Leveraging Cognitive Learning Strategies Requires Technology

by Justin Skycak on

While there is plenty of room for teachers to make better use of cognitive learning strategies in the classroom, teachers are victims of circumstance in a profession lacking effective accountability and incentive structures, and the end result is that students continue to receive mediocre educational experiences. Given a sufficient degree of accountability and incentives, there is no law of physics preventing a teacher from putting forth the work needed to deliver an optimal learning experience to a single student. However, in the absence of technology, it is impossible for a single human teacher to deliver an optimal learning experience to a classroom of many students with heterogeneous knowledge profiles, each of whom needs to work on different types of problems and receive immediate feedback on each of their attempts. This is why technology is necessary.

This post is part of the book The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). Suggested citation: Skycak, J., advised by Roberts, J. (2024). Leveraging Cognitive Learning Strategies Requires Technology. In The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). https://justinmath.com/leveraging-cognitive-learning-strategies-requires-technology/

The Problem: Cognitive Learning Strategies Remain Underused

It is common knowledge among researchers that the cognitive learning strategies discussed in previous chapters have the potential to drastically improve the depth, pace, and overall success of student learning. These strategies have been identified and researched extensively since the early to mid-1900s, with key findings being successfully reproduced over and over again since then. However, the story of the science of learning is a disappointing reality is that the practice of education has barely changed, and in many ways remains in direct opposition to these strategies.

The Blame: Teachers are Victims of Circumstance

So, what happened? Why does the potential of these cognitive learning strategies remain unrealized, and who – or what – is to blame?

I do not wish to direct the blame at teachers. For instance, recalling the history of mastery learning, one cannot blame Sherman (1992) – who did everything in his power to leverage mastery-based learning within his own classroom and promote its widespread adoption – for having his efforts opposed and ultimately overpowered by various forces at play within the education system. Likewise, one cannot blame other teachers who have thought about ways to capitalize on these cognitive learning strategies to improve student learning, but, for one reason or another, found it too difficult to integrate them into their classroom in practice.

Teachers are victims of circumstance. The education system – like any other system whose intended function (promoting learning) is limited by the scarce resources (teachers and funding) available to achieve that function – has developed its own conventions while seeking the closest thing to a solution to an intractable problem. As the education system has evolved over hundreds of years, these conventions have accumulated and ossified into hard-baked constraints that outlive their usefulness. Many constraints are no longer helpful to the goal of promoting learning, yet remain deeply ingrained and act to resist change.

As summarized by Sherman (1992):

  • "...[T]he investment in keeping things as they are may be impossible to overcome. ... Improving instruction is the goal, but only in the context of not changing anything that is important to any vested interest. ... [When the role of the teacher] does not conform to what most people think of as teaching; this is a problem and an obstacle to implementation."

The Solution: Technology Changes Everything

In the past, scarcity of resources (teachers and funding) has made it impossible to fully leverage cognitive learning strategies in traditional classrooms. This scarcity persists today. However, a new variable has also entered the equation: technology.

Technology changes everything. Individualized digital learning environments are now technologically possible and commercially viable. Technology not only lets us circumvent the opposing inertia in the education system, but also helps us leverage cognitive learning strategies to a degree that would not be feasible for even the most agreeable and hard-working human teacher.

Resistance to Additional Effort

One force keeping cognitive learning strategies out of the classroom is that they require additional effort from teachers and students. Again, we do not say this with the intent to cast blame – it is simply a fact that as humans, we tend to resist additional effort, especially when we (like teachers) are already tired or (like young students) do not fully understand the long-term consequences of our decisions.

Teachers are already under a high level of baseline stress while facing strenuous – and often conflicting – demands from administrators, parents, and students. When it comes to promoting learning, teachers can keep all parties satisfied (or, perhaps, not too dissatisfied) by checking the boxes on long-standing conventions of the educational system: some lectures, some homework, several quizzes, and a couple tests. There’s only so much you can deride a teacher for meeting the societal and institutional expectations that are placed on them, but not going above and beyond.

