Puzzling Science: Using the Rubik’s® Cube to Teach Problem Solving
an article by Brian Rohrig
A few years ago, my son Ben acquired a Rubik’s
cube. He became quite adept and could eventually
solve it in 30 seconds. I admired the many
hours he put into mastering the cube, so I asked
him to teach me. I was never good at tasks like this, and
though I am a science teacher, I am very right-brained—
and impatient. Despite these limitations, I decided to give it
a go. It took many weeks of frustration, but—with my son’s
help—I finally mastered the Rubik’s cube.
As I was trying to solve the cube, it dawned on me that
my students face similar frustrations when attempting to
solve the tasks I give them in class. But the difficulty of the
task and the fact that I succeeded made all the frustration
worth it. I was proud of my accomplishment, and it felt good
to learn something new. It gave me confidence that perhaps
someday I could learn how to draw, or play an instrument,
or learn another language.
For me, a big appeal of the Rubik’s cube was its finality. I
knew when I had succeeded—the cube was either solved or
it wasn’t. There was no ambiguity; the only way to improve
was to do it faster. To get my time down, I learned new
techniques and steps that were difficult at first, but became
easier with time. As I worked through this, I began to think
that perhaps my students could benefit from learning how
to solve the Rubik’s cube, as well.
I approached my principal and explained how the Rubik’s
cube could help students learn to problem solve. He gave me
the green light, and when school began the next year, I had
over 100 Rubik’s cubes in shiny new packages, waiting for
me in my classroom. That year, I was teaching ninth-grade
Physical Science, Biology, Chemistry, and Physics classes,
and decided to use the Rubik’s cube in each class. Since
then, I have limited its use to my ninth-grade Physical Science
class—though the cube was ultimately a success in all
of my classes. The methodology is also concrete enough for
Learning the ropes
A few weeks after school started, I began class one Monday
with a clip from The Pursuit of Happyness, a movie in
which Will Smith’s character impresses his future employer
by solving the Rubik’s cube. I then (half-jokingly) told my
students that they too could earn millions of dollars if they
learned to solve the cube. I handed one to each student and
told them they had seven weeks to solve it. Many were incredulous,
but—at the same time—excited to get to work.
That day, I taught students the first step, which is making
a cross on one side of the Rubik’s cube. The following Friday,
I gave a five-point quiz (about half the point value of a typical
homework assignment) in which students received full credit if
they could complete Step 1 within five minutes. Most students
December 2010 Wolves in the Wild
did so easily. Those who did not received half credit if they could
make a cross on one side by the end of the next class period.
The next Monday, I taught students Step 2. The goal of this
step is to make one whole side of the Rubik’s cube the same color.
That Friday, I gave a quiz on Step 2, in which students had five
minutes to complete one side of the cube. This quiz was worth
10 points—double the amount of the previous quiz, or the same
point value as a typical homework assignment. The sequential
nature of the cube was readily apparent, since students could
not do Step 2 if they had not first completed Step 1. I continually
emphasized this point—and would often make references to it
when discussing other topics that are sequential in nature.
This procedure was repeated each week for seven weeks.
On the final Friday, students had five minutes to solve the
entire Rubik’s cube (Step 7) for 340 points, or the equivalent
of a test grade. Most students solved it within this time frame
with no problem—many had solved it weeks earlier.
I then began giving weekly 50-point quizzes in which
students had to complete the cube 30 seconds faster each
week. (An alternative to this would be to challenge students
to improve their personal best times each week.) Eventually,
students had only three minutes to solve the cube. I then
quizzed them periodically throughout the year, so they did
not forget how to solve it. I made it a part of both the semester
and final exam.
Speeding things up
To be truly proficient at something requires doing it in a
timely manner. Basic reading and math proficiency is based
in large part on what you can accomplish in a certain time period.
