Dana Goldstein, a New York times reporter, asked on Twitter if there were any teachers willing to be interviewed for an article she was writing. I responded (I was on Twitter at this time), suggesting she view the video of a talk I gave in which I mention some of the problems with Common Core. https://www.youtube.com/watch?v=RlLbXZOoAMU (I even told her to start at minute 19:24 to save her some time).
Whether she watched it or not, I don’t know but the article she wrote does not seem to reflect any of the insights I provided. So I’m assuming that she was under a tight deadline and couldn’t be bothered with messy details.
She focuses primarily on reading, but does give a nod about the math standards:
On social media, angry parents shared photos of worksheets showing unfamiliar ways to solve math problems. One technique entailed “unbundling” numbers into multiples of 10, to help make adding and subtracting double- and triple-digit figures more intuitive. Another, called “number bonds,” required students to write the solutions of equations in stacked circles.
Both methods are commonly used in high-achieving nations. But to many American parents sitting at kitchen tables and squinting at their children’s homework, they were prime examples of bureaucrats reinventing the wheel and causing undue stress in the process.
What she reports is true; high-achieving nations do indeed use these techniques. What she leaves out however, might help us to understand what’s going on. The techniques to which she refers are nothing new and were used in US textbooks in earlier eras, like the 60’s, 50’s, 40’s and so on. The difference between then and now, is that the textbooks taught the standard methods or algorithms first—as an anchor—and students were then given problems (deemed “drill and kill” by those who hold practicing as mind numbing and counterproductive). Alternative techniques such as the “unbundling” of numbers (e.g., representing 235 as 200 + 30 + 5, or 2 x 100 + 3 x 10 + 5 x 1) and number bonds are nothing new. Number bonds were even part of the textbook I used in elementary school, shown below:
Source: Brownell,et al; 1955. Ginn and Company; New York.
Unlike the current practice in the US, the high performing countries alluded to in Goldstein’s article do not dwell upon these techniques for months on end. Nor is the teaching of standard algorithms withheld until students show understanding using alternative methods. Looking at Singapore’s Primary Math series for example, students are expected to be familiar with number bonds and development of mental strategies for ease of computation. But the difference between what we are seeing with textbooks aligning with Common Core and those used in Singapore is that mathematical development will evolve naturally with the build-up of levels of understanding. The Singapore textbooks do not insist that students use the specific methods that are embedded in Common Core’s standards.
For example, while the process of “making tens” is used in Singapore’s “Primary Math” first grade textbook, it is one of several strategies presented that students may choose to use. (See figure below for how “making tens” was explained in my 3rd grade textbook—and introduced after mastery of the standard algorithm for addition).
Source: Brownell, et al. (1955); Ginn and Company, NY.
There is no requirement that I’ve observed in Singapore’s textbooks that forces first graders to find friendly numbers like 10 or 20. This is probably because many first graders likely come to learn that 8 + 6 equals 14 through memorization, without having to repeatedly compose and decompose numbers to achieve the “deep understanding” of addition and subtraction that standards-writers feel is necessary for six-year-olds.
The Common Core grade-level standards are minimum levels of expectation and goals, and are to be met no later than that particular grade level. Thus, the standards do not prohibit teaching a particular standard earlier than the grade level in which it appears. But publishers have interpreted the standard to mean that the standard algorithm not appear until fourth grade. And in compliance with the Common Core’s “Progression Documents” for those publishers that introduce the standard algorithms earlier than the grade in which it appears in the Standards, the publishers’ test materials do not include questions on standard algorithms before their time.
The math reform influence upon Common Core’s standards manifests itself most obviously in the delaying of teaching standard algorithms. Delaying teaching of the standard algorithm for addition and subtraction of multi-digit numbers until fourth grade is thought to provide students with the conceptual understanding of adding and subtracting multi-digit numbers. The interim years (first through third grades) have students relying on place value strategies and drawings to add numbers. The means to help learn, explain and understand the procedure becomes a procedure unto itself to become memorized, resulting in a “rote understanding”.
Students are left with a panoply of methods (praised as a good thing because students should have more than one way to solve problems), that confuse more than enlighten. The methods are side dishes that ultimately become indistinguishable from the main dish of the standard algorithm. As a result, students can become confused—often profoundly so. As Robert Craigen, math professor at University of Manitoba describes it: “This out-loud articulation of ‘meaning’ in every stage is the arithmetic equivalent of forcing a reader to keep a finger on the page, sounding out every word, every time, with no progression of reading skill.”
None of this is discussed in the Times article—it would take too many words, I suppose. What readers are left with is the longstanding impression given by the bevy of education journalists that parents are a bunch of whiners and complainers who don’t realize a good thing when they see it.
She hints that perhaps Common Core wasn’t done right (albeit with respect to reading). “Still, not everyone agrees that the Common Core was faithfully implemented at the classroom level.”
I implement it by exercising my mathematical judgment and teaching it in an efficient and effective manner. That is, the way that students from affluent backgrounds may be learning it thanks to tutors and learning centers.
Reference: Brownell, Guy T., William A. Brownell, Irene Saubel. “Arithmetic We Need; Grade 3”; Ginn and Company. 1955.