# Four Phases

Let's say you've been in the business a while. You have routines you like probably a selection of go to activities. At the same time, from time to time you have a new idea and you're not sure if it's going to work out long term. For me, I'm never ready to give up on an idea until I've given it a chance to breathe. I go into understanding that I may not like the first attempt, and that in subsequent years it could make for something great. Forcing yourself to play out an idea over the course of three or four years is a hefty commitment. I thought I'd take a minute and talk through how I develop an activity to decide whether it makes the cut for the long haul.

### Phase 1: Experiment

In 2012 I was teaching Pre-Cal. We were looking at graphs of trigonometric functions. I showed students how to sketch them by hand using what they know about a function's amplitude and frequency. They each sketched two functions from a list I handed out and collected them in a poster by table:

Not bad, a little time consuming. After the activity concluded I decided the students weren't doing quite enough work and had no product demonstrating their thinking. A year later we try again.

### Phase 2: Refine

In 2013 we approached the topic again. I made some adjustments. The posters consumed a lot of space, so they're out. Students should do more than make a bare graph, so we'll make some simple statements about the function properties. The functions being graphed are still chosen from a predetermined list.

Two years of a similar plan showed me that I like this activity, but I don't love this activity. There's still not enough meat. I do all the thinking by predetermining the list of functions. Students miss out on playing with certain types of modifications simply because they didn't pick something off a list. We need a hard reboot.

### Phase 3: Redeploy

In 2014 I had a stronger plan. Students were going to do more of the mental lifting. This is the make or break year for the activity. Either this is going to have what I'm after or it's time to just forget and think of something else entirely. Students came up with six functions, all of which demonstrated increased/decreased amplitude and increased/decreased frequencies. They would make simple descriptions about which one was faster or slower. Bonus, we had iPads and a printer now, so the product could look a lot nicer.

Having the students come up with the functions was the winning piece here. There were good conversations and a lot of good clarifying questions about how to create what we were looking for. No more repetitions of the same functions over and over, each person had something unique. With that achieved, it's time to add features that will make this an activity I really look forward to.

### Phase 4: Keep or Scrap

In 2015 and 2016 this activity came back again but now it's really something great. Students design their own functions, have to write detailed descriptions, and now have more features to include in their pictures such as translations and centerlines.

2015

2016

The products this year are really something. My students from 2012 would scream at the demands of today's kids. You might be saying I iterated too slow and you might be right. Each year I picked a small aspect to change. I focused. If you're inexperienced writing an elaborate activity you've never watched play out before is highly likely to cause problems. Playing my trigonometric graphing activity out over the course of five school years has taught me what questions to anticipate, what concepts to stress more in our initial discussions, and what kind of structure kids need to safely string themselves out on a ledge and come back with something great.

The biggest advantage to slow, methodical iteration early on is that my subsequent activities have benefited tremendously. A new idea I have to today is far more likely to have the heavy lifting features I want by version two or even version one.

Start simple. Focus. Give yourself a big pat on the back when the kids of today help make the kids of three years from now even better.

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