A Year in the Life: Ambient Math Wins the Race to the Top!
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.
3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Looking back over the Common Core Grade 3 standards, I found this one:
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.
Why are these two standards so similar, and how significant are the slight differences? The prevailing feeling here is that overall, the Common Core math standards were too thoughtlessly cobbled together. And in both cases these standards are addressed and fulfilled with reams of worksheets. Instead and alternatively, straightforward concepts like estimation and rounding can be taught and learned quickly and easily, with little need for constant, repetitive practice and testing.
Requiring completion of multiple worksheets with abstract problem scenarios is a sense-dulling endeavor, and as such thwarts the true purpose of mathematics: experiencing the basic joy and beauty that numbers and their meaning and patterns can bring to our lives. If this is placed ahead of a fear-based reliance on repetitive work and constant testing, learning will occur. And it will occur with gusto and enthusiasm, laying the groundwork for genius and creativity, in service to a world that so sorely needs it!
The Math By Hand Grade 4 approach is creative, exploratory, hands-on and fun, with a solid grounding in the basics. A lively mix of reviewing factors and times tables through magic squares and other math patterning and tricks, along with form drawing, trickster tales, and learning long, complex verses and classic poetry by heart begins the math year.
This is followed by a thorough and concrete approach to teaching and learning fractions and decimals, their relationship, and how to compute with them. The year ends with an introduction to the number line with positive and negative numbers, mixed numbers and fractions, and a clear picture of how to use the 4 processes with it. Only then, at the very end of Grade 4, are basic algebra concepts introduced.
A methodical journey that exhibits a clear progression from one step to the next makes sense to the child who is struggling to grapple with too much information. Isn’t it our sacred duty as teachers and parents to make this journey doable for every child? And beyond doable, shouldn’t the journey be joyful, inspiring, and creative? Which brings us back to worksheets. No worksheet can meet the parameters and demands of a math approach that’s truly alive and engaging.
No amount of worksheet drudgery can match the mystery and exquisite presence of math as it’s found in nature, all around us. Open the child’s eyes to this wonder, while relating it to mathematical principles, and s/he will carry it forward into a life that meets the world with genius and love. Math is all about the mystery of life. Unless we acknowledge this, we’ve missed its essence and cannot convey it in our teaching. William Blake’s poem, Auguries of Innocence, begins with this verse, a testament to the mystery that at the same time confounds and sustains us.
To see a world in a grain of sand
And heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.
Both this sunflower and lobelia display the spiral of the Fibonacci sequence. Unless we acknowledge and teach the mysterious majesty of math, and instead bury it under mountains of meaningless worksheets and tests, we have missed a golden opportunity, while robbing our children of their very humanity.
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.