last pit she could see a faint stain of red. Four thin reeds lay in a groove, ready for the scribe to dip in the ink and write.

(Styluses, she thought they were called. Or styli? Have to ask Dad.)

Alex looked up to see her father walking toward her. Strangely, he seemed to be moving in slow motion. He froze in mid-step and stood statue-still. When she opened her mouth to speak to him, no sound came out.

At her feet, Rammy whimpered, then fell silent. Alex tried to turn her head, but she couldn’t move.

What could be happening to them?

What Really Happened

The Alexandria Jones stories were originally written for my math newsletter. Since it was a one-person operation, when I got the flu, all production ground to a halt.

I recovered just before the next issue was due out, in time to send a one-page apology to my subscribers, promising them that they would still get their full number of issues. I wrote the vignette above for the apology letter.

My newsletter also included puzzles and games unrelated to the Alexandria Jones stories. Here is a word problem from the May/June 1998 issue:

Can You Solve This Story Problem Challenge?

A certain famous cartoon cat snarfs down an 11″×13″ pan of lasagna in 3 seconds flat. Assuming the fat feline has a bottomless pit for a stomach and continues to eat at the same rate, how long will it take him to devour a pasta the size of the state of Illinois?

You may estimate the pan of lasagna to be one square foot. An 11″×13″ pan is actually one square inch shy of that, but it won’t change the solution enough to matter—simply round your final answer to two significant figures.

(As any science teacher will tell you, you should never copy down all the numbers your calculator spews out.)

If you get stumped, my recent post on conversion factors might be helpful.

And in case you were wondering, InfoPlease Almanac lists the total area of Illinois as 57,915 square miles.

A Not-Quite Answer

I won’t give the solution away, but to put the answer in perspective:

• Columbus landed in the New World 5 centuries ago.
• Jesus of Nazareth lived 20 centuries ago.
• And about 46 centuries ago, the ancient Egyptians were building pyramids.

To eat one pan of lasagna in 3 seconds sounds like a speed-eater to me, but it still would take an unimaginably long time to eat a pasta the size of just one mid-sized state.

Isn’t the world an amazing place?