One thing I've learned from teaching is that there's always something new to learn. For the kids, yes, but I'm talking about for the teacher.

The other day, I taught a lesson I've taught many times. Find the mode of a data set. That's the problem that they solve but the lesson is really about run time complexity, hidden complexity and using data structures in alternate ways.

I blogged about this before so you can get an earlier take there although the code isn't formatted correctly due to blog conversions.

As with the last time, the students had already written code to find the largest value in a list and also to find the frequency of an item in a list.

They had to write mode prior to the class. In the past, students would generally come up with something like this:

They'd use their existing knowledge and the 'find the largest' idiom to find the mode by:

• find the frequency of the first item and assume it's the mode so far
• for each item in the list
• find the frequency of that idem
• if it occurs more than the mode so far then it becomes the new

mode so far

There's a lot of good in this solution. The kids incrementally develop a solution, they use and exctend code and concepts they already know and understand and it's clear and understandable.

We would then run the code on larger and larger data sets and notice that it gets slow pretty quickly. This leads to an informal discussion of run time and the fact that there's hidden complexity – the call to freq in the main loop introduces a linear component so we have a loop within a loop and an N^2 routine.

The big takeaway is get a feel for run time and to be aware of hidden complexity. We then move to a linear solution by using a list as buckets. You can read more about that in the original post.

What was interesting this time around was that most of the kids came up with a solution more like this:

Instead of calculating the frequency inside the loop they made a list of frequencies. freq[0] had the frequency of l[0], freq[1] the frequency of l[1] etc. They then loop through that freq list to find the largest element and that's the index of the mode value in the original list.

It's functionally the same as the first solution but in some ways it's very different. They built the data set they needed ahead of time instead of calculating the data on the fly and they used the concept of parallel lists.

I like the solution and it didn't prevent us from getting to the run time stuff but this did give me something to think about.

Why did this class led them largely to a different solution than the classes I've taught in the class. There are a lot of things to ponder since it's a college class that meets twice a week with kids from a range of backgrounds (CS and otherwise) vs a high school class that meets 5 days a week and the kids all had the same in class experience prior to this lesson. Did I do something differently before hand? Some assignments? Something I modeled? I'm not sure but it's something I'm going to ponder.

It will interesting to see if this was a one shot deal and my current class will solve problems as I predict moving forward or if I'm going to get to see a lot of new things.