When a student in the Numerimurgy program is given credit, we are recognizing that this student has learned a credit’s worth of math skills, starting where they were when they started the class, rather than comparing them to an arbitrary benchmark of where they should be, a benchmark which was set by someone who does not know this student as a human being, nor the student’s needs, motivations, or goals. We also recognize that this student’s progress shows that they can learn at a pace that can carry them to any arbitrary benchmark should they choose to reach it, and if given the time and support to do so.
We do not wish to contribute to the intellectual-debt model of learning, which assumes that students can be ‘behind’ and need to ‘catch up,’ even on their first day. Instead, Numerimurgy is based on the idea that education should be about learning, and that learning can only begin at the point where the student is now and will only move effectively in the direction the student wants to go. Forcing other requirements onto a student without their consent is counterproductive and can result in math anxiety, math trauma, truancy, and dropping out of school.
That said, we also recognize that school districts, state departments of education, and other organizations have their own needs as well. This is why the individual skill-based Numerimurgy levels align with skills in the Common Core curriculum. Doing so makes translation from individual skill acquisition at a human level to more bureaucratically-driven considerations easier, while keeping in mind the real-world contexts students are being prepared for. The average year of school corresponds to 7 Numerimurgy levels, so this amount of progress should be given credit for a full year of math, all else being equal.
To look more closely at the mismatch between the idea of grade level/graduation requirements and what happens in the real world, the average American adult has approximately 6th grade math skills. Teachers of subjects other than math typically have closer to 8th grade math skills. Yet most jurisdictions require that teens (with brains that have not yet fully matured) master concepts most of their parents and teachers don’t remember how to do. The reality is this: students are being prepared for a world where some people do advanced mathematics, but most people don’t and don’t need to. There is a unique point for each student where learning more math is abstractly “good” but becomes a game of diminishing returns. What matters more is that each student continues to challenge themselves to challenge their minds and continue to learn.