For example, if it took one hour to read a single page of
a textbook, would that be considered proficient? If it took a
mechanic four hours to change the oil in a car, would that be
acceptable to the customer? Teachers may disagree on where
exactly to place the bar with respect to time, but most will
agree that, in general, the faster you can perform a task—and
perform it well—the more proficient you are.
Although I expect students to solve the Rubik’s cube faster
each week, I am lenient with the grades of those who exceed the
time limit—deducting a letter grade or less, depending on their
time. Nearly all of my students rise to the challenge and surpass
my expectations. Some solve the cube in about a minute—which
is likely the best they can do with the method I use.
It is especially gratifying to see students who have normally
struggled in class learn to solve the cube and feel a sense of accomplishment.
Nearly every student learns to solve the cube
(my classes have a 98–99% success rate), but each year I have
one or two students who—for various reasons—cannot solve
it. I have used the cube with my students for three years now,
and they seem to have an easier time each year. This could be
due to the expectation for success: I begin each year by telling
them that nearly every student the year before solved the
cube—and if those students could do it, they can too.
Weighing the benef i t s
Each Rubik’s cube comes with written instructions that students
can refer to, and the method I use is similar to this. There
are also a plethora of solutions online (see “On the web”). However,
to really learn to solve the Rubik’s cube, it is best to have a
personal tutor. Find someone who can solve the cube and ask
them to teach you. Once you master a step, write it down so
that you will remember it. Find the method that is easiest for
you, so you can then effectively teach your students.
I plan to continue using the cube for as long as I teach, as
mastering it provides the following benefits for students:
It builds confidence, especially with underachieving students. Often,
students who struggle with or do not like school excel at the
Rubik’s cube. They tend to like the hands-on approach and will
spend hours of their own time practicing and trying to improve.
I often tell these students that if they can solve the cube, then
surely they can do whatever else I am asking of them. Since most
people in the general population cannot solve the cube, students
who learn to do so feel good about themselves. They learn that
if they work hard enough, they can be successful.
It promotes cooperative learning. Although I am always available,
I seldom have to tutor students with the cube. They typically
prefer working with their classmates, provided they can get
quality help. It is encouraging to see students working together,
and as they help others, their own proficiency improves.
It provides students with a framework for solving problems.
Solving the Rubik’s cube will not put students at the high-
Rubik’s cube facts (Rubik’s Cube 2010).
u The Rubik’s cube was invented by Hungarian architect
Erno Rubik in 1974.
u The Rubik’s cube was originally called the Magic
u The Rubik’s cube first became available to the public in
1977. Since then, over 350 million cubes have been sold.
u There are 432,003,274,489,856,000 ways to arrange
the cube, but only one results in a solved cube.
u The world’s largest Rubik’s cube is on display in
Knoxville, Tennessee. It is 3 m tall and weighs over
u In addition to the standard 3 Å~ 3 Å~ 3 cubes-per-side
variety, Rubik’s cubes also come in the following
versions: 2 Å~ 2 Å~ 2, 4 Å~ 4 Å~ 4, 5 Å~ 5 Å~ 5, 6 Å~ 6 Å~ 6, and 7
Å~ 7 Å~ 7 cubes per side.
u The current world record for solving the cube is 7.08
seconds. This was set in 2008 by Erik Akkersdijck
at the Czech Open, sponsored by the World Cube
u The World Cube Association also recognizes records
for solving the cube blindfolded, with one hand, and
with both feet.
56 The Science Teacher
est levels of Bloom’s taxonomy (i.e., analysis, synthesis, and
evaluation), but students do have to first master the lower
levels of thinking before they can move on to the higher
levels. The sequential reasoning needed to solve the cube is
applicable to many other types of problems. Before students
can solve for an object’s density, for example, they must first
know its mass and volume. By breaking problems into steps,
even the most daunting ones can be solved.
Indeed, all scientific progress occurs in incremental steps,
with one discovery building upon another. Learning to solve the
Rubik’s cube is a good way to understand how scientific progress
occurs. The importance of these incremental steps is highlighted
in the National Science Education Standards, “The daily work
of science and engineering results in incremental advances in our
understanding of the world…” (NRC 1996, p. 201).
