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.