Standards are political documents. They are the result of legislation, statute, and bureaucracy. Standards also are imbued with authority by professional organizations, corporations, local administrators, and educators themselves. They are integrated into systems, policy, practice, and culture. Thus, standards are political in the rawest sense of the word — they have power.
In our current system, that power is inextricable from the standards themselves. The power carried by the standards can also be wield by any of the above people or groups. Their power ultimately shapes the experience of students and teachers and outlines the type of schools we have. Standards have the power to either constrict or widen our imagination about what math class can become. They also exert a very real power to limit what math class is.
The current standards strongly lack in their capacity to empower bold, new visions for math class, and their construction makes them apt and easy instruments for enforcing narrow and rigid forms of teaching and learning. As such, we need new high school mathematics standards that are both inspiring of broader visions for mathematics education and are written with a consciousness to their inherent power.
Power Over What Could Be
It is perhaps easiest to begin with a thought experiment. Imagine two math classes. First, a traditional, set and get class: desks in rows, students learning and repeating rote processes. Second, a learner-centered, vibrant, human, and transformative class: students engaged in deep, conceptual work that is the result of their interests and passions. Students doing projects that are relevant, that they have choice in, and that have real consequence in the community. Students able to grow at their own pace. A classroom where there is time for play and joy, where new mathematical ideas are invited, and tangents welcomed.
Now, read through the current high school mathematics standards. All 25-plus pages. Which class do they seem to describe more? Does reading the current standards make it harder or easier to dream of new and innovative classrooms?
The current high school mathematics standards read like a list of abstract and arcane rules and procedures: use the process of factorizing and completing the square…solve rational equations…find inverse functions…prove that a line parallel to one side of a triangle divides the other two proportionally…. They read like a slightly reworded table of contents of an outdated textbook. The current standards are probably best described as school-mathematics for school-mathematics sake.
One might counter by pointing to the Standards for Mathematical Practice (SMP). Certainly, the SMP represent a deeper, more conceptual approach to mathematics. But the weight of eight standards for practice simply cannot match the weight of the over 100 content standards (some of which contain multiple parts). The current standards place the bulk of their import and attention on the proceduralized skill that has long typified school-mathematics.
Thus, the current standards do not point us toward the new and innovative classrooms our students deserve. They draw a boundary around what mathematics education can be. Though some might argue that this boundary is only a base and can be built upon, it is a base so large that it effectively crowds out space for anything new. As the foundation for planning and curriculum, the power of the current standards severely limits our collective imagination about what math class could be.
Power Over What Is
The wonky technicality of standards documents may make them seem innocuous, but they can be and are used to exert real power over classrooms. If the current standards represent any intent to transform math class beyond a transmission model of learning, their form and content have allowed them to be tools for just the opposite.
First consider the mode of instruction incentivized by the current standards. The current standards facilitate a system where curriculum and instruction design begin by looking at the standard first and not at the learner. Practically, districts and schools funnel the standards into curriculum maps and guides and then select a small set to cover in over a period of time. Schools and teachers are encouraged to atomize these into even smaller learning targets.
The highly procedural orientation of the current standards positions them as the first step in a chain of deconstructing, analyzing, assessing isolated and technical skills. To put a finer point on it, the current standards very much facilitate a model that says, “This week we are solving quadratic equations in standard form where A=1….Quiz on Friday…Next week A does not equal 1!”
This is not necessarily to say that this is the theoretical model of teaching and learning intended in the current standards. Rather, it is the model of teaching and learning that the current standards incentivizes and imposes through their construction. For instance, the current standards are often defended by saying that they specify only the ‘what’ and not the ‘how.’ And yet, in enumerating the ‘what’ so precisely and at such length they can all but force a ‘how.’ Or to be more fair, they have contributed to system that pulls the ‘how’ closer to the more rote and traditional. Even if this was not intention of the writers it is certainly how the currents standards are being used, a result clearly a function of their form.
This type of power is certainly of a more abstract, systemic, and social nature. Such power alone can be difficult to resist or counter. Standards also enact more explicit power through administrators, bureaucrats, instructional coaches, etc.… Educators in these roles can and do use the current standards to enforce a transmission model of teaching and learning. They create policies and practices built on teachers dissecting and delivering standards to students who then reproduce standards in a way that is easily assessed for quantifiable data. Such policies and practices lend themselves more readily to a very narrow and rote type of mathematics. The current standards provide both the tools and rationale for facilitating this work as well as the power for enforcing it.
Thus, teachers must contend both with the systemic and social pressure deriving from the current standards as well as very real policy and practice requirements from people who have authority over them. This is not to ascribe any mal-intent (as the described above the standards themselves do not paint a wider picture of mathematics to begin with). Rather, it is to acknowledge that the form and content of the current standards enact power in very real ways that inhibit us from moving toward more holistic, learner-centered, humanizing, personalized, and deeper approaches to high school math.
Lastly, it must be mentioned that the current standards are written in such a way as to be easy fodder for standardized assessments at the national, state, and even local level. It is often argued that the standards should not be held responsible for the sins of assessment, but when the standards lend themselves so easily to standardized forms of assessment its difficult not to assign some culpability. Standardized assessment at any level, of course, introduces another dimension of power that is ultimately emboldened by our current standards.
Call for New Standards
Right now, there are movements for more learner-centered classrooms. There are movements to re-humanize mathematics, to make the study of math more just and historically situated, to do more project and context-based learning, to personalize learning, to honors different paces of learning, to make school more relevant in a world subject to computerization and automation… Certain mathematical content is becoming more relevant: data science, the math of elections and voting, algorithms… Some combination of these movements are embraced by nearly all educators most of whom acknowledge that school can no longer be what it always has been.
Some would argue that each of these movements could use our current standards for high school mathematics. In other words, asserting that our current standards are not mutually exclusive with, and maybe even support, such moves toward progress. In a theoretical sense, this might be true if the current standards were purely a resource that could be consulted (or ignored) secondary to pursuing any of the higher values of these movements. But such thinking ultimately ignores the very real power dynamic enforced by the current standards.
In many places, educators are making progress toward more innovate and inclusive mathematics classrooms. But too often they must do this is opposition to some form of authority that uses the current standards to justify old and transactional ways of doing things. Even more often educators are not given the space to take the risk necessary to build the new and exciting classrooms our children deserve – their bounds so slightly drawn by what the current standards will allow. And, perhaps most often, the current standards do not allow, let alone challenge, us to imagine math class as anything more than a carefully curated tour of an arcane and escalating grammar and syntax.
We need standards that walk a careful balance. They must point toward a more critical, learner-centered version of mathematics. One that honors history and context. One that wrestles with big and important questions. They must also be more conscious of their inherent power than the current standards. They must be written to minimize the degree to which they can be used to encourage rote and regressive practices. They must shift the ultimate power and responsibility for teaching and learning back to classroom, teacher, and student. In short, they must inspire us to better, fuller version of math class, but also mitigate the ways in which they can be used to require, compel, and coerce.
New standards will certainly not immediately reverse our systemic and cultural orientations toward standardization and the transmission model of education. New standards can, however, alleviate some of very real power and pressure educators feel to move in those directions. The new standards certainly will not fully or accurately capture the virtues of more just and humanizing approaches to teaching and learning. But they could call us to dream bigger about the types of math class that are possible and at least not get in the way of us getting there.
