Ice Cream and Inquiry
One of the questions asked most often of MYP Mathematics teachers is, “Mathematics is such a black and white subject. How do you teach it using inquiry which is, by design, very grey?”
Have you ever had a problem so enormous that you didn’t even know where to start? Something that seemed to have so many moving parts that you weren’t even sure you saw the whole problem? Well, that’s what Mr. Bronson's 8th grade students have been grappling with for the last couple of weeks.
A few weeks ago, all 8th grade students were asked the following question:
What would be the diameter of the puddle if the ice cream melted?
Then the questions started coming in. Some, you’d expect:
- What is the height of the cone?
- What is the diameter of a single scoop?
- Are there only 4 scoops or is there one packed down into the cone?
Some were much more scientific:
- Does melted ice cream have the same volume as frozen ice cream?
- When cream settles, what is its height?
Some came straight out of left field:
- Is the cone a good one or will the melted ice cream leak out?
- Is the air temperature hot enough to evaporate the ice cream?
All of these questions came long before a single formula question was ever asked.
Once the formula questions came in, the discussions really picked up. “We can’t use the formula for sphere, the scoops aren’t actually spheres.” “How will we find the volume of the cone when we can’t clearly see the top to estimate the diameter?”
This is where traditional mathematics blurs into engineering and applied mathematics. The tools that they were using for the calculations were the best that mathematics could provide. The numbers that they were using were best guess. They used the assumed height of the door to calculate the height of the cone. They used actual sugar cones to calculate the diameter of the cone by comparison. They used water displacement to calculate the amount of volume lost when ice cream melts. They used deductive reasoning to calculate the height of melted ice cream. The list goes on and on.
By the time the dust settled, they had done more math and science in a single problem than they would in a dozen more traditional problems. They wrote about margin of error and intellectual choices in the write up of their solution. Even though every student had his or her own unique solution to the problem, everyone was in the same general range. The specific numbers varied based on the calculations, choices, and results of the experiments done with actual ice cream in class (which created a whole new set of questions, since the students now questioned if flavor made a difference).
So, how does a MYP Mathematics teacher use inquiry to teach? By creating problems where the mathematics becomes secondary. The geometric formulas and algebraic skills become tools rather than the goal. The applications and, more importantly, the ramifications of applying perfect formulas to imperfect shapes, become the true driving force of the learning.
The mathematics learned was the same as any traditional geometry class covering the volume and area of 2D and 3D shapes. The understanding of what it means, why it exists, and how it is used will make a world of difference not just in their retention but in their ability to select and apply appropriate mathematics in future problems.
The ice cream probably helped, a little, too.