"I See" Mathing
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Math is more than memorized processes that produce "the answer." Drawings of base-10 pieces in addition, subtraction, multiplication, and division problems bring to life the essential learning metaphor: To see is to understand. Students learn that just as reading is more than the memorization of letters and words, math has deeper, far more interesting, meanings than the memorized building blocks of numbers and algorithms.
Greg Bergin taught in two elementary gifted and talented programs for 28 years. He now teaches sixth and seventh grade math. Over multiple years, he developed a coherent, easily-used and learned visual method of teaching students to see deeper into arithmetic, to its conceptual bases. With that knowledge, students become mathers who are able to see that an algorithm is a meaningful but "creatively lazy" means to an end. A mather, one who seeks meaning in math, is similarly free to create, to not be limited by any given algorithm, just as a writer is free to create and not be limited by what has come before.