MPS 4 & 5: 4 Processes Plays, Gem Counters, Real Numbers (#93)

A Year in the Life: Ambient Math Wins the Race to the Top!
Day 93

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.  Today’s post will focus on the third pair of standards,  listed in blue and followed by their ambient counterparts.

The Standards for Mathematic Practice, Grade 1
#4 and #5: Modeling and using tools.
4. Model with mathematics.

The 4 processes plays and stories are a rich example of and opportunity to practice this.  Everyday situations are experienced again and again as contexts for two or more of the processes to interact are provided.  And because each process plays a distinct and specific role in every story or situation, a deep understanding of their functions is taken in and is therefore able to always be used effectively.  Whether alone or in relationship to others, the 4 processes are paired with any specific problems or situations that call for them.  This, as with most Grade 1 material and instruction, helps to build an excellent foundation for knowing what functions can be tailored as a solution any time one is needed.  The in-depth look at the nature of the 4 processes, using their personalities, characterizations and temperaments enables an understanding that will serve far into the future, translated to even the most complex mathematical functions.

5. Use appropriate tools strategically.
The first contact with calculation happens in a concrete and well-supported way.  Glass gem counters are used to make the numbers and their interactions visible.  The progression from using manipulatives to calculating with pencils and paper happens in a series of several steps.  The real numbers that were made previously can transition from modeling in order to learn their forms, to being used as manipulatives in calculation.  The process could start with the glass gems, transition to real numbers, and finally move on to pencil and paper.   The glass gems manipulatives are useful for demonstrating equivalency as well.  Math By Hand uses color-coded strips for calculating with each of the processes, which can begin singly then be used side by side for equivalency.  See the bottom of the page for examples taken from the Math By Hand Grade 1 Binder.

For four days, each of the four pairs of Mathematical Practice Standards will be examined with an eye toward what works as developmentally appropriate math in Grade 1, ending with standards 7 & 8 next.  Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of that knowledge as a worthy goal.

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