It is encouraging to see students who have mastered the
cube look for shortcuts and better methods. Some students
do get to higher levels of thinking with the cube, as they seek
to understand its patterns and how to manipulate it to get
the desired result in a faster time.
It improves spatial awareness. The Rubik’s cube is an excellent
tool to enhance spatial reasoning. My students love to
make up different patterns and then challenge one another
to return the cube to its solved position. I think this shows
that students are becoming more adept at spatial reasoning—
they are not just memorizing a solution, but learning how to
manipulate three-dimensional (3-D) objects.
The importance of spatial reasoning is delineated on
the homepage of the National Science Foundation–funded
project entitled “Enhancing Spatial Reasoning and Visual
Cognition for Early Science and Engineering Students With
‘Hands-on’ Interactive Tools and Exercises”:
Many problems in science, engineering, and mathematics
are inherently spatial in nature. Understanding and reasoning
about atoms in a molecule, the design of mechanical and
electronic systems such as robots, layout of an integrated
circuit or microelectronic mechanical chip, transmission
of tension and compression forces in a structural system—
these problems all demand the ability to visualize and reason
spatially (Spatial Reasoning Visual Cognition 2010).
It exercises the brain. If you were to happen by a typical football
practice, you would see lots of things that seem unrelated to
football. For example, what does running through tires have to
do with the sport? Of course, these skills prepare players for the
real game—improving their strength, quickness, and agility.
Yet we often do little to develop the brain and get it into shape.
Any time genuine learning takes place, neuronal connections
are made in the brain. Any time a new skill is learned, the brain
develops and cognitive functioning improves.
It demonstrates the need for practice. If students solved the
cube once and then were not asked to solve it again until the
end of the year, could they still do it? Most probably could
not. In the rush to cover so much material, it is easy to teach
something once and never go back to it. And if students do
not remember it, then they have not really learned it.
By practicing the Rubik’s cube all year long, the need
for practice is reinforced. In many ways, the cube provides
a model for how all learning should progress: Students
are presented with a seemingly insurmountable problem,
then—through a lot of hard work—they solve the problem
by breaking it down into steps and continually practicing
and refining those steps. Only through continual practice is
true mastery achieved.
It represents a pure example of true learning. It could be argued
that true learning has occurred when we no longer need
to think. We do a plethora of things every day without really
thinking about how we do them—from tying our shoes to eating
with utensils. Each of these tasks required all of our focus
and concentration when we first learned to do them. But once
we mastered these skills, they became somewhat automatic.
Eventually, students become so proficient at the Rubik’s cube
that they can solve it without really thinking about it. Their motor
memory takes over and they solve the cube without using
their working memory at all. Once something becomes automatic
it is stored in the long-term memory—which is the goal
of all learning. A major goal of education is to help learners store
information in long-term memory and use that information on
later occasions to effectively solve problems (Vockell 2010).
Each year, I look forward to introducing the Rubik’s cube
in my classes. There is something special about this colorful,
3-D puzzle that seems to captivate the imagination of even
the most lethargic student. This activity has shown me that
every student has a tremendous amount of untapped potential,
waiting to be unlocked. The Rubik’s cube has been a
valuable key in unlocking it. n
Brian Rohrig (email@example.com) is a physical science and
physics teacher at Jonathan Alder High School in Plain City, Ohio.
On the web
Beginner’s Rubik’s cube solution: www.ryanheise.com/cube/beginner.html
National Research Council (NRC). 1996. National science education
standards. Washington, DC: National Academies Press.
Rubik’s Cube. 2010. Cube facts. www.rubiks.com
Spatial Reasoning Visual Cognition. 2010. Project summary.
Carnegie Melon University. http://code.arc.cmu.edu/spatial (accessed
September 8, 2010).
Vockell, E. 2010. Memory and information processing. In Educational
psychology: A practical approach. Calumet, IN: Purdue University–