These guiding principles propose a new set of standards for high school mathematics that, in general, should look nothing like the current ones. Everything from their structure, language, and underlying philosophies should indicate a new approach to high school mathematics. They should be standards that eschew standardization. The principles laid out here are not intended for reorganizing or re-aligning or editing the current standards, but for catalyzing a wholly new vision for what standards could be.
Fewer – There must be less than ten standards in total for all of high school. New standards share the ideal of depth articulated in previous standards but recognize that depth occurs within the learner and develops in many and varied ways. Depth cannot be manufactured at the standard level. Standards can only point toward depth — they cannot prescribe it. Thus, new standards must open space so that students and teachers in turn have space to actually pursue depth. That space can only exist when there are far fewer standards to address. ‘Fewer’ allows for deep, sustained investigation; for students and teachers to co-create learning experiences; for explorations, divergences, and tangents; and for seriously entertaining different perspectives. ‘Fewer’ allows for a bigger, more enduring, and more meaningful conception of high school mathematics.
Broader – Each new standard must be an open and widely-framed and enduring question, pursuit, tension, or capacity (eQPTC) that honors learners as humans with experience and in context who both are shaped by and who also have the capacity to shape mathematics. Each should be worthy of ceaseless investigation. A single standard should be something that can be explored from different perspectives, in different ways, and to different depths over the course of a secondary experience – it is never ‘mastered’ and is regularly revisited. eQPTCs are not explicitly tied to traditional content and are certainly not monads of knowledge and skill. Rather, eQPTCs recognize the large exchanges between the discipline of mathematics and people. Each standard should be written as a single statement or question possibly followed by a short paragraph of exposition.
Learner-Centric – The language of the new standards must not refer to external, decontextualized monads of knowledge. Instead, new standards must be written from the perspective of questions, identities, and capacities that begin within the learner. Similarly, the new standards must be written in a language that is understandable to students and presented in form that students can interrogate and digest. In contrast to the current standards, the language, style, and presentation of the new standards must shift power to the learner and away from the practitioner. New standards should support a truly learner-centered classroom and facilitate learners using them to plan and reflect on their own learning experiences. This must be done in a way not to encourage a checklist or grading mentality, but so each standard invites different and deeper reflection with each visit.
Concept Connections, Not Requirements – The eQPTCs are the totality of the new standards. But each eQPTC may also suggest content that could be used to develop it. Any content included would explicitly not be part of the ‘required’ standards, but merely possible ways of addressing the larger eEPTC. Any included content must be larger mathematical concepts and questions that themselves also allow for further exploration, multiple perspectives, and divergent thinking. Included concepts may also connect with multiple eQPTC. Moreover, potential content should also include ideas not found in traditional high school curricula, for example big data, game theory, topology, algorithms, or the mathematics of voting. Description of such content should be limited to single words or phrases.
No Technical Procedures or Skills – eQPTC must be written in a way so as not to explicitly include any technical procedure or skills. Certainly, anything that can be demonstrated in a series of steps and then repeated should not be included in the new standards. New standards must challenge the long obsession textbook-school math. Yet, new standards should also not explicitly eschew the value of skills. A high-level standards document simply is not the appropriate place to include them. New standards call students to bigger questions and ideas that will inherently motivate the need for skill, but that skill need not be prescribed less the tail wag the dog.
