Tag: FOIL

Categories
Algebra

Don’t F*$& ing Curse in Math Class

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.

Like Foil.

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

 

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Categories
Algebra Middle School

3 Phrases from Math Class we Need to Expunge.

A brief twitter exchange last night between myself and the great NY math educator Mike Pershan caused me to get off my rear to assemble a post which I had kicking around my head for some time now, a list of terms and shortcuts we use in math class which, while well-intentioned and used everyday by many math teachers, aren’t necessaily helpful in causing kids to understand their underlying math concepts.

Twitter

In a recent in-service with middle-school math teachers, I used a video by Phil Daro (one of the authors of the Common Core math standards) to have colleagues reflect upon the practice of “answer getting”, short-term strategies employed by teachers to get students through their immediate math assessment, but with little long-term value in math understanding.  Click on the “Against Answer-Getting” tab for the video.

So, here is my first list of nominees for elimination, and some strategies for helping students develop underlying algebraic ideas.  It probably won’t be my only list, and I welcome your candidates and thoughts.

SAME-CHANGE-CHANGE (aka KEEP-CHANGE-CHANGE):

This is a device I often see in pre-algebra classrooms, often times as a poster for easy reference, other times as a mantra for the students to help complete worksheet problems.  From the site Algebra-Class.com:

TIP: For subtracting integers only, remember the phrase

“Keep – change – change“
So, we have a short and snappy device which helps us with just one specific type of integer problem.  It’s not wrong, just too specific, and do students understand why it works?
What to do instead:
Let students develop their own summaries of integer problems, and create their own posters which describe their findings.  Use integer zero-pair chips or online applets, like from the National Library of Virtual Manipulatives (search for “chips”).  Number line applets can also help students visualize addition and sibtraction problems.  Have students write stories about given integer and subtraction problems, and have students peer-assess work for proper use of math terms.  Eventually, have students debate the possible equivalence of integer pairs:
  • 5 – (-2) and 5 + 2
  • a + (-b) and a – b
  • a – b and b – a

FOIL

The ad-laden math site Coolmath gives its own snazzy description of foil:

We’ve got a cool little trick called “FOIL” for multiplying binomials….it’s really just an easy way to do the distributive property twice, which would be really messy and confusing to do.

YEY!  You mean I can multiply stuff without that nasty and scary distributive property, without actually talking about the distributive property!  Yey shortcuts!  I’m in! {insert sad face}

Folks, ditch FOIL, and use the opportunity to talk about the double-distributive property.  Re-write the binomials as an equivalent expression and multiply.  Set the stage for factoring and note how much more understanding factoring by parts takes on.  And, now we can tackle those “messy” trinomials too.

CANCEL (LIKE) TERMS

Try this exercise tomorrow: take a class tht has been through Algebra 1, and as an opener tomorrow ask them to explain what the phrase “Cancel Like Terms” means when dealing with a rational expression.  Or, if that is a bit too scary, simply ask your students what it means to recude a fraction.  This is a nice activity to do as a Google form, and have students assess the explanations.  Many students will give an example as a definition, which is not what we are looking for here.  How many students discuss factors, GCF’s, numerators or denominators?

Reducing a rational expression means to divide both the numerator and the denominator by the greatest common factor of both numerator and denominator.  (Incidentally, also try having your students provide steps for finding a GCF.  This one also reveals what your students understand.)  The great part about this procedure for reducing is that it works equally well for each of the following expressions:

To many of our students, cancel is digested as “cross-out stuff”.  We have better vocabulary for it, so let’s encourage its use.