We’re Saying the Same Thing, Dept.

One well-known gambit that is used by those seeking math reforms in debates with those who take a traditional view of math education is to show how much both camps have in common. That is, traditionalists don’t rely solely on whole-class and direct instruction; they incorporate discovery and have students work in groups from time-to-time. And progressives don’t rely solely on discovery approaches and collaboration. The reformer will use this in arguments and say “I think we’re both saying the same things.”

Actually, speaking as a traditionalist, we’re not.  Yes, some people have a lot of success using student-centered, inquiry-based techniques, and others have success using traditional approaches.  But there is the question of “balance”: how much of each is being used.  There’s also the issue of misrepresenting how traditional math is and has been taught: i.e., traditional math teaching relies on “rote memorization” without context or understanding, or connecting concepts to prior ones.

Another gambit used in the argument is one that is featured in a guest blog at Rick Hess’ “Straight Up” blog.  In it, the guest blogger, Alex Baron, states:

[G]iven the multifarious nature of students, teachers, and school contexts, it seems clear that no single prescription would work for all, or even most, students. However, policymakers proceed with “research-based” inputs as if they would work for everyone, even though this contravenes our foundational sense that no two students are the same.

There are variations in effectiveness depending on the student. But that doesn’t negate research that demonstrates positive effects on large populations of students, such as Sweller’s “worked example effect”, scaffolding and “guided discovery”.  Despite such evidence, there will always be those who claim “Ah, but there are exceptions.”

Yes, there are.  One rather inconvenient exception is that students with learning disabilities seem to do better with explicit instruction than with discovery-oriented and other reform type approaches. And in fact, such exception raises the inconvenient question of whether and to what extent the reform-type approaches may be causing the increases in math learning disabilities over the years. And if that is the case, why not rely on the remedy in the first place? (See in particular this article, an updated version of which appears in this collection of articles on math education.)  In addition, there are many exceptions to the approach that “understanding” must always come before procedure.  With respect to the latter, many people have interpreted Common Core standards as requiring “instructional shifts” that place understanding first. (See this article.)

I am reminded of something said by Vern Williams, a middle school math teacher who served on the President’s National Math Advisory Panel in 2006-2008:

I have always stated that if a reform minded teacher produces competent, intellectually passionate students, they will absolutely escape any criticism on my part. But the opposite seems never to occur. Regardless of stellar results, the traditional teacher will always be criticized for being a self centered sage on the stage, controlling student learning and running a draconian classroom. Their students may be the happiest most accomplished students of all time but the teacher will never be good and pure until they cross over to the reform side.

I guess there is no end to the gambits of “we’re all saying the same thing” and “no one size fits all”.


2 thoughts on “We’re Saying the Same Thing, Dept.

  1. Alex Baron says:
    “Whereas math features correct answers, the complexities of life usually don’t.”

    Um, what subject are you teaching, math or “life?” BTW, math treats no one right answer in many ways, as with multi-objective optimization and searching for a Pareto front. I know the person who developed “Set-Based Design” for flexible product development. I’ve developed many different merit functions for optimization. Some of my programs have drawn optimal contours of two independent variables to see all solutions within 10% of the optimal value. Just look in Consumer Reports to see their weighting functions. The comment above demonstrates ignorance. Multi-dimensional optimization is a fascinating mathematical subject, but these educators have absolutely no clue. I recently gave a formal paper on large scale multi-disciplinary optimization where the variables can extend over the infinite variations of geometry. Math deals quite well with the infinite complexities of life, whatever merit functions you chose.

    My recent work creates an open source programming framework that allows subject matter experts in any field to define merit functions and to combine different stand-alone calculations to find new solutions without writing a line of code. So much for trying to get all kids to “code.” They should be working hard to become subject matter experts.

    Also, from a previous thread, Carol Dweck says:
    “We’re working to reframe the question, “What does it mean to be good at math?””

    This is still obscene.

    Back to Alex:
    “Although most of us acknowledge the lack of a single path forward that will work for all—that is, we’ll always be “lost” because there isn’t a singular way to educate the infinitude of student needs—we don’t seem to be open-mindedly wandering.”

    PBL isn’t opt-in or out. I never saw “different learning styles” EVER chosen by the student, and traditional and memorization were never even considered as options. Then there are the low slope CCSS expectations that guarantee that the only ones properly prepared for the math track split in 7th grade are those students who get help at home or tutors with enforcement of proper skills. The goal is not better “open-minded” wandering when you know what works for all of the successful cases.

    “In education, to implement an intervention is necessarily to modify it. A teacher’s personality, attitude, and other qualities deeply affect how an intervention is rolled out to students, whose own limitless diversity also reciprocally changes the intervention. Obviously, the same is true for the diversity of school contexts.”

    So who’s variables or “style” define the process, content, and expectations: students or teachers? Alex claims that student “diversity also reciprocally changes the intervention”, but he isn’t offering them an individual opt-in or opt-out choice in the matter. We all know that differentiated instruction does not work. It’s evolved into differentiated learning where teachers choose the “style” according to their needs and then claim that individual students can get something out of a common in-class group project at their own level. Meanwhile, STEM parents do all of the necessary pushing of daily mastery of p-sets at home and with tutors – the ONLY process that is shown to create success. Alex wants teachers to be able to individually wander according to their own style, but students don’t have any power to “reciprocally change the intervention”, let alone opt-out. It’s all about them.

    “My hope is to dismantle that unsavory accretion and transform it into something that the students will, well, savor.”

    That defines success – to have a process where the kids look engaged? If they then don’t succeed, it’s their fault. Just point to those who do succeed and don’t ask them what they did at home or with tutors.

    “What does it mean to be good at math?””
    Savoring. It’s all about them – the process and not results that open career doors.


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