Thinking Mathematically -- Response to 'Being Stuck'

When I first read this chapter I was transported back to the ultra-difficult questions often posed in my intro Calculus courses. When these questions were assigned to me I would be flooded with anxiety because these were still tied to traditional assessment. Given the stakes of a grade, the focus entirely shifted to getting the right answer, ultimately defeating the purpose of these outside-the-box word problems. 

So my first stop was right at the beginning of the chapter, since it immediately presented ideas contrary to my experience as a math student. I was told that being stuck was a valuable step in the solution process, but I was never really told how to navigate this "stuck" feeling. Furthermore, with quick turnaround deadlines, being stuck was not valued in the "hidden curriculum." I appreciated the authors valuing of the interim steps of a solution. For example, writing out what you know and what you wish you could do, even if you don't know how to get there. 

My second stop was when the author introduced writing "AHA!". This in conjunction with Susan's assignment to try solving a question from this book using a two-column approach where we explain our steps, made me think of math as a narrative. We tell a story when we solve a question, which is only emphasized by using words to also describe the mathematical process.

Lastly, I attempted the Leapfrogs problem (p. 52), trying 4 and 6 total pins. When I did the 4-pin problem I managed to get the minimum 8-move solution; however, my 6-pin problem had 18 steps. I didn't find the idea of the minimum number of steps very intuitive and my more natural inclination was to determine the repeatable algorithm (not the number of moves).