How Many Peanuts Should the Penguin Feed the Elephant?
When I was young, I loved puzzles. My favorite childhood toys were the Rubik’s Cube and the wooden tangram set my grandmother gave me. I’d request logic problems over bedtime stories from my father. He preferred withholding puzzles until morning to prevent me from staying up all night solving them.
When I was young, I hated math. First of all, I’m dyslexic, and math was always taught in a language-heavy way. More importantly, nobody informed me that math is used to solve puzzles! It was presented as vocabulary, rules and procedures to memorize. It wasn’t until my dad starting drawing pictures of word problems that math became fun. With pictures, language was no longer a barrier. Boring word problems transformed into fascinating puzzles. Why couldn’t school present math this way? This was the hardest puzzle for me to fathom, and it became the question that shaped the rest of my life.
Presenting Math Visually
For the past 15 years, I’ve spent practically every waking hour researching and developing methods to present math visually in ways that are intellectually stimulating and not dependent on language. My team and I have learned more about what doesn’t work than what does, but our most recent string of success suggests we’re on the right track.
Our current understanding is that there are four essential components for students: they must experience, connect, practice and apply each math concept and skill before truly owning the knowledge. However, today’s classroom teachers use a lot of practice, some application, and make a few connections, but provide almost no opportunities for students to experience for themselves how and why math works. Let’s look at one example: Dividing by fractions. If your schooling was anything like mine, you may recall some variation of: “Ours not to reason why, just invert and multiply.” We were given a procedure to memorize, practice and blindly apply without any conceptual understanding of fraction division. Now consider how a visual puzzle game can fix this issue by having students help a penguin determine how many peanuts it takes to feed an elephant.
The game begins simply with whole-number division where it might take 6 peanuts to feed 3 small elephants. How many peanuts will one of these elephants eat? Easy. These must be dainty 2-peanut eaters since 6 divided by 3 is 2.
After mastering whole-number division, students move on to fractional situations such as 6 peanuts feeding 1/2 of an elephant. But the question is the same, “How many peanuts does it take to feed one of these larger elephants?” Students readily figure out that if it takes 6 peanuts to feed half the elephant then it takes twice as many (12 peanuts) to feed the whole elephant. They begin to see how 6 divided by 1/2 is equivalent to 6 times 2. More importantly, students directly experience the math, developing their own conceptual understanding, and making connections between whole-number and fraction division.
Fostering a Love of Math
As the puzzles progress, students practice with various sized elephants and different fractional divisions. They transition from purely visual problems to solving symbolic ones. Once mastery is demonstrated, the software presents situations where students apply fraction division to situations beyond pachyderms and legumes. In a nutshell, during the course of this game, students experience fraction division firsthand and connect it to prior knowledge, practice it to mastery and apply it to new situations. This is our current model of how to ensure students develop a deep understanding of math, and it’s working for the hundreds of thousands of students using the program. We’re seeing large gains on standardized tests, and an almost unanimous love of math through this approach.
For the last 15 years, I’ve been able to use technology to replicate the role my father played with me for over a million students—creating visual puzzles to reveal the beauty of mathematics. It’s been a long journey, and there’s a long way to go, but the possibility of math success for every student is very definitely in sight.
Matthew Peterson is Co-Founder, Senior Institute Scientist and Chief Technical Officer of the MIND Research Institute that uses instructional software to teach students math using a non-language-based approach.