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Patterns of Math Basics
If students would be permitted (i.e., forced) to use number lines and multiplication grids or Noble's Columns© until they no longer required them (because they remember 4 + 3 = 7 and 2 x 5 = 10), math scores would improve. It is tough enough to learn any concept when it is only seen for a week. It seems almost impossible if students are trying to grasp a concept before they have a grip on combining the individual numbers zero through ten via addition, subtraction, multiplication or division.
The Patterns of Math Book constructs a framework of learning centered on the basic understanding of the relationships of these eleven numbers to one another, and reinforces that understanding with a patterned repetition of means to a solution.