The same applies to students. Like a child who prefers to eat junk food and watch TV, but manages to complete their chores and eat the vegetables on their dinner plate, there’s only so much you can deride a student for showing up to class, being undisruptive, and performing well enough on homework and tests to earn a passing grade, but not going above and beyond to maximize their learning and retention – especially when they are too young to fully grasp the long-term impact of their present habits on their future life.

Additionally, it is unreasonable to expect students to be highly motivated to maximize their learning in every subject when a reality of human nature is that most people are unmotivated to do most things. The tiny subset of things that a person is motivated to do in life are called their career and hobbies, and most people only have at most one career and a few hobbies. Everything else – i.e., the vast majority of things – are chores.

Active Learning

Active learning requires teachers to spend more time and effort preparing and managing classroom activities. True active learning requires every individual student to be actively engaged on every piece of material to be learned.

To implement true active learning in a math classroom, a teacher must continually supply problems, enforce that each student is attempting the problems, and check each student’s solution to each problem, providing corrective feedback whenever a solution is incorrect. Enforcing that students are doing the problems can be particularly difficult and frustrating, since all but the most motivated students will typically avoid mentally taxing work when possible. (While it’s true that more students may become motivated to put forth a high level of effort and maintain it in the absence of supervision if they enter a state of flow, there is typically an initial “activation energy” that must be overcome before reaching the flow experience, similar to how one might not look forward to working out but actually have a lot of fun and feel proud of their effort once they get going with it.)

Additionally, active learning requires the teacher to make lots of on-the-fly decisions, which can feel overwhelming to teachers who are more comfortable planning everything out beforehand. What the class does next should depend on whether students were able to do what the teacher originally asked them to do. These decisions can get especially tricky when the class becomes “split” with many students being able to do the original activity and being ready to move on to something more challenging, but many other students struggling and needing more practice (or even remedial support) with the original activity. No active learning lesson plan survives contact with a class full of students of varying abilities.

On the whole, it’s way easier for a teacher to just talk and write on the board and “check the box” on active learning (without really leveraging it) by making sure that students appear to be listening, having some discussion with the smartest kids in the class, and maybe displaying a few problems and asking who wants to come up to the board to present a solution.

Non-Interference, Interleaving, and Spaced Repetition

Shuffling Instructional Material

Due to associative interference, conceptually related pieces of knowledge can interfere with each other’s recall, especially when taught simultaneously or in close succession. To minimize the impact of interference, new concepts should be taught alongside dissimilar material. However, it is easier for teachers to work in batch, creating week-by-week class lesson plans around groups of related material.

Additionally, the instructional material that’s provided to teachers is typically structured around curricular units of related content. While it may make sense to structure a reference book this way (for ease of lookup), this organization does not reflect the optimal order to actually teach the material. As a result, a teacher wishing to leverage non-interference would have to invest additional time and effort into “shuffling” their instructional material while ensuring that every topic comes later than its prerequisites in the shuffled order.

Similar effort is required to leverage interleaving, which involves spreading out review problems over multiple review assignments that each cover a broad mix of previously-learned topics. Most textbooks are structured the opposite way – in blocks, where a single skill is practiced many times consecutively. As a result, a teacher typically cannot just grab an interleaved assignment “off the shelf” – rather, they will need to invest time and effort to manually allocate problems across interleaved assignments and keep track of how much practice they’ve given the class on each topic.

Opening a Can of Worms on Forgetting

Interleaving can open a can of worms on who doesn’t remember what: when students are doing a variety of different things and are not able to mindlessly apply one type of procedure to one type of problem, they may need reminders of how and when to apply various solution techniques, they may make a variety of different types of mistakes, and they may have scattered questions in class the next day about the previous day’s homework. The same thing happens during spaced repetition, which involves spacing out reviews over time.

