Today’s blog comes straight out of the classroom. My *Aviation Mathematics I* classroom, to be specific. I want to share with you what happened when I “flipped the script” and began class with a problem that I asked students to solve *before* I ever taught them anything. Spoiler alert: it was GREAT!

The problem presented above was given to my class on Day 2 after a brief introduction of Polya’s problem solving process and an agreed-upon class definition (given below) of a “** problem**”:

Something that you don’t know how to do.

We began by me telling the students they were welcome to use their devices to look up anything they thought would be relevant or helpful. I illustrated what I meant by mentioning that when I read this problem I immediately wondered, “What is a jet stream?” I thought I knew, but wanted to be sure, so I did a Google search and found this:

I particularly loved the Jet Stream Map Menu site (where the above graphic came from) and my students and I had a lively discussion about the wonders available to us all via technology. Once I knew they knew what I meant about appropriate usage of their devices and looking up whatever they needed, I simply said, “*Ok, I want you to work on solving this problem. You can work by yourself if that’s better for you or if you’re feeling anti-social, or, if you are feeling anxious by this problem or simply want someone to discuss it with, you may work with a partner. Either way, I’m going to give you a few minutes to work, then we will discuss as a whole class.*"

I walked around while students either worked independently or in pairs. Since it was only the second day of class, I had to remind them it was ok to talk during this part of class and to encourage them to “figure it out” (reminding them of Polya’s process and the possible heuristics we’d decided may be useful to try). It was SO wonderful to evesdrop and hear things like:

But the jet’s speed doesn’t change, we just have to account for whether it’s going with the jet stream or against it.

It’s asking us to find TWO things! We need two equations if we want to solve for both.

Next, I asked for people to come up and present their work. We had three approaches, briefly described below:

- “Kenny” presented an approach based on averaging the jet’s speed with the wind and its speed against the wind in order to “negate” the effect of the wind in order to find the speed in still air.
- “Abdul” presented an approach based on algebraic reasoning using variables to represent the jet’s speed and the speed of the jet stream then solving the system of (linear) equations.
- “Shiva” presented an approach based on the difference between the jet’s speed with the wind and its speed with the wind.

Some of the beautiful discussion that arose:

- allowed students to feel more confident in their solution when they were able to confirm it using another approach
- caused some students to realize their approach didn’t work because the answers they obtained were not reasonable
- helped students to define common mathematical and algebraic terms in a context that made sense and made connections

I plan to follow it up next week with an extension where we solve the problem using graphing. Then, I will ask them to Create - Swap - Grade: (1) create a unique problem similar to the one we solved in class (2) swap problems with a partner and solve theirs (3) swap back and grade the problem their partner just solved.

As always, I'd love to hear from you. Especially, I would love to hear if you have additional ideas for problems in aviation mathematics that you’ve used with students.

**References:**

Link for course syllabus

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**The Solver Blog**

**Author: ****Dr. Diana S. Perdue**