Count the tropes, Dept.

With respect to the poster below, questions abound.

Why is scaffolding only for “diverse learners”? And what IS a diverse learner? And must classroom routines be co-created? Why is teacher authority a bad thing?

Why are students now called “learners”? There really is no need to invent a whole new vocabulary. It may make you think you’re important, but most people see through it. And in the schools I’ve taught, we talk about the students or kids.

And what is with “learner agency”? It used to be “ownership” which was bad enough–now we have “agency”. Of course it pertains to “self-directed learning”. Nothing wrong with students doing things on their own but they do have to receive instruction somewhere along the line. Novices are not experts–but the chart makes no allowance for where a student (or learner) might be on that spectrum.

Finally there’s “productive struggle”. Yes, students should have to stretch beyond initial worked examples. But if they’re struggling, give them some help. Though the chart makers would cringe at this, sometimes students are ready to absorb a direct answer to a question. If so, then just tell them!Edugraphic


Edu-Soap Operas, Dept.

The first in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” is now appearing at Truth in American Education.

Here’s an excerpt:

Various Narratives, Growth Mindsets, and an Introduction to One of my Parole Officers

If you are reading this, you either have never heard of me and are curious, or you have heard of me and have pretty much bought into my “narrative” of math education.

I tire of the word “narrative” (almost as much as I tire of the word “nuance”) which I see in just about everything I read nowadays. I thought I’d charge it rent, so to speak, since it seemed appropriate for the teaching experiences I’m about to describe. I’m currently teaching seventh and eighth grade math at a K-8 Catholic school in a small town in California. Prior to that, I taught seventh and eighth grade math for two years at a K-8 public school in another small town in California, which is where I will start this particular narrative.

It is a one-school district so superintendent and principal were always close by. After receiving praise from the superintendent both formally and informally, I received a lay-off notice. Such notices are common in teaching, with the newest teachers receiving such notices and usually getting hired back in the fall.  Nevertheless mine was final.

It is tempting to make my termination fit various narratives pertaining to the kind of teachers the teaching would like to see less of. Specifically teachers like me who choose to teach using explicit instruction; who use Mary Dolciani’s 1962 algebra textbook in lieu of the official one; who believe that understanding does not always have to be achieved before learning a procedure; who post the names of students achieving the top three test scores; who answer students’ questions rather playing “read my mind” type of games in the attempt to get them to discover the answer themselves, and attain “deep understanding”.  However logical, compelling and righteously indignant such narrative might be, my termination will have to remain a mystery.


Read the rest here.  

The So-Called “Instructional Shifts” of the Common Core and What They Mean

Long-winded Introduction/Preamble

The San Luis Coastal Unified School District is in the central coast area of California. It includes schools in San Luis Obispo and the nearby towns of Morro Bay and Los Osos. The district, under the direction of the current superintendent, follows the trend of  teaching that adheres to constructivist-oriented approaches; i.e., inquiry type lessons, with teachers facilitating rather than teaching. The math text used starting in middle school through sophmore year in high school is CPM, an inquiry-based program.

The district is so much beholden to this philosophy that part of the interview procedure for teaching jobs entails giving a mini-lesson to students, which is in turn rated according to criteria in the Danielson Framework.  The Danielson Framework is (according to their website) “a research-based set of components of instruction, aligned to the INTASC standards, and grounded in a constructivist view of learning and teaching.”

In other words, traditional-minded teachers need not consider applying for a teaching job in the District.  (For followers of my writings, I wrote about two teaching assignments in the District in “Confessions of a 21st Century Math Teacher”.)

I am always curious about math teaching positions that are advertised in the District.  As of this writing, two positions are open. The application always asks for the same essay-type question which I’ve always found intriguing: “Describe your knowledge of the shifts occurring in Common Core State Standards.”

The “shifts” in the Common Core State Standards (CCSS) are not something that are stated as standards. Rather, people who subscribe to the view that the CCSS are game changing, refer to the change of the game as the “shifts”–a change in how math is being taught because of the standards themselves.

Inside Common Core’s “Instructional Shifts”

The “shifts” in math instruction are discussed on Common Core’s website. There are three shifts defined: 1) Greater focus on fewer topics,  2) Coherence: Linking topics and thinking across grades, and 3) Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity.

The first shift is a nod to the notion that previous standards and what they covered resulted in curricula “a mile wide and an inch deep” which has been the prevailing criticism of how math has been taught for the past several decades.  It suggests that math has/is taught “without understanding” and succumbs to rote memorization.