Opening this can of worms is actually a good thing because it provides an immense amount of information about what each student needs to work on – but it can feel overwhelming for teachers to have so many student needs at one time, especially when the teacher is under pressure for the class to cover a set amount of content by a fixed deadline, and the teacher feels like remediating student forgetting is “slowing down” their progress towards that goal.

Of course, good teachers understand the importance of continual review and periodically revisit previously-learned material to help their students retain it. However, as discussed previously, optimizing retention through true spaced repetition requires a massive, inhuman amount of bookkeeping and computation. Carrying out even a loose approximation of spaced repetition for the class as a whole requires an immense level of effort. Given the additional stress that continual review creates for teachers, it’s easier to just stick to the status quo and cram a class or two of review before each major test.

Testing Effect

Good, highly-engaged teachers understand the importance of quizzes and give regular weekly or biweekly quizzes (which is reasonably frequent, though a higher frequency would be ideal). However, unless these quizzes are built into some existing curriculum that they are working from, it takes a lot of work to create those quizzes, grade them, and go over mistakes with students. And that’s not all:

  • Ideally, students who don't do so well will be given the opportunity to demonstrate learning from their mistakes on a retake quiz with different (but similar) questions -- which effectively doubles the teacher's workload relating to quizzes.
  • In a class of more than a handful of students, there is always a good chance that one or more students will be absent due to sickness, medical appointments, or other things, in which case the teacher has to schedule make-up quizzes.
  • Especially at the high school and university levels, a minority of students may cause further headache by routinely complaining that questions they missed were unfair (and should be thrown out) or begging for undeserved partial credit.

Considering that most full-time teachers teach about 5-6 different classes each day, it’s an infeasible amount of work to quiz students every few days. Giving regular weekly or biweekly quizzes in all of one’s classes is hard enough. Realistically, given the additional stress that teachers experience when they give additional quizzes, it’s easier to just stick to the status quo and quiz students at the bare minimum frequency required to meet one’s professional expectations.


Managing a gamified metric like eXperience Points (XP), and other gamified features like leaderboards, takes an immense amount of bookkeeping. It can be done, but it takes a really engaged teacher, and even then, it’s typically too much work for a teacher to integrate every single learning task into the gamification structure. Gamification is typically not a part of a teacher’s professional expectations, so it’s easier for teachers to just forego it.

Tutoring the King's Kid: How Would You Teach if Your Life Depended On It?

The issues described above are not impossible to overcome manually. Each issue is solvable, but the solution requires a lot of work from the teacher. There is no law of physics preventing the teacher from putting forth that work, but the degree of accountability and incentives in place is not sufficient to motivate the teacher to do so.

(I again emphasize that this is not the fault of teachers, who are victims of circumstance in a profession lacking effective accountability and incentive structures. Who wants to work harder than necessary if they know they’re not going to be rewarded for it, and there is no punishment for mediocre work? Nobody.)

To intuitively understand the importance of accountability and incentives, it may help to imagine yourself as an educator in a life-or-death situation, where the outcome of the situation depends on whether you can teach a student effectively enough that they are able to unequivocally demonstrate their learning to a third party. Below is a retelling of Jason Roberts’s Tutoring the King’s Kid anecdote:

  • "Suppose that you are an educator back in medieval times, and you work within the kingdom of the wealthiest, but also the fiercest, king in all the world. The king's child has participated in a school within the kingdom, but the king has been unhappy with the results: the child has gone to school for over a year, and has learned how to count, but remains unable to solve any problem requiring simple application of arithmetic.

    One day, the king sends for you to appear immediately at his throne. When you show up, he commands you to teach simple arithmetic to his child as your sole duty for the next month. The child shall spend the entirety of each school day with you, and in exactly one month, the king shall ask his child five questions, each one requiring the addition, subtraction, multiplication, or division of two numbers, each number being one or two digits long. The child will have two minutes to complete each question, and their performance on this test will determine your fate.

