Education Week reports on how the Common Core math standards are taken as the “scapegoat” and “bogeyman” for the current state of math education. It starts with a quote from 1972 by a math professor regarding the 60’s new math:
“When persons with advanced math degrees do not agree upon the answer in a 4th grade math book, something is wrong. … I beg of you, please read the math books children are using. … The extended use of set theory is almost obscene. Set theory is a post-graduate exercise, not suitable for children who can not even multiply yet.”
The quote, the article explains, comes from a new book by Matt Larson (current president of NCTM) in which he talks about math education.
Regarding the quote from the math professor, Larson says this:
“In fact, it’s pulled from a 1972 Washington Post article about New Math, the shift in mathematics instruction that began in the late 1950s. New Math emphasized conceptual understanding over rote memorization—not unlike the common core.”
Ignore for the moment the continued mischaracterization of traditionally taught math (i.e., conceptual understanding vs rote memorization). What is interesting is that it suggests that 60’s New Math and Common Core both have their share of Chicken Littles and that in both cases such complaints were/are unsubstantiated. According to Larson (and others) such complaints come about because people don’t like things that are different than how they learned.
Liana Heiten, the reporter for this article quotes Diane Briars, former NCTM president:
” “Any time a district moves to building more conceptual understanding into their mathematics program, and students are coming home with either homework that looks unfamiliar or … with different computational methods than parents have seen before, there’s always going to be questions,” Diane Briars, who preceeded Larson as NCTM president, told me for a 2014 story on how schools are teaching parents about the common core.”
In fact there were some objectionable aspects to the 60’s New Math so such complaints were not without substance. The 1972 quote from a math professor, while framed by Larson and Education Week as an exaggeration, was echoed by many people at that time. The math taught in the lower grades during the 60’s New Math era relied on a set-theoretical approach that was too formal for many students, not to mention the teachers. Interestingly, NCTM distanced itself from the 60’s New Math when it fell out of fashion in the mid 70’s, though NCTM’s 1989 (and later, 2000) math standards pushed “understanding” over “procedures” as had the 60’s New Math in part.
As for Common Core math standards, although they call for fluency with math facts, and require learning the standard algorithms, its interpretation and implementation –like the NCTM standards which dominated math education philosophies in the edu-establishment for the past two decades or so–also has been implemented along the ideologies of reform math.
The alternative strategies for adding, subtracting, multiplying and dividing which are suggested in the CC math standards have generated many complaints and articles in the press. But they are nothing new; they have been around for years in the textbooks used in the eras of traditionally taught math. But it used to be that the standard algorithms were taught first, as a main dish. The alternative methods were introduced over a period of a few years as side dishes to help students do mental math, and to help clarify what was going on within the standard algorithms. But interpretations of CC have resulted in delaying the teaching of these standard algorithms until the grade level in which they appear in the CC standards. The standard algorithm for multidigit addition for example, appears in the CC 4th grade standards. While this means it is to be learned no later than the fourth grade, popular interpretation and implementation of these standards is to delay its teaching until 4th grade, and to teach only the alternative methods in earlier grades.
Jason Zimba one of the lead writers of the CC math standards has gone on record stating that the standard algorithms can be taught earlier than the grade in which it appears in the CC standards, and Zimba even recommends that that be done. But reform ideologies have prevailed: The reasons for delay go along with reform-oriented ideas, that teaching the standard algorithms first eclipse the conceptual underpinnings of how they work and students will not “understand”–i.e., it is equated with “rote memorization”.
Furthermore, although the CC website claims that the standards do not dictate pedagogy, it says that “shifts” in instructional strategies are necessary. It calls for coherence in teaching:
“Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts. … Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years.”
The implication is that this has never been done before. In fact, it might be the case that the textbooks and programs of the last 25+ years, in adhering to NCTM’s math-reform flavored standards did away with such coherence in the lower grades, relying instead on more of a “spiral approach”. But current interpretation is that traditionally taught math was a series of unconnected topics. And perhaps this shift in instructional strategy has led to the teaching of standard algorithms later rather than earlier, in the prevalent belief that doing otherwise leads to “tricks” or “mnemonics” and that the procedures cannot be taught with “understanding”.
Looks like NCTM’s current president is doing his part to sustain that fantasy.