In 2006 and 2007, a National Math Advisory Panel was put together to review the current state of math education in the US and make recommendations on what should be taught (and learned) in K-8. In the course of putting together their report, there was considerable argument over the inclusion of the word “the” when applied to “standard algorithms”. Some members of the panel wanted the recommendation for students to learn multidigit addition and subtraction to refer to “a” standard algorithm. The use of the word “a” left open what the definition of standard algorithm is. Some believed that any method that relied upon place value, be it pictures, or alternatives to what we’ve come to know as “the” standard algorithm (adding or subtracting in columns, starting from the ‘ones’ column and carrying and borrowing–or ‘regrouping’ as some would insist these operations be called) should be what students learn.
The knock-down drag out was finally resolved with “the standard algorithm” being the recommendation.
I was therefore surprised to read Arizona’s revision of the Common Core math standards. The fourth grade Common Core (CC) standards require students to learn “the” standard algorithm for multi-digit addition and subtraction. (The fact that it can be taught earlier than fourth grade and that CC does not prohibit such teaching is another topic; suffice to say that many schools, and textbooks wait until fourth grade to teach it, relying on alternative methods in the preceding grades.) Arizona’s revised standards replace the word “the” with “a”, thus representing a step backward from the hard-fought battle that took place within the NMAP.
One can see a summary of what the public comments were in the linked document above. One public comment stated:
“I LOVE the change from “the” to “a.” This small change reflects a bigger understanding we are trying to push!”
The thought process here is that standard algorithms obscure the understanding of what’s going on when one does such operations. It also embodies a philosophy of many progressivist types that I call the “students must understand or they will die” philosophy.
Other comments supported the use of the word “the”:
“This was the progression. 2nd grade used models and strategies, 3rd used strategies and algorithms (plural), 4th grade used the standard algorithm There are many different algorithms…but only one STANDARD algorithm.”
“I understand the intention, but this standard is not distinct enough from the third-grade standard which states that students should fluently add and subtract whole numbers. The third-grade standard needs work!”
As if these weren’t enough, there were strenuous objections to the choice of “a” over “the” by two people Arizona called upon to review and comment upon the revisions: Jim Migram (retired math professor from Stanford who has fought for clear and effective math education in K-12 for over 20 years) and Ze’ev Wurman, another stalwart fighter in the quest for proper math education.
They commented as follows:
Milgram: This is nonsense, and classic educationese. It is based on a complete misunderstanding of what algorithms actually are, and starts a process in which students in this country gradually lose the capacity to do the advanced mathematics that is essential in going into STEM and related areas.
Wurman:The removal of the “the” is a gross mistake. The National Mathematics Advisory Panel, certainly a much bigger authority than McREL, purposely inserted the “the” into its recommendations to teach “the standard algorithms.” While there are many possible algorithms for arithmetic, only a single set is “standard” and it deserves to have the definite article. All around the world people use the four standard (arithmetic) algorithms and the few differences one see across the world are cosmetic, trivial, and non-essential. Pretending that there are multiple standard algorithms for the four arithmetic operations is mathematically ignorant or intentionally misleading.
Despite such warnings and reasoning, the progressivist approach has remained, with the Arizona workgroup commenting:
“No revision necessary. A standard algorithm is valuing all students and what they bring to the classroom as recognized by the public comments.”
And there you have it. Meet the new boss: worse than the old one.