Tom Loveless of Brookings Institution coined the phrase “dog whistles of reform math” when referring to the Common Core math standards. He was referring to code words embedded within the standards that serve as cues for reform-minded/progressivist educators in interpreting what are purported to be pedagogically neutral standards.
A recent article discusses this back-and-forth and contrasts traditionalists against progressives in the usual manner. Representing the reform side of the arguments inthe article, are Alan Schonfield, a mathematician from UC Berkeley, and Steven Leinwand, a lead research analyst at the American Institutes for Research (AIR):
“The idea of practicing and practicing and regurgitating a procedure flies in the face of everything we know about how to take this body of knowledge called mathematics and have it work for everyone,” rather than just those at the top of the class, said Leinwand.
He argues that despite the noise, the Common Core, and the similar math standards states have held onto, are working for parents, students, and teachers. He rejects the arguments made by the traditionalists, whom he said are only animated about protecting their supply of high achieving math majors, rather than ensuring that each student has a solid foundation in the subject.
“Why the hell, after 100 years of that kind of math teaching” said Leinwand of the traditionalists, “was the U.S. doing so poorly, until recently?”
Aside from the usual mischaracterizations of traditionally taught math, I was particularly interested in this last statement of Leinwand’s and wondered what data he was using to bolster his argument given the rise of the remediation courses in math that college students have been taking over the past two decades. (Some of these issues have been discussed previously here.)
I was also interested in a statement attributed to Schonfield on the debate overthe interpretation of the standards vs the standards themselves:
In an email exchange with InsideSources, Schoenfeld said that the Common Core had become a “Rorschach test” that people use to project their feelings about education. So while the debate over math practices is real, and the Common Core aligned math standards actually are more amenable to progressive teaching styles, the math standards themselves do not mandate how the subject should be taught.
It is true that on the Common Core website, we are assured that “These Standards do not dictate curriculum or teaching methods”. But his statement that the standards are “more amenable” to the ideas of reformers/progressivists aligns with Tom Loveless’ “dog whistle” theory which would explain why many of the Common Core inspired assignments shown on television or the internet, bear the reform/progressivist imprints: student-centered and discovery-driven assignments; group-based and real-life-relevant; touted as fostering ‘critical-thinking.
The dog whistles that are picked up by reformers/progressivists are embedded in the standards:
- “…explain the reasoning used.” (2nd year/1st grade)
- “Explain why addition and subtraction strategies work, using place value and the properties of operations. (3rd year/2nd grade)
- “Understand the relationship between numbers and quantities… (K)
- “Understand a fraction as a number on the number line…” (4th year/3rd grade)
The dog whistles of “understand” and “explain” feed into a key component of Common Core: A set of 8 standards called “Standards for Mathematical Practice” or SMP’s. The SMPs are eight practices that 1) supposedly embody the work habits and general mode of thought of mathematicians, 2) were defined largely by non-mathematicians. They also were based on what were called “process standards” in NCTM’s standards and were one of the main mechanisms for putting into action the reform math practices.
The SMPs are these:
1.Make sense of problem solving and persevere in solving them
2.Reason abstractly and quantitatively
3.Construct viable arguments and critique the reasoning of others
4.Model with mathematics
5.Use appropriate tools strategically
6.Attend to precision
7.Look for and make use of structure
8.Look for and express regularity in repeated reasoning
Taken at face value, they are seemingly benign. For example, there’s nothing wrong with the first point: “Make sense of problem solving and persevering in solving them.” Who wouldn’t want this? But the words “problem solving” are a signal for convoluted “real world” problems and “just in time” learning. The SMPs are largely interpreted as a means to teach “habits of mind” often outside of the context of the math courses from which they would arise naturally.
They don’t have to be interpreted this way. But the reformers/progressivists’ view of CC in general and the SMP’s in particular is that they require inquiry activities and collaborative group work, students solving problems in more than one way and most importantly for “explaining their answers” rather than simply showing their work.
For this last, the assumption is if students cannot explain their reasoning, in writing or otherwise, students lack understanding. But since students in lower and middle grades are novices and lack skill in articulating ideas, such explanations often have little mathematical value. It often amounts to students engaging in the exercise of guessing (or learning) what the teacher wants to hear. More “rote understanding” via “rote explaining”
It is my hope that we come to some agreement on how best to teach math, and in that vein, in closing, I offer these guardedly optimistic statements:
- Whether understanding or procedure comes first ought to be driven by subject matter and student need — not by educational ideology
- Prior learning and knowledge is the greatest determinant of what children can learn, regardless of their physical age.
- Curricula should be both mathematically coherent and logically sequenced for learning from novice to expert.
- “Discovery” should not be conflated with “teaching understanding” as if they are one and the same
- Mistakes in educational practices should not be clung to just because of the time spent making them