    Being the wealthiest king in all the world, he has decided that if the child answers at least four of the five questions correctly, then he will grant you a fortune so extravagant that you can live out the rest of your life to the same level of luxury as a lesser king. However, if the child answers three or fewer questions correctly, then you shall be executed the following day."

In this situation, you’re motivated to put in the work to overcome each of the issues described earlier. The instructional experience becomes entirely student-centered, leveraging cognitive learning strategies as much as humanly possible.

  • "Suddenly, you realize that you don't care at all about how much time, effort, and stress you have to endure to make this child learn. Your own feelings are completely out of the picture. All that matters is whether the child comes to know their arithmetic facts by heart, understand the meaning of the operations deeply enough to know when to apply each one in problem-solving contexts, and quickly and reliably calculate the result of any arithmetic operation with numbers up to two digits long.

    To accomplish this, every moment you have with the child will be devoted to getting the child to the point where they are able to do all of these things independently.

    • You will of course introduce each skill along with a quick demonstration, but you won't ramble about anything that's irrelevant because your goal will be to have them start attempting to solve problems on each skill as soon as possible.

    • You will provide corrective feedback on every single problem that they solve, talking them through the correct solution whenever they make a mistake. If they do well, you will quickly move them onwards to more difficult problems, but if they struggle, you will give them however much practice they need to master the skill before moving forwards.

    • You will cover a mix of different topics every day and continually feed them review problems on previously-learned skills (but not too much review -- just a "minimal effective dose" to restore their memory on any topics that they might be in danger of forgetting).

    • You will also provide frequent timed quizzes on a mixture of different problem types, go over their quizzes with them, give them more practice on anything they missed on the quizzes, and give them a retake to make sure they learned from their mistakes.

    • Lastly, you will gamify the experience in a way that incentivizes the child to put their best effort forward all the time."

Heterogeneity of Student Knowledge Profiles

Tutoring the King’s Kid vs Teaching Many Kings’ Kids

The “tutoring the king’s kid” anecdote illustrates that there is no law of physics preventing a teacher from putting forth the work needed to deliver an optimal learning experience to a single student: rather, it is a matter of accountability and incentives.

However, a key assumption in the anecdote is that the teacher is working with a single student. If the same story were told with a class full of 30 children, each from a king who will execute the teacher if their own child fails the test, then it would emphasize a different perspective: the teacher may be doomed because no matter how hard the they try, they will not be able to deliver that same optimal learning experience to every student in the class. Regardless of the level of accountability and incentives, the amount of work required would be inhuman.

Loosely speaking, it boils down to the physics of learning. The reason why it’s so much harder to teach 30 students than to teach a single student is that the 30 students all have unique, heterogeneous knowledge profiles.

Differences in Background Knowledge

Students who earned different grades in a prerequisite math course typically come into the next course with vastly different knowledge profiles. For instance, students who received a C in the prerequisite course typically have far more foundational knowledge gaps than students who received an A (though even students who received an A usually have some foundational knowledge gaps, even if they tend to be fewer and/or less severe).

Moreover, and more subtly, even students who earned the exact same grade in a prerequisite math course typically have vastly different knowledge profiles from each other. Any two students who mastered the same amount of material in the prerequisite course may completely differ in the material that they were unable to master. One student may have struggled with fractions, while another may have struggled with decimals. One student may have struggled with solving equations, while another may have struggled with graphing functions.


Student Knowledge Profiles Naturally Tend Towards Heterogeneity

Even in an unrealistic hypothetical scenario where all the students in a class were academic “clones” of one another with exactly the same knowledge profiles, learning speeds, and levels of motivation, their knowledge profiles would naturally diverge over time as the class went on. Despite having the same academic profile, each student would be missing class or spacing out at different times, and as a result, some students would struggle with some topics more than others. (Missing class and spacing out are effectively the same thing, just on different time scales: they differ only in frequency and duration.)

