Bad PD # 517

At a six-hour PD I had the misfortune of having to attend, the moderator put this slide on the screen in a defense against the call for evidence that certain teaching practices are effective. It was a slide from a presentation by David Theriault, who teaches English and has a blog:


Essentially, Mr. Theriault felt that the question about having research to back up a practice was irritating. What he calls research is what he sees in the classroom. I’ve heard it many times before in a “It works for me” type defense.

Well, traditionally taught math worked for me, but I’m fairly certain the moderator of the PD as well as Theriault and others would not find that acceptable.

The PD was full of the usual platitudes that “worksheets are bad, experiential learning is good”. The penultimate task of the day had us drawing specific geometric figures using a computer language that we had to figure out without instruction.  The person next to me was familiar with the language so he taught it to me, using direct and explicit instruction. Others learned in the same way.  The moderator was very pleased with the fact that we learned from each other rather than from him since he seemed to think it proved his point that teachers should facilitate what is supposedly innate in students. Except for the fact that this wasn’t innate; the person who taught it to me learned it the old fashioned way.

We then had to construct a one-page lesson plan on any topic.  My partner for this task was a woman from a neighboring school who, like me, taught math in middle school. I suggested a plan to teach why the invert and multiply rule works for fractional division.  She got hung up on providing a context for division. I couldn’t get beyond her hang-up and reminded her we only had a few minutes left. Time ran out, and she got into a conversation with the moderator about her hang-up and I left.

The teachers at my school never talked about that PD, and I notice they never asked the moderator back.

I offer you this as one of a continuing series of bad PD that infiltrates our education system.


Arrogant jerks, Dept.

In a recent column in the Washington Post, Jay Mathews has written what has become the emblematic anthem against algebra II in high school

I can understand the argument against requiring algebra II for graduation, since at one time that was the case. Students only needed two years of math, and that usually consisted of algebra I and geometry.  But his argument seems to be to get rid of it altogether and in its place have courses that are more relevant like statistics.

He ignores the fact that if you really want to pursue statistics, you will have to have some facility in the topics taught in algebra 2.  So what is he suggesting? Students should take that in college?

But there are ways to ease algebra II out of high schools. Gregg Robertson, longtime principal of Washington-Liberty High School in Arlington, Va., noted that his math department has courses in probability and statistics, both regular and Advanced Placement, as well as a dual-enrollment quantitative reasoning course through Northern Virginia Community College.

I think I’m reading that right. Easing algebra II out of high schools means it isn’t an option for anyone. Unless he wants to walk it back and say “What I meant was ‘easing it out of graduation requirements’ “.  But he didn’t say that.

Mathews relies on the tired old arguments that supposedly give him credence: He took both algebra II and also calculus. He’s never used it in his life. There; that’s proof of its uselessness for you.  Many people are not scientists, engineers, or mathematicians. Why not ask them if they’ve ever used these courses that are deemed so useless?  Maybe such information would propel journos like Mathews to write more relevant columns.

Puff Piece, Dept.

Just read a rambling article in the Atlanta Journal Constitution by Maureen Dowd that points fingers and doesn’t come to any conclusions. Main point: math ed has been bad in GA for many years so why blame Common Core.

Citing parents’ laments that they wish math could be taught as it was 30 years ago, Dowd asks whether this is really a solution. She states: “But did students learn math more effectively a generation ago? When the Program for the International Assessment of Adult Competencies evaluated numeracy skills of adults in 23 countries, 20 outperformed the United States.”

The study cited aggregates populations from ages 16 to 65. Thus, there are different types of math teaching people were exposed to based on age. However she leaves out this finding, stated in the study: “In the study, people from ages 16-65 in over twenty countries, including the U.S., were given the same exam consisting of math computations and word problems. According to the study, “the percentage of U.S. adults between 55 and 65 years old who scored at the highest proficiency level (4/5) was not significantly different than the international average for this age group.”

She also cites Elizabeth Green’s NY Times article from a few years ago (Why American’s Stink at Math) and pulls this quote:

“The story is the same every time: a big, excited push, followed by mass confusion and then a return to conventional practices. The trouble always starts when teachers are told to put innovative ideas into practice without much guidance on how to do it. In the hands of unprepared teachers, the reforms turn to nonsense, perplexing students more than helping them.”

In other words, the methods of math reform would work if they were only done right–but they’re never done right. There is much to contest there.

Lastly, she talks about Japan’s “integrated approach” to math, which Georgia will emulate. Japan isn’t the only country to take an integrated approach to math in high school; many European countries do this also. But they do it fairly well. The U.S. has done a horrible job of it; one need only look at the integrated approaches used here: IMP, Core Plus, MVP math.

In short: A typical puff piece that refuses to look at research that would upend the opinions expressed in the article.

Selective Reporting, Dept.

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. (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.


Following the lead of others, Dept.

A blogger who calls herself Quirky Teacher announced that she was finished with Twitter. She gave good reasons, and the more I thought about it, the more I realized that I’m just as tired of Twitter as she is.

Therefore, I too will be closing my account. I find I spend too much time trying to be right, being snarky when others say something that I deem to be 1) wrong, 2) idiotic, or 3) both, and trying to cajole others into ganging up on those whose opinions I find irritating.

I am also tired of the word “nuance” which is the usual rejoinder by those who do not agree with someone’s argument and criticize it by saying it lacks nuance.  I am tired of tweets promoting “smart and thoughtful posts” by edu-pundits and/or journalists who think they have the ultimate scoop on education.

It does have good attributes, but it is one of those precious “conversations” that rarely reaches any resolution and just seeks to further infuriate those who are furiating.

In ending my account, I am resisting the urge to tweet about this particular post.