Using Spaced Recall to
Encourage Expert Practice
Eugene Torigoe
Dominic Licata
Thiel College
PERC 2016
[email protected]
Introduction
Problems
This is a formative methodology to help
students gain appreciation for expert
practices such are translating between
representations, and to understand the
value of reasoning through a solution
rather than relying on memorization.
Because students are asked to recall the
solution over a period of weeks, they
find that pure memorization is
cumbersome, and that strategically
memorizing and then working your way
to the solution to be much easier.
Collision:
Two balls traveling along the x-axis collide. Ball A has a mass of m, and a velocity of
11v to the right. Ball B has a mass of 2m, and a velocity of v to the left. When the
balls collide, they stick together. Use the conservation of momentum to determine
the speed and direction of the two balls after the collision in terms of m and/or v.
Momentum: p = mv
Conservation of momentum: pAi + pBi = pAf + pBf
Pendulum:
A pendulum (a ball connected to a thin string) has a mass m is hung from the rear view
mirror of a car. When the car is at rest the pendulum hangs down in the vertical
direction. When the car has constant acceleration in the forward direction the
pendulum is at a stable angle θ from the vertical. Draw a free body diagram for the
forces on the mass m due to the gravitational force mg and the tension T. Use
Newton’s 2nd Law to find an expression for the acceleration, a, in terms of the angle θ
and the gravitational constant g.
Newton’s 2nd Law in the s-direction: 𝐹𝑠 = 𝑚𝑎𝑠
𝑜𝑝𝑝
𝑎𝑑𝑗
𝑜𝑝𝑝
Trigonometry: sin 𝜃 =
, cos 𝜃 =
, tan 𝜃 =
ℎ𝑦𝑝
𝑎𝑑𝑗
Transfer Problems N = 9
Procedure
Trends
1) View a video of a
3) A week later, recall
worked example problem, the solution (spaced
while taking notes.
recall). And repeat this
once a week, over a
2) Study notes, and then
period of weeks. Use
recall the solution
notes for feedback after
without assistance only a
each recall as necessary.
few minutes after
watching the video
4) Solve a related
(immediate recall).
transfer problem.
1) High Scores for Immediate Recall
2) Lowest score for first Spaced
Recall
3) Steady to improved score for
more spaced recall attempts.
4) Students can remember the
diagrams, but not equations
5) Transfer problems generally
lower than last spaced recall, but
not the lowest.
Survey (N = 9)/Interviews (N = 4)
At first memorized, but when
began to reason
through (a lot easier)
It is therefore of first-rate importance that you know how to “triangulate” –
that is, to know how to figure something out from what you already know.
It is absolutely necessary.
- Richard Feynman, Feynman’s Tips on Physics
N = 11
Heat Engine:
A heat engine operates between a hot thermal reservoir at a temperature TH and a
cold thermal reservoir at TC. Create an energy flow diagram for the thermal reservoirs
and the heat engine, and use it to derive a symbolic expression for the thermal
efficiency, η, (pronounced eta) of the heat engine in terms of the heat from the high
temperature reservoir QH and the heat to the cold temperature reservoir QC.
ℎ𝑦𝑝
At first I just memorized it.
However, as time progressed I
approached the problems with
more reason
It isn’t a good idea to memorize everything. In fact, it’s impossible in the
long run to do everything by memory. That doesn’t mean to do nothing by
memory … but you should be able to re-create anything that you forgot.
The [transfer problems] helped because I
was able to apply basic/general techniques
from the original ones to the new q’s. The
first question we did [heat engine
problem] I feel like I just memorized the
problem and had trouble applying the
techniques [to the transfer problem].
So tell me, do you think there is any
change in the way you use diagrams
since when you started this process?
Yeah a little more I learned to look into
the actual diagram, and look at what it
is telling me, not that it’s just there as a
picture to help explain the problem
N = 11
Discussion
Almost all of the students found the exercise to be helpful.
Many expressed that they gained an appreciation for working
through a problem rather than just memorizing it, and to use
diagrams to generate equations.
The transfer problems served as feedback on how well they
understood the reasoning behind their work.
Some students failed to make progress, and their notes did not
seem to offer enough quality feedback.
N = 11
N = 11
Future Work
1) Better Feedback –
Instructor presentations to
encourage expert practice
2) More transfer problems to
show the advantages of
general procedures.
3) Pre and Post
Epistemological Surveys.