I'm not a math teacher but I've been following the conversation here as various participants have been trying to correct the article's author's "math". . . aware all along they were trying to unscrew the unscrewable.
It's not a "wrong equation" because it's not an equation. . . It's a descriptive result of transformation steps of "decomposing" the expression. Decomposing is taking a number apart. For example 5,689 decomposes to 5,000 + 600 + 80 + 9. They are using "warp" for their stepping through the decomposition process to get to their new approach.
We were all taught to add and subtract working a column of numbers from right to left. This common core method teaches a faster, equally valid way using something we all do instinctually when estimating an addition, going left to right, adding the MOST significant figure first, then the next, and so on, ending with the least significant column (if we even bother having by that column a pretty good feel for the estimate), rather than starting with the ones column as we had been taught.
The way we were taught is related to counting—arithmetic—small numbers. The newer way being taught is related to manipulating numbers in groups—mathematics—large numbers. One, the first, I think, is detail oriented, the second more concerned with the overall gross effect. The second can result on faster, more general, estimated, results, that can look at the bigger results and ignore the accurate. The one we learned requires slogging through the least significant detail before reaching the most important data, there's gives that important data and the detail may never be looked at because the estimates were "good enough."
Does every student NEED to know the "decomsition" theory by which the arithmetic and mathematics work, or do they need to learn the rote mechanical systems we learned that will work for counting things?
I have no problem with an understanding of “number decomposition” for students in 4th grade and above. And students should be taught that process.
But Piaget would argue that some children as old as 8 still have not developed beyond conservation of number maturation.
Finally some number facts just have to be memorized and internalized such as the Times Tables. Failing to master these tables makes math computations painfully difficult.
Rote/memorization of basic number facts first is the way to go. Understanding number systems and logical reasoning is built on that foundation.
I compare it to learning a new language. You memorize the basic phrases to get by and then go about understanding grammar and sentence structure. As in most things the WHAT precedes the WHY.
As for whether to teach addition from right to left or left to right, call me old fashioned but I still think right to left serves the child better.
And decomposition strategy has to hit the grouping/carrying/borrrowing wall eventually. It can’t get around it. Try ‘decompositioning’ 95 + 69 without carrying and grouping.
And ‘decompositioning’ left to right is even more ridiculously difficult when you try subtracting 69 from 95. You are expecting a child to see 2 steps ahead. He takes 60 away from 90, and then realizes he has to borrow from the 90 to take 9 away from 5. Going right to left, the student sees the problem immediately.
Young children have a quicker grasp of carrying/grouping the ones and tens place values than the hundreds and thousands. That alone is why computing from right to left seems preferable for kids learning math.