For the first time in many years, I find myself teaching a unit on polynomials to 9th graders. Time to back up one of my pet peeves, and put my money where my mouth is. Some of my recent tweets may provide some clues to one of my least-favorite math acronyms….
My students seem amused by my swear cup…
I shared my thoughts on binomial multiplication, and gave a little plug to Nix The Tricks in the recent ATMOPAV (Association of Math Teachers of Philadelphia and Vicinity) newsletter. The article is reproduced below, and I hope you enjoy it. I serve as second vice-president of this organization, and invite you to visit our website and enjoy our spring newsletter.
A CROWD-SOURCED MATH PUBLICATION:NIX THE TRICKS
There are many words which have “curse” status in my classroom. Some of these words are universally agreed to be “bad” – words which will result in a fast trip out of my class, and probably a phone call home. But other words are on a second tier of curses – words which make me cringe, and which require a donation to the math swear jar.
Yes, that FOIL. Our old “First – Outside – Inside – Last” friend. It’s banned from my classroom.
It’s not that FOIL is bad…heck, it’s quite a universal term in the math world. The problem is that FOIL, while well-intentioned, is a trick. It’s a trick for a specific situation: multiplying two binomials. What happens when we multiply a monomial by a binomial, or even a binomial and a trinomial? I suggest FOSSIL here, to account for the Stuff inSide.
The problem with FOIL is that it removes the most important math property involved in the multiplication from the conversation: the distributive property. And we replace this key property with a cute acronym which is only useful to one specific scenario.
Last year on my blog (mathcoachblog.com) I proposed a list of terms often overheard in math class which require some re-evaluation. Terms which confound the deeper mathematics happening, and which distract from genuine understanding. Besides FOIL, I also proposed the “Same-Change-Change” method for subtracting integers, and “cancelling like terms”. Many teachers I follow on Twitter shared similar thoughts about not only terms, but also short-cuts often presented in math class. Tina Cardone, a teacher from Massachusetts, started a Google Doc where teachers could contribute not only tricks, but proposed replacements for classroom shortcuts. The response from the Twitter-world was robust, with not only tricks and terms proposed, but also conversations regarding best practices for concept attainment.
The response was so overwhelming that Tina compiled the online discussions into a free, downloadable resource for teachers: Nix The Tricks. The document can be found at www.nixthetricks.com, and a printed version is now available on Amazon.
Nix The Tricks currently contains over 25 “tricks” used in math classes, categorized by concept. Along with a description of the trick, suggested fixes to help students develop deeper understanding of the underlying mathematics are presented.
The “Butterfly Method” for adding fractions is an example of the math tricks found in the document. Do a quick Google search for “butterfly method adding fractions” and you’ll find many well-intentioned teachers offering this method as a means to master fraction addition. But is student understanding of fraction operations enhanced by this method? What are the consequences later in algebra when the same student, who mastered butterflies, now must add rational, algebraic expressions? How should this topic be approached in elementary school in order to develop ongoing understanding? Download the document and find commentary on this, and many other math tricks.
I am proud to have been part of this project, and continue to seek out new “tricks” to add to the mix. The document is a tribute to the power of Twitter, where many conversations developed while debating the validity and helpfulness of tricks. The group continues to seek new ideas to make Nix The Tricks grow. To participate, follow me (@bobloch) or Tina Cardone (@crstn85) on Twitter, or contribute your ideas on the website: www.nixthetricks.com