Designed for Humans – New standards must explicitly call for a mathematics that embraces pursuits fundamental to our human experience. They must name the need for things like cultivating joy, developing a sense of awe and wonder, practicing creativity, play and struggle, and allowing for failure and un(re)solved problems, etc… This principle many manifest as an individual eQPTC or some larger cross-cutting feature of the new standards. *
Historical and Critical – New standards must call out the need to understand the historical context in which mathematics develops. They must highlight the importance of investigating the mathematical contributions, practices, and expressions of multiple cultures. Moreover, they must engage learners in developing a critical lens for analyzing how power and group dynamics have affected and continue to affect the development of mathematics. This includes analyzing the power of mathematics itself and its role in oppression and liberation. New standards must not develop a mathematics that is isolated, deceptively abstract, or falsely universalized. They must develop a mathematics that is situated, transparent, and critical. Learners must see the full story of math and their role in writing it. New standards may explicitly point learners to examining their relationship to math and their mathematical identity. The principle many manifest as an individual eQPTC or some larger cross-cutting feature of the new standards. *
Mathematx Informed –Mathematx, as conceptualized Gutiérrez (2017), may be difficult to envision within the current structure of school (and certainly within the structure of the current standards). New standards, however, must at the least not be written to exclude the growth of Mathematx in classrooms. The underlying philosophies of In Lak’ech, Reciprocity, and Nepantla may in many ways be inconsistent with the philosophies traditionally associated with standards. But new standards should be wholly different approach to standards, one that completely re-conceptualizes the meaning of standards themselves. As such, writers of new standards must seriously consider how they can be informed by a Mathematx lens and consider possible ways that new standards could be written to cultivate a living Mathematx. *
Concurrent and Equal – There must be neither order nor hierarchy in the new standards. The development of mathematical thinking is not wholly linear. So, the new standards must not imply that certain eQPTC come before or after others. In fact, it must be clear that eQPTCs may intersect and overlap. Students should revisit eQPTCs each time finding new discoveries and connections. eQPTCs are not meant to be stand-alones but are intended to be simultaneous and weaving pursuits in any mathematics experience.
An x-Standard – There must be a standard intentionally left blank – literal space allocated and clearly demarcated in the document for a standard that is not there. An x-standard recognizes that no enumeration of mathematical thinking or ideas is complete. It is a reminder that educators must make space to recognize the mathematics already practiced by learners and their community (which may not be codified in the standards). It also affords space for thoughts, ideas, and questions that emerge within mathematical learning communities themselves and encourages educators and learners to view themselves as shapers of what mathematics is. An x-standard also acknowledges that no matter how inclusive the writing process, standards will always reflect a limited and biased view of the authors. An x-standard offers a line of defense for educators and students wishing to pursue any of the above.
Portable – new mathematics standards must be able to survive the dissolution of the mathematics class. Innovative schools are moving away from traditional class structure and toward interdisciplinary projects, deeper learning experiences, etc… Standards must represent a mathematical lens that could be honed, applied, or modified in multiple settings. The current standards lend themselves more to an artificial mapping of abstract mathematical procedures to other content – a distortion of mathematical practice. Instead, and more reflective of actual mathematical practice, the portability of the new standards should allow students to see and develop the mathematics in context and in experiences that happen outside of math classrooms.
Short, Intentional Presentation – New mathematics standards should be able to presented in a document that is a single page front and back — two at most. The values undergirding new secondary standards must be visible in their presentation.
Statement of Limitation – New standards must include a statement of how they are not intended to be used. For instance, they should not be considered exhaustive or prescriptive of a student’s mathematical experience. They should not be things to be completed or checked off. They should not be sequenced or paced. Such a statement cannot, of course, prevent malfeasance, but it can give educators a defense when standards are being used inappropriately.
*Important Note: The guiding principles of Designed for Humans, Historical and Critical, and Mathematx Informed are intended to be implemented in coherence with the larger conceptual framework of these guiding principles. These guiding principles should not result in a laundry list of ‘important’ historical moments, or a dozen sub-standards of identity development, or the list of indictors of joy. The implementation of these three principles must still adhere to the ‘fewer’ and ‘broader’ guidelines. The idea is not to standardize these deep and human approaches to education. Rather, the hope is to completely re-orient our understanding of what standards can be. The incorporation of such major shifts, while cohering with other guiding principles, should influence the entire writing and framework of the new standards.
What’s Next
The guiding principles laid out above are not indented to lay a rigid or dogmatic claim on a vision for future standards. They are just a starting place, and they certainly should be interrogated by diverse and wide-ranging set of educators. These guiding principles are intended only as a statement of broad ambition showing how dramatically different our high school mathematics standards need to be.
It is also important to state that I outline these guiding principles not as an endorsement of a standards approach to education, but in recognition of the cultural and political reality that standards seem to be have become entrenched in our educational system. If standards are to be a part of our educational landscape, they should be shaped so they are less damaging, more inclusive, and more responsible with how they wield power. This is one attempt to frame how a drastically different approach might look.
