Standards2030

Granularity of Knowledge

The KMS decomposes knowledge into its smallest meaningful units. This granularity enables precise tracking, flexible recombination, and detailed analysis of learning objectives.

During my career in K-12 science education, the Big Ideas philosophy has been ascendant. This is the idea that kids should spend their time thinking about unifying concepts of science, ideas having the power to explain many seemingly-disparate phenomena, like Cell Theory and Conservation of Energy. I’ve heard teachers say “I teach the things that students will remember years after they’ve left my class.”

I’m on the other side of this. I like the Little Ideas, ideas like “Ribosomes translate messenger RNA to synthesize proteins”. I think they are beautiful, and I want kids to have the opportunity to learn and remember as many of them as they can. This is doubly true because kids are at the peak of their ability to learn and remember things!

Furthermore, I doubt that Big Ideas play much of a role in facilitating learning, at least not initially. I believe that most people learn by first accumulating little pieces of knowledge and only later, maybe, realizing that these pieces are particular instances of a unifying idea.

While I am energized by Little Ideas, the KMS strives to contain all of the ideas of a domain of knowledge. Operationally, this means

• The KMS breaks down knowledge into its smallest feasible units.
• No idea is intrinsically more important than any other; there is no concept of “importance” built into the tool.

Of course, the KMS contains statements of big ideas like energy conservation. Out of the box, these are no more important than any other statement, but you can give them whatever prominence you want by the way that you incorporate them in learning goals and describe them in a taxonomy.

Two-Dimensional Knowledge

The KMS assumes two dimensions of knowledge: what students know (Statements), and what students can do with that knowledge (Actions).

Here is how I came to this conclusion. In United States K-12 Science Education, the influential Next Generation Science Standards (NGSS) use three dimensions. The first two roughly correspond to concepts and skills. The third is the Big Ideas described above. My background is in physics so I am no stranger to Big Ideas; I have used conservation laws many many times. But I have never understood how they are a separate dimension from content. Consider “Energy is a conserved quantity” or, applied to a particular context, $\mathrm{GPE}_1 + \mathrm{KE}_1 = \mathrm{GPE}_2 + \mathrm{KE}_2$. That’s content. And I have never understood how to assess a Big Idea. I could check whether the student used the conservation of energy to get the correct final speed, but once again, that’s content. Am I supposed to assess how excited the student gets when thinking about energy conservation?

One can easily imagine even more dimensions: Environmental Impact, Social Justice, Depth of Knowledge…Once you permit multiple dimensions, there’s no stopping point. In reaction to this, my intent was to make the KMS one-dimensional, including only content, the KMS Statements. But after some thought I had to admit that this is not adequate, at least not for K-12 Physics. It’s not useful to state, for example, “Velocity is the instantaneous rate of change of position” without describing what the student is supposed to do with it. So I was forced to include the second dimension of Actions.

But I’m drawing the line at two dimensions! At least until I come across a knowledge domain that truly needs a third.

I think that the KMS could easily represent a one-dimensional knowledge domain in its current structure, perhaps by rendering all of the material as Statements and combining with a dummy Action to form Learning Goals. Extending to a third dimension would not be impossible, but it would require a substantial change in the database schema and would likely result in a substantial increase in complexity.

Hard Prerequisites

Prerequisite relationships between statements and between actions represent logical dependencies. In other words, if Statement A is a prerequisite to Statement B, then understanding B is impossible without first understanding A. This is sometimes referred to as a “hard” prerequisite. It is not a “taught before” or “nice-to-have” relationship. The restriction to hard prerequisites comes with several qualifications.

First, you can define whatever prerequisites you want. However, the course sequencing algorithms will treat them as hard prerequisites, so they may constrain sequencing in ways that you did not intend.

Second, the KMS does in fact quietly employ a “taught before” prerequisite. In the Syllabus module, instructors decide how to sequence entities that are not related by hard prerequisites. The result is a “pedagogical sequence” of learning goals that is cast onto a calendar.

Third, the restriction to hard prerequisites is not forced by technological limitations. Graph tools—databases like Neo4j, Amazon Neptune, and ArangoDB, and graphing software like GoJS (used in the KMS)—fully support multiple types of relationships among entities.

Ultimately, the decision to emphasize only hard prerequisites is based on concern that exposing multiple relationship types would make the tool too complex. This decision is a topic of ongoing discussion.

Learning Goals as Compound Objectives

Learning goals combine one or more statements with one or more actions to form complete educational objectives. This reflects the reality that meaningful learning involves both knowing facts and being able to apply them.

Not Constrained by Hierarchy

Knowledge resists top-down hierarchical organization. The category system provides optional organizational structure without enforcing a strict hieararchy. Terms can serve as both category names and category values, enabling multi-level organization where useful while avoiding the constraints of forced tree structures.

My takeaway from my professional experience is that hierarchies are not satisfying. Inevitably there’s something that doesn’t fit anywhere well, or that fits in more than one bucket, and you waste time arguing about it.

Sometimes the buckets themselves are weird. At a previous employer, my team was handed this organizational scheme: Biology, Physics, Chemistry, Earth Science, Space Science…and Botany. Yup, both biology and botany. I bet you thought botany was part of biology. We did too, but someone influential in the past thought differently, and my little team didn’t have the juice to change it. So we set up our own reasonable internal system, that made sense to us and suited our needs—I think it was Life Science, Physical Science, Materials Science, Earth Science, and Space Science—and translated to the ridiculous official categories when needed.

I hope you are never in a situation like this, but if you are, rest assured that the KMS can implement any of these organizational schemes just fine. The point is that the KMS is not organized top-down according to some heirarchy. The KMS is built bottom-up, on statements and actions. And as has been stated before, out of the box, no one is more important than any other, and they are not attached to any classification scheme.

Separation of Content from Pedagogy

The KMS separates “what to teach” (Knowledge Space) from “how and when to teach it” (Human/Time Space). This allows educators to make pedagogical decisions independently of content authoring, and enables the same content to serve multiple teaching contexts.

Democratization of Standards

This pertains to K-12 education. Historically, content standards have been produced by panels of luminaries and presented to the public in a fixed format, a pdf. The public’s choice was to adopt the document in its entirety, or not adopt it.

I want to open standards-writing to everyone. The KMS makes this possible by providing the content base (knowledge bases) and tools to generate standards from knowledge bases. I also want standards to be customizable. KMS users will be able to edit standards created by another user in the KMS environment. Furthermore, KMS users will be able to import any other set of standards, re-build it with KMS entities like statements, actions, and learning goals, and thereby gain complete control over it, for customization if desired.