The Problem Solving Process was developed to make the perception-action cycle (see The Science of ST Math) easier to bring into your classroom. The goal is to get students involved in the process of learning which requires noticing what is going on (in an ST Math puzzle, on the soccer field, or learning an instrument) and then starting a cycle of predicting, testing, and analyzing. When the learning is successful, it's connected to what is already known and extends knowledge.

Let's find out what it feels like!

Start playing the game below. It's a little harder than the ones you may have been playing so you can see how the process works on a game you have to think about. Play the game and open up a section at a time and answer the questions that are asked. Then close that one and open the next all while you're playing.

If you want to get the big picture first, open up all the steps and read through them but come back and play!

Notice and Wonder - I notice (make sense of the problem) and I wonder (what question I am solving) so I can think of a possible solution pathway. 
Predict and Justify - I predict (think about, name a strategy & describe what will happen when I try it) and I justify (explain why I chose this strategy) so I can test my prediction. 
Test and Observe - I test (try my strategy/test my prediction) and observe (see the results of my test), so I can understand how my strategy worked.
Analyze and Learn - I analyze (compare my prediction to my observation), and I learn (what worked/didn’t work) so I know how to refine my strategy or use the strategy in other problems.
Connect and Extend - I connect (What did I learn? What is this related to? How does it fit with what I know?) and I extend (Where do I go from here? How do I represent this symbolically or with another visual model?) so I can deepen my understanding.