4.OA 2: Word Problems. Are They Problematic? (#248)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 248

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 4.OA
Use the four operations with whole numbers to solve problems.
2. Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Word problems!  The bane of many teachers, teacher/parents, and students.  There is something very cold, calculating, and alienating about scenarios thinly disguised as math problems, wherein strangers perform unfathomable tasks or disconnected acts.  Love this one from the comic strip Peanuts.


In both the Waldorf and Math By Hand systems, there is a steeping in the four processes and how they relate to each other.  Differentiation between them is deeply rooted and easily accessed, so that there’s a natural, instinctual reflex as to which process is appropriate to each particular situation or need.  The sort of drawings required by this standard are less than optimal.  In fact, they tend to be repetitive and demeaning.  Here’s an example, from a Homeschool Addict blog post.


Is this rigorous and deep?  Or is it counterproductive, in the sense that math now becomes a drudgery rather than a creative and exciting endeavor?  Let’s not waste our children’s time and ability with this sort of repetitive, labor intensive work.  Drawings that are more complex and promote true flexibility of thinking are more appropriate, like this form drawing from Tara Gregory’s Pinterest page.


Of course, we want our children to be flexible thinkers, to be able to think on their feet, and be open to solving any problem that comes their way.  Waldorf simply says that this is a quality that needs to be carefully nurtured and grown, through many, varied means.  That this quality can not be hammered in, can not be tested to death, that it must be beautifully taught and learned.

I will close with a clip from one of my favorite movies, Desk Set, with Spencer Tracy and Katherine Hepburn.  Watch the whole clip if you like, because these two are just magic together.  Or cut to the mathematical chase at 3:23 to see Kate handle any complicated word problem that’s thrown her way.  I think it’s a pretty safe bet that the Hepburn character was not subjected to Common Core type math, but attained her prodigious math talent through a broad and eclectic education.

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 4 math CCSS and their ambient counterparts.

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