“Nothing,” say some of my students.

“You can always find the value of x,” say some others.

“It’s useful in real life,” says one.

“No it isn’t!” says another.

By this point we’ve moved far afield from the original question. So I ask “how about this?” We look at this stela:

Posted by Rama, CC BY-SA 3.0 fr, https:/tinyurl.com/2p8wsc7d

“It may not look like algebra, but it certainly is beautiful,” I claim, “and it really is algebra—if you can read Middle Egyptian.”

OK, let’s shift gears. “Tell me in a sentence what algebra is.”

Almost everyone writes something like “It’s the part of math where you solve equations” or the equivalent. I point to what we’ve been doing recently in Algebra II: no equation-solving in sight! So we brainstorm other ideas:

• Letters stand for numbers.
• Formulas.
• Graphing.
• <silence>

At this point I ask the students to read a book review! The book is Algebra the Beautiful: An Ode to Math’s Least-Loved Subject, by G. Arnell Williams; the review is written by Judith Grabiner, published in the Journal of Humanistic Mathematics, Volume 13 Number 1 (January 2023). When they read the review, they find out what the two Big Ideas of algebra are, and why algebra is beautiful. Go read the review, and maybe you’ll learn something even without reading the book being reviewed.

Those two big ideas? According to Williams, they are:

• “Let x equal”
• “For any a and b…”

I still prefer geometry, but I have to admit that Williams, as explained by Grabiner, makes a compelling point.

Categories: Math, Teaching & Learning