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| I am a novice, not an expert. |
Children are novices not experts. Their academic learning is rule-based at first, which is the way arithmetic should be taught but often isn't. Breznitz & Hemingway (Maximum Brainpower) write, "We are quite good at rule-based thinking, [which] has led to the development of fields such as mathematics, geometry, physics, and, of course, computer science."
Children "master a skill initially by following a set of rules." Learning the standard algorithms is rule-based and mechanical. Proficiency in arithmetic requires a place-value system, the automation of single-digit number facts, knowing the behavior of numbers (axioms), and applying factual and procedural knowledge to solve a problem. Being proficient in math does not make you an expert--far from it. Kids don't think like adults because they have not had a lifetime of experience to supplement rule-thinking. Real experts cannot explain what they do.
Ordinary kids can learn arithmetic if they learn a place value system, the standard algorithms, the single-digit number facts, and practice for mastery. Mathematician Steven Strogatz (The Joy of x), writes, "Any calculation involving a pair of numbers, no matter how big, can be performed by applying the same sets of facts, over and over again, recursively. It sounds mechanical, and that's the point." It is mechanical. Arithmetic is rule-based.
R. Barker Bausell (Too Simple To Fail) writes, "Children who are given more instruction learn more than those who are given less. Too much time is squandered in the classroom. Time on task is essential, but too many educators do not maximize time in academic learning. In short, teachers should use efficient instructional methods, but many do not.
We have state standards, mostly Common Core, but in math, for example, the standards are not broken down to a hierarchy of learning objectives that are specific, discrete, and measurable (Robert Mager: Preparing Instructional Objectives). Moreover, teachers often use time-consuming, minimal guidance methods such as hands-on or discovery. They are inefficient compared to explicit teaching.
Bausell explains, "Using discovery learning, in which children are guided to uncover principles that took some of our best minds centuries to come up with, is also contraindicated (and borders upon the ridiculous.) It would make a lot more sense to give students the principles they need to begin with, then teach them how those principles are applied."
Note: Do not confuse cleverness with giftedness or expertise.
© 2017 LT/ThinkAlgebra
