Categories
Uncategorized

What Betty Crocker Can Teach Us About the Common Core

Despite my attempts to maintain a somewhat healthy diet, I still succomb often to sweets. If there are cookies or cupcakes in the teacher planning room, I’m there…and often regretting the indulgence later.

I especially enjoy chocolate cake.  My fingers tremble in anticipation just as I type those wonderful words – chocolate cake.

It’s a great day for baking, so I did an online search for a real kick-butt chocoloate cake recipe.  There were many, many great candidates, but I stumbled upon a recipe touting itself as Heavenly Chocolate Cake

Heavenly, you say?…tell me more…

Need to make sure I have all of the ingredients around, or else it is off to the grocery store:

  • Eggs
  • Milk
  • Sugar
  • Flour

Check, check, check, check….we are good so far.

  • Bicarbonate of Soda – uhhhh…what?
  • Instant espresso – is this really necessary?
  • Powdered gelatine

{{Sigh}}….let’s look ahead. Maybe I can skip some of this stuff?  Perhaps the instructions will give me an out here:

Let chocolate mixture cool to room temperature. Whip the double cream to soft peaks and fold into the chocolate mixture.

What are soft peaks? And is folding just a fancy way of stirring, or is that whisking?

Be careful not to over cook and curdle the mixture. Pour egg-milk mixture through a strainer into the melted chocolate. Melt the gelatine and water

Do I own a strainer? And how do I know when I have reached the event horizon for curdling?

OK, I surrender. I’m probably a little over my head here.  Fortunately, there is an option for the cooking-challenged like me:

Box

StepsThanks to Mrs. Crocker and her boxed wonderfulness, I can make a tasty cake in just 30 minutes!  Eggs, oil and water.   And just 3 simple steps: heat – stir – bake. These are some steps I can get behind!

And just that quickly, I am enjoying cake!  It’s the way I have always made cake, and the cake has always been quite tasty. My mom made cakes using this recipe; don’t go telling me that your cake is any better!

But in my heart, I know it’s no match for the Heavenly Chocolate Cake, which I salivate for.  I once had a cake like that which a neighbor made: such a memorable cake – I want more of that cake! So many sophisitcated flavors.  I can admire its beuaty, subtlety, its intricacies and I am aspire to be just half of the kitchen pro my neighbor is.


It occurs to me that Betty Crocker’s cake products share a lot with the ongoing debate over the necessity of Common Core math methods: the cakes you bake are simple and satisying, but in no way are they a suitable replacement for the genuine cooking experience in both the path taken, and the finished product.

NOTE: I understand that the Common Core does not suggest a method for mathematical operations.  Many of the methods confused as Common Core methods have been around for quite a long time, and are commonplace in math programs. Ideally, it would be wonderful to discuss these methods separate from the Common Core debate.  My intent here is provide a justification for seemingly more convoluted methods, through the lens of the Standards for Mathematical Practice.

A worksheet full of correct answers doesn’t mean you are good at math, in the same way that successfully baking a Betty Crocker cake isn’t cooking.  There’s a real disconnect over what it means to do math.  And the disconnect is not just between what educators expect from students and what parents hope to see from schools.  There are also wide differences from teacher to teacher, and school to school.  Yesterday, I ran across a post concerning an “insane how-to-add guide” which represents the worst of both worlds: a frustrated parent wondering why so many steps are needed to add, and a weak addition “guide” which is overly helpful.  Math, like cooking, cannot be diluted down to simple steps without a loss in complexity and reflection. In my recent post on Common Core subtraction, I suggested that reflection and adaptation are far more important to me as a math teacher than filled worksheets.

Betty Crocker = Core Standards. Gourmet cooking = Standards for Mathematical Practice.  I’m still here enjoying my cake, and I’ll likely make Betty Crocker cakes again.  Maybe next time I’ll toss in some extra chocolate chips, but the cake won’t be much different from the mandated recipe.  A true chef can experiment with flavor profiles, adjust and develop new ideas for cakes.  They can “Make Sense of Cakes and Persevere is Baking Them” (even if a few attempts don’t taste so heavenly) and “Construct their own Recipes and Critique the Recipes of Others”.  The end result – the cake – is still the star of the show.