The second shift is another attack on how math has been perceived to have been taught, (aka mischaracterizing) stating that there has been no connection between mathematical ideas, and that topics are taught in isolation–again “without understanding” and using rote memorization techniques.

Which brings us to the third shift, “rigor” to which I want to devote the most attention and focus.  The website translates “rigor” as “Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity.” The site also mentions that students should attain fluency with core functions such as multiplication (and by extension, multiplication of fractions): “Students must be able to access concepts from a number of perspectives in order to see math as more than a set of mnemonics or discrete procedures.”  Again, a nod to the notion that before Common Core, math was taught as a set of procedures “without understanding” using, yes, rote memorization.

This shift has been interpreted and implemented by having students use time consuming procedures that supposedly elucidate the conceptual underpinning behind things like multidigit multiplication, fraction multiplication and other topics.

I learned of the connection between these “instructional shifts” and the current practice of drilling understanding in a conversation I had with one of the key writers and designers of the EngageNY/Eureka Math program. EngageNY started in New York state to fulfill Common Core and is now being used in many school districts across the United States. I noted that on the EngageNY website, the “key shifts” in math instruction went from the three on the original Common Core website  to six. The last one of these six is called “dual intensity.” According to my contact at EngageNY, it’s an interpretation of Common Core’s definition of “rigor.” It states:

Dual Intensity: Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.

He told me the original definition of rigor at the Common Core website was a stroke of genius that made it hard for anti-intellectuals to speak of “rigorous” in loosey-goosey ways. He was able to justify EngageNY/Eureka’s emphasis on fluency. So while his intentions were good—to use the definition of “rigor” to increase the emphasis on procedural fluency—it appears he is taking the reformist party line of ensuring that “understanding” takes precedence and occurs before learning the standard algorithms or procedures.

In our discussion, I pointed to EngageNY’s insistence on students drawing diagrams to show place value in adding and subtracting numbers that required regrouping (a.k.a. “carrying” and “borrowing”—words now anathema in this new age of math understanding). I asked if students were barred from using the standard algorithm until they acquired “mastery” of the pictorial procedure.

His answer was evasive, along the lines of “Of course we want students to use numbers and not be dependent on diagrams, but it’s important that they understand how the algorithms work.” He eventually stated that Eureka “doesn’t do standard algorithms until students know the prerequisites needed to do them.”

Thus, despite Common Core’s proclamations that the standards do not prescribe pedagogical approaches, it appears their definition of “rigor” leaves room for interpretations that conclude understanding must come before procedure.

What Does This All Mean?

What this means for me is that I do not subscribe to this philosophy. I believe it is injurious to students and defeats the purpose of providing understanding by burdening their overloaded working memories.

I am essentially providing this essay as a public service to anyone who is thinking of applying for the various teaching positions in the San Luis Coastal USD.  If you do apply for the positions, resist the temptation to provide a link to this page when they ask you about the Common Core shifts.

But I think you knew that going in.


Tales of Professional Development, Dept.

Last year, the principal of the school where I taught wanted me and the other math teacher to attend six all day professional development sessions over the course of the school year. According to the flyer advertising the PD the sessions encouraged “collaboration” amongst the math teachers in the county where I taught. It was to be  facilitated by someone who believes that students who are faltering but need just a little more time to get it are lacking some key bit of information. Her solution is “just in time” learning in which the problem dictates what the student needs to know in order to solve it.  I don’t think much of “just in time” learning and have written about it elsewhere so will spare you any rants about it.

I was distressed about having to attend the PD.  My distress was not only because of missing six days of teaching. It was the idea of sitting around with other teachers sharing dubious ideas, including but not limited to the virtues of working in groups, “just in time” learning, differentiated instruction and other ineffective practices that pass as superior to the traditional methods that are derided as “having failed thousands of students”.

So when I learned the PD had been cancelled because I and the other math teacher, James, at my school were the only two people who had signed up for it, I was delighted.

My delight was rather short-lived, however. The moderator was one who didn’t give up easily.  She met with our principal and came up with the alternative of having a two hour meeting with the two of us at our school in the early part of the day before our classes started. To her this was a win-win since she got to deliver her PD and we wouldn’t have to miss any class time.