Everyone spaces out sometimes – even adults. It happens constantly, even to people who are consciously trying to pay attention. People have a hard time focusing when they have other things on their minds: what they’re going to eat for lunch, their plans for the weekend, anxiety about a personal relationship, etc. The author of this book spaced out at least twice while writing the four paragraphs in this subsection.

This is especially true for students, who also face an endless list of mini-distractions in a classroom. For instance, a student might need to spend 30 seconds ruffling through their backpack for another pencil/pen or piece of paper (or their friend might ask them for one of those things). Or, a student may need to miss several minutes of class to use the bathroom.

Regardless of whether it is their fault or not, students are momentarily distracted at different times and they miss things. These differences compound over time unless the teacher immediately detects and fully remediates them at the instant that they arise – but this requires an inhuman amount of work, so teachers aren’t doing it unless they have technology that does it.

Every Student in the Class Effectively Needs a Private Tutor

The heterogeneity of student knowledge profiles means that different students need different amounts of practice, on different skills, at different times. Consequently, to deliver an optimal learning experience to all students in the class, the teacher must effectively function as a private tutor for every individual student. Needless to say, no matter how a teacher attempts this, it’s an intractable problem if their class consists of more than a few students. Even if a teacher tries their hardest, they will not be able to deliver an optimal learning experience to every student in the class.

To fully leverage the cognitive learning strategies discussed in this book, and deliver an optimal learning experience to every student in the class, every individual student needs to be fully engaged in productive problem-solving, with immediate feedback (including remedial support when necessary), on the specific types of problems, and in the specific types of settings (e.g., with vs without reference material, blocked vs interleaved, timed vs untimed), that will move the needle the most for their personal learning progress at that specific moment in time. This needs to be happening throughout the entirety of class time, the only exceptions being those brief moments when a student is introduced to a new topic and observes a worked example before jumping into active problem-solving.

However, when students have heterogeneous knowledge profiles, it’s at best extremely difficult, and at worst (and most commonly) impossible, to find a type of problem that is productive for all students in the class. Even if a teacher chooses a type of problem that is appropriate for what they perceive to be the “class average” knowledge profile, it will typically be too hard for many students and too easy for many others (an unproductive use of time for those students either way).

To even know the specific problem types that each student needs to work on, the teacher has to separately track each student’s progress on each problem type, manage a spaced repetition schedule of when each student needs to review each topic, and continually update each schedule based on the student’s performance (which can be incredibly complicated given that each time a student learns or reviews an advanced topic, they’re implicitly reviewing many simpler topics, all of whose repetition schedules need to be adjusted as a result, depending on how the student performed). This is an inhuman amount of bookkeeping and computation.

Furthermore, even on the rare occasion that a teacher manages to find a type of problem that is productive for all students in the class, different students will require different amounts of practice to master the solution technique. Some students will catch on quickly and be ready to move on to more difficult problems after solving just a couple problems of the given type, while other students will require many more attempts before they are able to solve problems of the given type successfully on their own. Additionally, some students will solve problems quickly while others will require more time.

In the absence of technology, it is impossible for a single human teacher to deliver an optimal learning experience to a classroom of many students with heterogeneous knowledge profiles, who all need to work on different types of problems and receive immediate feedback on each attempt. However, technology changes everything. Learning platforms that automatically leverage cognitive learning strategies to their fullest extent can deliver an optimized, adaptive, personalized learning experience to each individual student. Students can be perpetually engaged in productive problem-solving, with immediate feedback (and remediation when necessary), on the specific types of problems (and in the specific types of settings) that will move the needle the most for their personal learning progress.


Sherman, J. G. (1992). Reflections on PSI: Good news and bad. Journal of Applied Behavior Analysis, 25(1), 59.

This post is part of the book The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). Suggested citation: Skycak, J., advised by Roberts, J. (2024). Leveraging Cognitive Learning Strategies Requires Technology. In The Math Academy Way: Using the Power of Science to Supercharge Student Learning (Working Draft, Jan 2024). https://justinmath.com/leveraging-cognitive-learning-strategies-requires-technology/