Puzzling Science: Using the Rubik’s® Cube to Teach Problem Solving
an article by Brian Rohrig, Science Teacher, v77 n9 p54-56 Dec 2010
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 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 Benefits
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 highest 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.
Brian Rohrig (firstname.lastname@example.org) 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– Calumet. http://education.calumet.purdue.edu/vockell/edPsybook
Posted here with permission of the author.