However, I wanted to share this picture:
This is work a student did for her weekly reflection. She did it on a whiteboard and then pasted an image of this into the Google Doc we share together. This is her very own whiteboard- I got a new set last summer and relegated my old ones to the backup squad (because I couldn't bring myself to junk them completely). When some of my students commented on the new boards, I told them the story. They clamored to be allowed to take the old boards home- they love doing work on them! Heart warming, I tell you what!
By the way, if you're wondering about the optimization problem I made up, it's pasted below...
A person’s productivity, P, can be modeled as the product of their mental acuity (MA) and the time that he or she spends working. A graduate student in advanced mathematics is busy 16 hours of the day, so she has 8 hours that can be devoted to either sleep or work. The problem is that the amount of sleep she gets drastically affects her mental acuity. She has monitored her daily output and believes that her mental acuity is best modeled as MA=100-12*(8-t)^2 where t is the amount of sleep she gets every night. She has been working so hard that her mental acuity is at an all-time low, so she needs your help to determine how much time she should spend working to optimize her output.
If you’re stuck, she feels like she would probably start by writing down an expression for the amount of time she spends working in terms of her free time and the amount of time she spends sleeping.
And yes, for those intrepid readers, I do realize, courtesy of one of my students, that my MA function implies that mental acuity will peak at 0 hours of sleep. Quite the oversight- I'll do better next year. Speaking of mental acuity as a function of time spent sleeping...
