# 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

younger students.

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

Using the

Rubik’s cube

to teach

problem solving

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.

55

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

Cube.

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

500 kg!

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

Association.

u The World Cube Association also recognizes records

for solving the cube blindfolded, with one hand, and

with both feet.

56 The Science Teacher

Puzzling Science

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).

Conclusion

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 (blrohrig@columbus.rr.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

References

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–

Calumet. http://education.calumet.purdue.edu/vockell/edPsybook