3.OA 8: Life-Sourced Word Problems, Too Soon for Algebra? (#194)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 194

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Operations and Algebraic Thinking 3.OA
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
8. Solve two-step word problems using the four operations.  Represent these problems using equations with a letter standing in for the unknown quantity.  Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

An online search for Grade 3 Common Core word problems turned up the usual suspects.  Anonymous boys and girls juggling quantities of various objects between and among themselves.  “If John has 28 pieces of candy and Jane has 12 less, how many pieces of candy do John and Jane have altogether?”  Hmmmmm.  What do these detached scenarios accomplish, really?  They may be able to teach the bare facts successfully, but at what price?  Boredom and alienation?

The Waldorf Grade 3 curriculum is rich in opportunities to practice life rather than word problems.  “If John is building a chicken coop and he needs eight 12 foot boards for two walls, and eight 6 foot boards for one wall, how many board feet does he need altogether?  If the boards cost 76 cents per linear foot, how much will it cost to build the three walls?”  Now the crucial difference here is that John really is building this chicken coop with his teacher/parents/class and they all really do need to know if the chicken  coop cost is within their means.  Guarantee: no third grader will fall asleep over this kind of math practice.

A letter standing in for the unknown quantity.  This was accomplished in essence in Grade 1, only without the letter.  A white square is used to represent the unknown quantity in equations practice with the color-coded strips, in all four operations.  This will translate nicely to its algebraic equivalent when the time is right.  My online search also turned up the use of parentheses.  It may be too soon for this level of abstraction.  Algebraic thinking could happen now, but without the formal language.

Drawings are a big part of Common Core math.  But the drawings tend to be crude and somewhat scribbled.  It’s recommended that students draw elements of their problem-solving as they go.  One example I found online involved Jack and Jill, the number of buckets they each owned to begin with, and the number of buckets each one of them left on top of the hill before bringing the remaining buckets down the hill.  Then it asked how many buckets remained (down at the bottom of the hill) altogether?  Now not only does this chop up a perfectly good nursery rhyme, but it also leaves something to be desired in its execution, as the buckets are drawn as counters, repetitively and crudely. 

This sort of scribbling does not meet the young child where s/he needs to be met, creating work that’s beautiful, full of integrity and purpose.  Assess the reasonableness of answers.  Reasoning is not quite ripe and ready at 9.  Math facts should be just that, facts.  Analysis will only produce confusion at this point.  As for mental computation, this can happen beautifully and successfully in the context of the morning circle and other math skills practice with movement.  A wonderful example of thinking on their feet!  Rounding happens often in the context of skills practice, both oral and written.  Once the rules are established, rounding is simple and as always, practice makes perfect.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Tune in tomorrow for more Grade 3 math CCSS and their ambient counterparts.



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