Five Pillars of the Mind by Tracey Tokuhama-Espinosa

Author:Tracey Tokuhama-Espinosa
Language: eng
Format: epub
Publisher: W. W. Norton & Company
Published: 2019-01-28T16:00:00+00:00

Mathematics

The conceptualization of mathematical magnitude is innate; even young, preverbal children understand quantity. Children soon learn to incorporate symbol-to-magnitude relationships as they master basic counting (1, 2, 3…), then see the same relationship represented on a number line. Students’ understanding of comparative data can easily be reinforced in classroom exchanges. For example, teachers can call attention to the ratios between groups of individuals in a classroom, such as the number of dark-haired students to blondes, or the total number of students to teachers (relationships). Teachers can constantly remind students of the vital role the order of operations plays in successfully completing a math problem by showing students how patterns of errors occur when order is changed: for example, when a learner violates the PEMDAS rule and performs subtraction as a first rather than last step in a math problem (see Table 9). A 3rd grade teacher could help students categorize the kinds of typical errors made when learning how to multiply, which will foster learner autonomy and hone students’ metacognitive skills (see Table 13). A high school math teacher could remind students of the different mathematical symbols that evolve with math complexity; the patterns in statistical analysis found in formulas and outcomes; and the relationships between equivalencies or the categories of mathematical thinking, such as arithmetic, algebra, analysis, geometry, probability, and so on.

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