Yeah, you clearly didn’t get the argument at all. A good student or learner would read Dr. Cheng’s comments and ask why or how, but you have a rigid way of looking at things, which is what math shouldn’t be teaching at all.
Why, then, do students who "successfully" engaged in repeated practice of the division of fractions not retain their skill in this activity? Why do so many college graduates not recall how to divide 11/31 by -53/97?
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because they haven't MASTERED this basic math skill. Use of calculators and other manipulatives have inhibited their ability to do so. Simply "knowing" isn't good enuf. Without mastery long term memory cannot occur http://www.psy.cmu.edu/~siegler/Siegler-etal-inpressPsySci.pdf ….
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@TaraMathBC: See Bahrick & Hall (1991) J. Exp. Psych.: General, 120, pp. 20-33. Learners of algebra whose practice persisted only while it was imposed on them did not retain much. If practice is miserable, no one will persist in it once the obligation to persist is removed. - 9 more replies
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