Sustaining the Fantasy, Dept.

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.

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One thought on “Sustaining the Fantasy, Dept.

  1. “It happened before common core with me,” a Toledo, Ohio, mother said for that story. As soon as the class received a new textbook, “I could never help my daughter with homework.”

    That’s because we’ve had more than two decades of curricula like MathLand, TERC, and Everyday Math that tells teachers to “trust the spiral.” With CCSS, these curricula still exist and are just rejiggered a little bit. Trying to compare modern complaints with those about the math of the 50’s and 60’s is either a desperate attempt to ignore the issues that many of us have been raising for decades, or a complete ignorance of what’s going on.

    The biggest change since I was learning math in those days is the use of full inclusion and differentiated instruction, which is a complete failure. Differentiation and tracking are now hidden at home and with tutors and they focus on ensuring mastery of basic skills using traditional tools like flash cards and work sheets. You can’t “trust the spiral” because that does not get the mastery job done, it hides the tracking at home and increases the academic gap. Go ahead and teach top-down using concepts, discovery, and classroom group engagement. Does it work? Has it worked over the last 20 years? There is noting new in CCSS. Has anyone asked the parents of the best students what they had to do at home? Ask us. It’s not difficult.

    I would tell you that I had to ensure basic math skills at home for my “math brain” son in K-6. We even used to get notes sent home telling us parents to work on “math facts.” That’s an incredible show of incompetence. Magically, all of that disappeared in 7th grade when our state required math certification for teachers and we replaced CMP with a proper (and traditional) Glencoe textbook series. This led to a traditional textbook path of AP Calculus track classes and textbooks in high school taught by many people who spent a career in industry. I never heard a peep of educational demagoguery from them.

    Many of us hoped that CCSS would solve the issue of ensuring grade-by-grade mastery of basic skills in K-6. It did not. It let them off the hook to continue with their top-down, conceptual understanding (only), classroom engagement, “trust the spiral” teaching. The CCSS tests might contain slightly more emphasis on skills, but it’s hard to tell when skills are wrapped inside of vague understanding wrappers. CCSS is fundamentally flawed. Yearly tests for understanding and general problem solving are a year late and many tutoring dollars short. What are teachers, potted plants? They are the ones best able to judge the development and balance of understanding and skills. One parent/teacher meeting I was in years ago (pre-CCSS) found that our school’s “problem solving” results went down. The result was to increase the work on problem solving – whatever that was. Yearly test are, at best, a way to see if anything is fundamentally wrong at a school, and that can be done just by testing basic skills. CCSS cannot drive a good education. Only schools, teachers, and good curricula can do that. That’s not likely to happen when K-6 pedagogues have no clue what many of us parents have to do at home.

    Also, PARCC officially declares that K-6 is a NO-STEM zone. They expect students to catch up by taking summer classes or doubling up math in high school. No. For those kids, it’s all over by 7th grade because the students making it to algebra in 8th grade and a STEM career are the ones helped at home and with tutors who ensured mastery of basic skills. Ask us. I dare you.

    Mastery of skills is not rote learning. Do I have to repeat that? There is no top-down path to success in math. That’s a fairy tale promoted by educational pedagogues who think that their (content and skills hating) academic turf is of primary importance. It’s amazing how those ideas change in high school with teachers who value content and skills.

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