We tried it out one time. I happen to know a bit about her background because I took a look at her blog.  She’s a fan of Phil Daro, who is largely responsible for the Common Core math mess, and getting California to adopt the standards. He talks a lot about how in traditionally taught math, students are taught “answer getting” but not understanding in math. It was evident that she bought in heavily to the idea of “answer getting” vs “understanding” during our confab with her.

She began our two-hour collaboration by talking about how the state tests that are aligned with Common Core in California are not about “answer getting” anymore—rather students must explain their answers. The tests now evaluate whether students are able to see problems in more than one way. Which raises the question of why a student is deemed to lack “deeper understanding” if they get the answer in one way, but cannot show additional ways. She said the tests aim at certain “targets” which are more the Common Core Standards of Mathematical Practice (SMP) than they are of Common Core’s content standards. The SMPs are generic competencies like “persevere in solving problems”, “find structure and repeated reasoning in problems”:  things that would come about anyway from practice of content, rather than trying to develop “habits of mind” outside of the context of content.

Given that the focus of the test is on vague and largely immeasurable competencies, she went on to say that on the state test, students can get full credit on problems where they have to provide explanations even if they get the numerical answer wrong–provided the reasoning and process are correct. (Full confession: I give partial credit to my students if they set up a problem correctly, but I do take off points for numerical mistakes.)

But now she was warming up to what she really wanted to talk about. She said that explaining answers is tough for students and for this reason there is a need for “discourse” in the classroom and “rich tasks”.

I was doing a good job of keeping my mouth shut, but at this point I could contain myself no longer and asked “Could you define what a ‘rich task’ is?”

She answered as follows: “It’s a problem that has multiple entry points and has various levels of cognitive demands.  Every student can be successful on at least part of it.”

This, of course, says nothing very eloquently.  I had had some experience with rich problems so I knew exactly the type of problem to which she was referring; problems like “A rectangle with an area of 20 has what dimensions?” or something similar.

The one-sided conversation she was having continued for a few more minutes.  Apparently she loved math while in school but was doing what she described as “following the rules and getting an answer”.  (And she had given us forewarning that “answer getting” is not a desired outcome.)  Later when she taught math, she found she couldn’t explain to students all the time what were the underlying reasons.  I found this interesting given that I do understand a lot of the underlying reasons, and I had the same traditional math background she described—and she was a math major like me.

At this point James could take it no longer. He said that meeting for two hours for five sessions was superfluous if it was just the two of us. “I teach three different math classes plus doing IT for the school and don’t have time to delve into alternative approaches other than to follow the script and curriculum as laid out in the book.”

She took this as another “entry point”—the two of us must have seemed to her like a rich problem.  “Books are just tools,” she proclaimed.  “They may be strong in one area but weak in another. Traditional textbooks tend to be lacking in opportunities for conceptual understanding and are old school in their approach.”

She sensed that both of us were more than willing to let her dig her own grave here.  She quickly added, “Though there’s nothing wrong with old school.”

I saw no need to tell her I use a 1962 textbook by Dolciani for my algebra class.

She asked if we relied on our textbook for a “script”, meaning scope and sequence.  She turned to me and asked “Do you read just one textbook?”

“I read lots of textbooks,” I said.  She looked surprised.

“He’s also written books,” James said.

“Oh, how nice!” she said and feigned an interest by asking me what they were about. I gave a “rich” answer. “Math education,” I said.

“Wonderful!” she said.

I then tried to summarize our feelings by saying that the collaboration idea seemed superfluous. Neither of us teaches in a vacuum. I read lots of textbooks and talk to lots of teachers.  James had a lot more experience than I do (he’s been teaching for 22 years) so he has acquired knowledge as well.  I didn’t think that this 2-hour collaboration every month was going to add much more. In addition I said I was getting mixed messages.

“On the one hand I’m told by the administration that I’m doing great, and I hear from parents that I’m doing great,” I said.  “But then I’m told that I MUST attend this PD. Is there something about my teaching that’s lacking?  What is this about?”

She assured us that there’s nothing lacking in our teaching and that she’s sure we are both fantastic teachers.

I said “What is it then?  Is this about test scores? Is that it? They think this will raise test scores?”

She had no answer for this except something that I can’t remember.

She saw the handwriting on the wall and said “No use beating a dead horse” and said she would talk to the administration about it.   I felt a bit sorry for her, but not that much.

Later on in the day I met with the principal on another matter. Normally she is quite cheery but she didn’t look happy to see me, so I knew she was disappointed.

But the next day she was cheerful again, life went on as normal and another of life’s disappointments had passed.