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At their young age, it typically takes children the ritual of performing arithmetic algorithms at least several dozens of times if not a hundred times to get th
by kccqzy 2mo ago
At their young age, it typically takes children the ritual of performing arithmetic algorithms at least several dozens of times if not a hundred times to get them to understand and internalize the algorithm itself. You can't actually teach the algorithm itself because they haven't studied basic algebra yet, so the only approximation is using the algorithm on multiple numbers. Then afterwards just give them a calculator.
In contrast, in high school, when a student has sufficient mental maturity to understand algorithms abstractly, it suffices to have the student do a few integrations by hand (say using the integration by parts technique) and then hand them a computer algebra system.
- fluoridation 2mo ago>Then afterwards just give them a calculator. If problems were properly designed the students shouldn't even need calculators. In math the specific numerical value of a result is far less important than how it relates to the inputs. Raw calculation doesn't develop the intuition of when one operation is more appropriate than another.
- kccqzy 2mo agoAbsolutely not. Properly designed problems involve numbers that simulate the real world (Benford’s law). Specifically choosing numbers that are easier to compute mentally or by hand would lead students to doubt themselves whenever they encounter something difficult to compute, so you can consider that either cheating or giving them undue psychological stress.
- fluoridation 2mo agoIn math they shouldn't be computing at all, they should just be performing symbolic manipulations.