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By Jo Boaler, Professor of Mathematics Education, co-founder youcubed
With the help of Cathy Williams, co-founder youcubed & Amanda Confer, Stanford University
Updated January 28th, 2015
In the Ignite Talk “There IS a Difference,” K-5 math educator Graham Fletcher explains the subtle yet powerful difference between memorization and from memory.
Efficiency - Efficiency implies that the student does not get bogged down in many steps or lose track of the logic in the strategy. An efficient strategy is one that the student can carry out easily, keeping track of sub-problems and making use of intermediate results to solve the problem.
Accuracy - Accuracy depends on several aspects of the problem-solving process, among them, careful recording, the knowledge of basic number combinations and other important number relationships, and concern for double-checking results.
Flexibility - Flexibility requires the knowledge of more than one approach to solving a particular kind of problem. Students need to be flexible and choose an appropriate strategy for solving the problem at hand. They can use one method to solve a problem and another method to double-check the results.
Multiplication Fluency
Multiplication Fluency
Students first learn multiplication as repeated addition, often count equal groups by ones and rely on materials such as counters. Students are simotaneously developing multiplicative number word sequences, (commonly referred to as skip counting, i.e. 5, 10, 15, 20), to support this learning. Over time students make remarkable progressions. They learn how to reason abstractly with numbers and no longer rely on counting by ones. (Wright, p. 142). Long before students are exposed to typical multiplication flash cards, an appropraite tool is one that honors this progression and builds conceptual understanding of multiplication as equal groups. Graham Fletcher provides an excellent resource to support this progression. His multiplication subitizing cards are an excellent, updated "flash card" for students! Print them out and cut them up. First work with the cards that have all of the groups of dots visible, then progress to the cards that have all but one of the groups shaded.
Wright, Robert. Developing Number Knowledge. Sage, 2012, p.142.
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