I never passed English in high school. Can you tell?

Grade school was a miserable experience. As a socially immature individual with attention deficit hyperactivity disorder, public education and I were never moving at the same speed. Most days were a constant struggle between acting out and doing just enough to get the teachers to leave me alone so that I could read whatever book I’d brought from home. The experience mercifully ended when I sat in the vice principal’s office facing two options: take and pass the GED or face expulsion.

So whose fault was it? That’s a trick question.

To blame any teacher of mine is a ridiculous notion. Even properly medicated, an individual with ADHD is highly driven to seek out that which is most stimulating to them – be it acting out in uninteresting classes or completely ignoring instruction in favor of reading ahead in the book. To spend as much time as is necessary to handle a student like I was is simply not feasible or rational within our current system. There are 30+ other students who require less effort to achieve greater academic success.

Am I to blame then? Well, if the intention was for me to learn to conform and thrive within the given constraints, I failed spectacularly. At the same time though, how realistic is it to expect someone who is twice their mental age in some areas and half their age in others to succeed in a fixed pace, rigidly structured learning environment?

I failed to adapt to the system, and the system failed to adapt to me. If the goal is to see me educated, where should the responsibility of adaptation ultimately lie? My argument is that adaptability must be intrinsic to the educational process. What is needed is an ever evolving, always on “teacher” with infinite patience and the capability of drilling down to minute granularity any subject matter it is versed in.

Science fiction? No, it’s the future of education.

In this post I am going to lay out a framework for adaptive education. Long-term, it can be fully automated, but it doesn’t need to be in order for the major benefits to be realized. Automated or not, our next generation educational system should possess the traits of granularity, assessability, adaptability, flexibility, and accessibility:

Granularity

Students often possess a mismatched and incomplete set of the prior knowledge required to grasp a new concept. This is something well understood by a skilled tutor or a teacher inheriting students from another program or grade level. There are many reasons for this – insufficient prior instruction, lack of unified lesson plans, student aptitude for different concepts and even the entropic process of neuronal re-purposing that the brain does over time i.e., forgetting stuff.

To correct this, the system must be able to break a concept down into its constituent components – what I call granularity. Consider this mathematical expression:

2 x (3 + 4) = ?

This is simple algebra, right? It’s actually a combination of concepts: multiplication, addition, order of operations and equality. Further broken down, the symbols 2, 3 and 4 represent quantities. Imagine attempting to solve this expression if you don’t know how to add 3 to 4 or even that the symbol 2 represents a quantity equal to the number of thumbs you (should) have.

Granularity can be achieved by constructing a sufficiently comprehensive knowledge tree for each concept:

The tree gives us a path from the high-level (in this case, what I’ve called “Algebra”) to the low level (say, addition or even using numbers). From this we can algorithmically determine what pre-requisites are needed to master any concept, and which areas to focus on if remedial instruction is required.

How exactly does this work? To tailor instruction for a particular student, a knowledge tree should be traversed in depth-first search order, skipping nodes representing concepts already mastered. This flow chart demonstrates the full procedure for “Algebra”:

You’ll notice that regardless of what prior information the student has, the proper path to teach them falls out automatically. For example, there is a student who has mastered the concepts of “Numbers” and “Multiplication.” To teach them “Algebra”, the system would take the following steps:

1. Teach the student “Addition”
2. Teach the student “Order of Operations”
3. Teach the student “Equality”
4. Teach the student “Algebra”

Knowledge trees should be as granular as possible; each node ideally represents only a single, discrete concept. The “Addition” node I have in my tree above does not include the addition of complex numbers. Complex numbers would have their own node, as would their addition and multiplication. Each of these would have as children the addition and multiplication of real numbers as well as the “complex numbers” node itself.

See how the “Algebra” node does not seem to introduce any new concepts? This is OK. “Algebra” is an amalgamation of many concepts, and it is useful to know whether a student can utilize several of them at once to solve larger problems.

Amalgamation nodes can also be a collection of concepts that represent a discipline or trade. For instance, an employer may be looking for a “Math Whiz” to figure out some company problems. They may define “Math Whiz” to include the concepts of “Mutli-variable Calculus” and “Ordinary Differential Equations”, which are of course amalgamations themselves.

Assessability

One of the most controversial issues in education today is determining student “success” or “achievement”, particularly in regards to linking it to teacher compensation. I’d like to sidestep that entire conversation with my own, apolitical definition of assessment: a percentage score of demonstrated proficiency in a concept. It exists in two forms:

A running assessment is the set of in-process evaluations that occur during instruction. In colloquial vernacular, this is your “pop quiz” that a teacher may assign after a short reading assignment or upon conclusion of an instructional video. Running assessments help evaluate the effectiveness of particular instruction, but are usually not used for determining if a concept has been mastered by the student. The target score for a running assessment should be 100%. Any less indicates insufficient knowledge transfer or comprehension, and further instruction is required.

Formal assessments are given once instruction is complete, after reflection and studying by the student. This is your “final exam” by which mastery is tested. The actual form will of course vary per subject, but what is clear is that two interpretations of a student’s score are necessary.

The classic percentile interpretation determines how well a student performed relative to others who took the assessment within the same time period. A score of 50th percentile is desirable, as it indicates that the student was not over or under prepared by the system before evaluation.

The other interpretation is an absolute level of mastery. Tests should be designed so that a 90% indicates sufficient mastery to apply the concept while learning new ones that would depend upon it. For instance, a student should never be expected to answer “2 x (3 + 4) = ?” until they have answered correctly 90% or more questions of the form “2 x 7 = ?” and “3 + 4 = ?”.

Ultimately, mastery is a “yes” or “no” question. Administrators can create whatever feel-good classifications they want above that (e.g., “the 99% club”), but a student’s mastery is dependent upon a 90% or higher score in the final assessment, and nothing else. Otherwise the system is incapable of properly guiding a student’s path.

Why 90%?

To ensure consistency in the skill levels over an accumulation of many concepts. If students are granted mastery over a larger range, say, 70% to 100%, then over time mediocrity could accumulate into a hard-to-diagnose deficiency in knowledge. It is not 100% because we’re not evaluating robots.

If you set the mastery score to 90%, how will students be able to excel?

Students will excel by unlocking access to new concepts faster than their peers. I’ll explain this in further detail later.

Adaptability

At one point in my schooling, it was determined that I had an SLD in English. As a result, I was placed in a special class designed to “help people like me.” A frequent activity in there was taking turns reading passages from our textbook out loud and then discussing what we read. Most of my peers struggled to pronounce words and read at anything approaching a normal speaking pace. I, however, took great delight in inverting my book and reading (and pronouncing) my passages backwards at full speed, feigning some exotic form of dyslexia.

Like I said, I was socially immature.

My problem wasn’t a learning disability. I was philosophically opposed to the subject as it was presented. Did I mention I’m an INTP? (NOTE: I make no claim regarding the efficacy of Meyers-Briggs testing). I found the reading and discussion of one’s personal opinion on works of fiction to be so abhorrent that I refused to engage in any activity related to the subject of English from about 6th grade on. Due to a failure to identify the actual problem (a lack of interest) I was incorrectly placed into a program where I did little more than interfere with the instruction of those who legitimately required the extra attention. It was the exact opposite of what should have been done.

I tell this story because it makes an important point: humans are not so readily classifiable, particularly when it comes to education.

For maximum effectiveness, a learning system must be dynamically tailored to the individual needs of each student, and the decisions it makes constantly verified. The aforementioned granularity and assessability are the basic tools to do this, using them in an educational feedback loop is how we achieve adaptability.

So how should this feedback loop work? Follow me to the next page: