Pedagogy

We have designed PhysicsGraph for effectiveness and engagement. When the two conflict, we value pedagogical effectiveness more than engagement.

We draw directly from learning science and game design, as well as from inspirations such as MathAcademy and 3blue1brown.

Bloom's 2-Sigma Opportunity

Educational psychologist Benjamin Bloom observed that one-on-one tutoring could massively increase the success of any student - according to his research, by two standard deviations.

  • "the average tutored student was above 98% of the students in the control class"
  • “about 90% of the tutored students ... attained the level of summative achievement reached by only the highest 20%" of the control class”

Tutoring can greatly benefit any student, no matter where they start on the distribution.

Bloom called this the “2-sigma Problem” because one-on-one tutoring is "too costly for most societies to bear on a large scale”.

In the rest of this document we will show the specific attributes that make one-on-one tutoring so effective, and how these can now be replicated for a much lower cost.

Mastery Learning

In Bloom’s experiments, the tutored student was required to demonstrate mastery before moving on.

Bloom had a group in his paper called 'mastery learning', which improved scores by 1 standard deviation. What we describe as "mastery learning" applies to both this group and the 1:1 tutoring group.

If the student failed to demonstrate mastery, then they were given more educational support and practice, and then tested again. This continues until they demonstrate mastery, at which point they can move on.

A learning platform such as PhysicsGraph can track student mastery at a very granular level, and provide personalized sequencing based on each student’s state. We achieve this at a much lower cost than a one on one tutor.

Deliberate Practice

Not all practice is equally effective.

Deliberate practice:

  • Is targeted at specific skills (often the student’s weak points)
  • Is calibrated to be difficult but doable
  • Improves skills significantly faster than free-form practice

Another way to frame deliberate practice is “productive struggle”

If there is no struggle, then it is probably too easy and will be inefficient in building skills. If it is too hard, then the struggle will not be productive and is creating more frustration than learning.

Minimizing Cognitive Load

Working memory is the temporary store of information that is available for use and processing. It is a limited resource, and it varies by student. When a student feels overwhelmed, that is a sign that they are being asked to use more working memory than they have available.

The easiest way to free up more working memory is to minimize distractions and eliminate multi-tasking, so that the entirety of working memory is available for use on physics problems.

The other way to free up working memory is for the student to compress the information. This happens naturally as the student masters material. While early students may struggle with multiplication, the multiplication facts for a prepared physics student take up almost no working memory. 4x5=20 is essentially "free" for such a student, leaving room to use the working memory for other purposes.

So when building a curriculum, we must:

  1. Minimize the amount of new information in each lesson, so that the student can learn effectively without being overwhelmed.
  2. Present information in a way that is easy to compress, so that in future lessons it will not take up significant space in working memory - leaving them free to learn new material

Engagement and motivation

We believe there is a lot to learn from videogames on how to create an engaging experience. At the same time, we purposefully discard any tactic that distracts the student or contradicts effective pedagogy. We must keep engagement high without compromising learning.

We have three core systems for engaging the student

  • Tight feedback loop within lessons. We’ve discussed how this minimizes cognitive load, which is great for learning, but it also makes for a more engaging experience when you can immediately see the results of your work.
  • Show visual progress. When finishing a lesson, you’re treated to an animation showing what lessons you’ve unlocked - in a way designed to look and feel like unlocking new levels in a videogame. It also is extremely helpful in situating what you’re learning in relationship to a lot of the other concepts and skills in physics.
  • “Gamification”. All the standard gamification tricks like XP, progress bars, daily goals, and leaderboards. We use them because they’re effective, but we recognize that they should never replace good lesson design. We only show them while outside the lessons, so that they don’t become distracting.

Spaced Repetition

Students forget material quickly if it is not reviewed. Spaced repetition is the technique of reviewing the material at the optimal time in order to remember the material long-term. We have a dedicated page on spaced repetition that covers this in more detail.