Reform math shortchanges them.
In reform math and now Common Core state standards, which are often interpreted as reform math, students have been taught many alternative strategies for different numbers or situations. Consequently, many ways make simple arithmetic more complicated, mystifying, and confusing. Core arithmetic is straightforward and focused, but not reform math, which marginalizes or delays traditional arithmetic. Often, students are taught 3 or 4 strategies (procedures) to calculate one operation. The alternative approaches overload a beginner's working memory and confuse students. More importantly, they do not prepare students for algebra. In contrast to reform math, the standard algorithms for the four whole number operations do prepare students for algebra and should be primary and taught first, but they are not. The multiple strategies of reform math shortchange or push aside the critical importance of the standard algorithms.
In fact, the standard algorithms solve the reform math dilemma of many alternative strategies and cognitive load. Each of the four whole number operations has one standard way for calculating called the standard algorithm, which always works no matter the numbers. Think of all the time wasted on alternative strategies when the instructional time should have been spent on learning the standard algorithms (core arithmetic), along with practicing and reviewing. Students should practice 20 to 30 problems a day, five days a week, even 1st-grade students.
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| The number 37 means 3tens+3ones. |
In 1st-grade whole number addition, the place value system is adding ones to ones, tens to tens, and so on. Students need to memorize the single-digit math facts and break down numbers by place value to make the standard algorithms work.
In short, the standard algorithm boils down to single-digit number facts in a place value system. It is the quintessential model of place value, and "the case for the importance of the standard algorithms for whole number operations cannot be overstated," explains W. Stephen Wilson, Ph.D., Professor of Mathematics, Johns Hopkins University. Moreover, the study of the place value system should begin in 1st grade with the meaning of numbers. Numbers should be taught as place value, e.g., 12 is 1ten+2ones or t + 2, and so on. Place value is core mathematics, and it leads directly to the standard algorithms.
Wilson points out, "The place value system, fractions, and the standard algorithms all contribute greatly to algebra readiness."
To Be Continued
Excuse typos and other errors.
©2017 LT/ThinkAlgebra
