Steven and Michael are second grade boys. They are practicing addition and their teacher challenged them to build a “math tower.” They began with 7 + 8 = 15. To that they added 27. That equals 42. Then they added 63. Then 268 and 487 and 2482. The sum reached 3342. Then they added more. Where did the numbers come from that they kept adding on? They chose them. When did they stop? Well, do you know the story of Strega Nona who cooked spaghetti in a magic pot? The spaghetti flowed and flowed and flowed out of the pot until the entire village was flooded in spaghetti. The boys’ math problem was like that magic pot.
When you are learning addition, you need to practice. They did that. Every day for three weeks they eagerly got out their growing math tower and added on. Two third grade boys saw them at work and said, “That looks like fun!” so they started their own math tower. Finally the answer reached 39 digits. More than millions, more than billions or trillions reached the undecillions. They used a chart in their classroom as a guide for how to read large numbers.
They’re learning to add. Kids in other schools learn to add, too. What makes the work of any different? They chose the numbers themselves. And they chose to push the problem to monumental proportions. In fact, they had to tape many sheets of grid paper together in order to record their work, and the final product is taller than the boys are. Elementary students will challenge themselves to do big projects if we do not set arbitrary limits. We want children to learn to extend their grasp, to “hitch their wagon to a star.” This is more important than the narrow curriculum objective of learning to add. For comparison, the state-wide curriculum guide (Texas Essential Knowledge and Skills, or TEKS) calls for second grade students to learn to read and write numbers up to 999. It also calls for second grade students to add and subtract two-digit numbers. And who picks the numbers? Usually the text book. No reasonable curriculum guide or text book or teacher would ask second grade boys to add 39 digit numbers. Yet they chose to do so themselves. They were exploring their own limits as they solidified their understanding of addition and the number system. They were learning about the nature of work and found joy in accomplishment. This was not drudgery. They were working with great enthusiasm.
Ironically, the same day I admired their finished work, I received an unsolicited e-mail from Applied Scholastics International. The subject line read, “If your dream is to motivate students, here’s your answer.” Motivate students? I Googled that phrase and found 749,000 entries. That’s not a 39-digit number, but it’s quite a few. Traditional schools are built on the model where the teacher tells the students what to do and they do it. But it must not work well enough because the teachers are looking for ways to motivate students. They offer rewards. If you do well, you get a gold star or an A. If you do the best, you’re ranked number one. And still there are 749,000 entries aimed to help teachers motivate students.
Dr. Montessori observed that children are already motivated to learn. We don’t need to impose motivation on them. In fact, if we give them a little encouragement, they’ll do far more than we would dare ask. What about those two third grade boys? They finished their problem when it reached the octodecillions: 59 digits. But then they’re third graders, and they’ve been practicing longer than the younger boys who inspired them.