Basic skills matter.  Being “right” matters.  But true chefs, and mature math students, can demonstrate understanding through explanation, exploration, and tackling rich problems.

The recipe with the least number of steps ultimately leads to a less-satisfying product. I recognize that my cake is good, but not great.  I’d really like to experience the Heavenly cake, but understand that it will require time and effort.  Worksheets allow for lists of correct answers, but this is not the most-satisfying mathematics. Effective math teachers cause thinking. We can add fractions, but what next? How do we use this skill? How can we extend it to other ideas? Can we explain how to add fractions to other?  There may be some brain sweat, and many eggs to crack, before we reach our goal.  When we start building new flavor profiles from fractions, exponents, graphs and equations….that’s when we are doing math.

And now, off for some jogging to burn off the cake….

 

 

 

 

 

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

 

Categories
Algebra

Hitting the Home Stretch: Exponents, GCF’s and LCM’s

This is a busy stretch in my school year.  My 2 Prob/Stat classes are nearing the end of new material with PA Keystone Exams in Algebra 1 looming. For my College Prep class, about half have not yet taken the Keystone while the rest took it last year as 8th graders. In Academic, all students will take the Keystone in May.  Combine this with my AP Stats class taking their final exam this week, with the AP Exam next week, and my track and field meet responsibilities building as the season reaches its peak; it’s a hectic time of year.

In both of my Prob/Stat classes, we are beginning unit on polynomials.  The Prob/Stat class is a course we offer between Algebra 1 and 2. While the course contains much Prob/Stat material, we also clean up some concepts from algebra.  Unlike other algebraic units like systems of equations where there are many rich examples and opportunities to differentiate, the start of a polynomials unit often feels static. Here are two activities I have used this week for Laws of Exponents and GCFs/LCM’s.

LAWS OF EXPONENTS – TRUE/FALSE GROUPS

This activity worked equally well in my college-prep group (for whom this was review material), and my academic group (where this was mostly new).  The file below contains 16 cards with numeric statements.  Break your class into teams of 2, 3 or 4.  The job of the group is to identify the true statements and the false statements.  For this activity I banned all calculators.

View this document on Scribd

The letters on the cards are not anything the kids need to worry about, but allow me to easily check progress. The cards with vowels are all the false statements.

I was surprised at how much trouble my college-prep group had with building the correct false pile.  To reach some consensus on the false pile, I asked every group to hold up one card they knew to be absolutely, positively false.  Many groups mistakenly agreed that any number raised to the zero power was worth zero, which led to a class argument on who was right.

Tomorrow, we will look more closely at the falses.  In the file above, note that the cards are arranged in groups of 4. In the first group, we will review the addition rules for exponents; then the subtraction rule in the next group of 4; then the multiplication rule for the next group.  In the end, this felt much more satisfying, with increased engagement and peer discussion than simply listing rules on the board.

GCFs and LCMs SPEED DATING

The speed dating concept is one many math teachers have stolen from the great Kate Nowack, and it worked perfectly in my Academic class to work through greatest common factors and least common multiples.  After doing just one example on the board, desks were arranged  into a pairs facing each other, down one long row.

Speed Dating

All students were given a card with a monomial.  They then worked with their partner facing them, and found the GCF of the two monomials.  The first time around, my co-teacher and I provided help to just about all groups.  After teams found their GCF’s, all students on the right-hand side stood and moved down one seat and worked with their new partner.  There were so many plusses to this activity:

  • all students were repsonsible for their own monomial
  • all students were engaged: no hiding behind a worksheet
  • students worked together, and with different partners each time

Some of the cards I handed out are shown here.  I tried to have a variety of cards which clearly shared factors, with different powers of x and y.

cards

I was very impressed with how my class performed on this activity, and we moved onto a second round where LCM’s were found. This time I had students trade cards, and the left-hand side shifted down each time.

Let your kids work together, discuss and find patterns – the notes then write themselves.