Historically, maximization problems have been a problem for calculus students. Not so much in finding critical points from functions and classifying them, but finding the objective function to begin with. Students rely on basic examples to mimic. We wonder why they can’t carry out more complicated examples. They are able to model simple physical situations after much practice, but flounder when faced with slightly more complicated problems because they don’t understand the complication well.
As the maximization and minimization problems become more complicated, using a table to organize examples of what is being modeled becomes more and more useful. Let’s look at another examples of how this might work.
Problem A rectangular tank with a square base, an open top, and a volume of 8788 ft3 is to be constructed of sheet metal. Find the dimensions of the tank that has the minimum surface area.
In the middle of a stressful semester, returning emails from fellow teammates are not the highest priority. Trying to collaborate on a document via email is even more challenging. If several students are working on the same document simultaneously and making changes, it is a nightmare to keep track of the changes. This is where a shared document can help.
Even Batman and Robin needed a common foe to bring them together as a team. Each week they faced off against more and more challenging criminals. As they became better crime fighters, their opposition had to step up their game. By the second season, we saw first two…then three or four master criminals working together to pull off some heist or to defeat the dynamic duo one and for all. The message was that they could do more as a team than any one could do alone.
This is my hope my collaborative teams…together they can do more than any one of them can do alone. However, you can’t throw four or five students together and expect them to be productive right away. Ease them into working together and then have them make some decisions together.
The easiest way to assign students to teams is to simply assign them randomly and wait for the fallout. Left on their own, students have a tendency to socialize, not work toward a common goal. A group without a leader is likely to flounder aimlessly until the very last minute. A group without any technology skills will often implode. To be effective, the groups need to be an appropriate mixture. I needed Batman AND Robin (and maybe Batgirl). They had complimentary skills…experience and youthful enthusiasm….brains and support. Teams that have these types of complimentary skills, are most likely to succeed.