In our previous examples, one important question was left unanswered: how can we determine when a student actually has mastered the memorization of a certain subject? This is an important question, because if we don't know when a student has memorized sufficiently, we don't know when to move on, which means we must estimate, further exacerbating the inefficiency of the system (it is highly unlikely that we move on at exactly the right moment if we are estimating).
Thus, a more effective appraisal of the students' readiness leads to a more effective teaching environment.
We really have two options for appraising students' progress: self-reporting or observation reporting (a role we assign to the teacher, for the sake of simplicity). In a traditional environment, both are costly activities.
If a pupil must determine his or her own state of readiness, there are two main problems. First, they don't know the material - that's why they're learning it! If they don't know what they're supposed to be learning, they must be provided with and understand a clear expectation of learning. Second, once they have this expectation, they must engage in self-evaluation during the the learning process. This self-evaluation is a distraction to the memorization phase (imagine our students making tally marks on correct/incorrect answers as they try and drill times tables). A main draw back to this method, though, is a lack of consistency and reliability among students. Some students will pass themselves too easily. Some will not be diligent in self-observation. Accuracy is hoped for, but not improbable. Thus, self-reporting is not feasible.
Observation reporting in a traditional environment is also unfortunately inefficient. The teacher theoretically is more free to conduct the evaluation, as he or she already understands the relevant material and is free to dedicate some mental processing power observing the students. However, the teacher doesn't have just one student to evaluate - they have an entire class full of them! Thus the observation step distracts less from students' thought processes, but it takes far too much time: if the teacher attempts to ascertain each students' progress between every question, the class will probably spend more time evaluating than learning. It is therefore impractical for a continual evaluation phase, and this is why evaluation often comes after longer intervals in the forms of quizzes, tests, and homework.
With the aide of technology, however, memorization can be highly adaptive, individualized, instantaneous, and in real time.
A prime example of this concept is found in one of my favorite learning platforms: Duolingo.
Duolingo is a fantastic and free resource for learning foreign languages. At the time of writing, Duolingo offers 66 courses between 23 different languages to 120 million users around the world. And Duolingo acts as both teacher and evaluator for all 120 million in real time on an individual basis.
When you initially begin using Duolingo, you have the option of taking a placement exam, to determine your proficiency. During the exam Duolingo is already adapting to you much as a personal evaluator would: it begins with easier questions, and continually progresses until you struggle, honing in on your real proficiency. Once it knows this information the real learning begins, but the evaluation does not. Your teacher keeps track of every question you've ever answered and how well you did. It remembers which words you "peeked" at, or spelled wrong. It remembers when you learned that word, and the last time you saw it, and feeds that information into an algorithm which estimates how likely you are to remember that word still, and drills you on words you probably struggle with more.
Here's a picture of some of the Spanish words Duolingo has taught me, together with their part of speech, the last time I saw it, and their "word strength:"
Does it have its drawbacks? Sure. For example, Duolingo isn't my only Spanish learning resource. Despite the fact that Duolingo believes I'm 2/4 on my word strength of "libro," I think that's one of the words I'm least likely to forget. Which means I'm going to drill it more than I probably should. Duolingo can't take that into account though, because it knows nothing of my "extracurricular activities." And of course, the algorithms can always be improved. But on the whole, the system works quite well for ensuring that I drill what I need to drill, when I need to drill it. This is one reason why a 2012 study found that 34 hours of Duolingo may be equal to a semester of college Spanish.
This method can and should be used in all learning environments. Though its application to language is quite simple, it can also be applied to the arts, reading and mathematics. There are already numerous platforms with this aim: Memrise, Newsela, and Khanacademy, to name a few.
Not only are these resources more effective than endless drills and exercises from textbooks to notebooks, these resources are free - an important point considering that collegeboard.com puts the average annual spending on books and supplies at universities at around $1,300 per student.
The teacher, of course has incentive to use such services: these are digital TAs who grade thousands of questions instantly without any wages.
So again, the question is: why do we continue to enroll thousands of students in an educational facility with an ineffective evaluation method when there are low cost, high benefit alternatives available?
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