Journaling in Math Class

My first experience with teaching was at a summer camp for high schoolers. One of the routines involved each student writing in a journal at the end of class to record their accomplishments of the day. I've carried this routine into all of my classes, from pre-algebra to AP calculus, and it makes my classroom unique. (This post is part of Explore MTBoS, for Mission 1.)

I am ashamed to admit that I have sullied the good intentions of this routine by using it to meet the administration's strange requirements like "students must engage with the written objective" by asking them to journal on "How did you meet today's objective?" before reaching the more interesting second question (wrote about that and had a discussion in the comments). Other years I haven't had the requirement so I struggled to phrase the question in a way that would get the students writing about "least common multiples" instead of "hot dogs and buns" or "p. 132."  I've asked "What math did you learn?" but without the results I was really hoping for; it just wasn't reflective enough and that's what a journal is supposed to be, a place to reflect on class. This year I think I've got it: 

What did you notice or wonder during class?
(Plus a varying second question, which I analyzed and listed once)

This phrasing finally allows me to say:

• I don't want to know what you did, I want to know what you thought. 
• Its impossible to be awake in my class for 90 minutes and not have a single thought. In the past it was possible to not meet the objective or not learn any new math, but "I didn't notice or wonder anything" is 100% cop out and once I call kids on it they start sharing. 

Bonus- the answers to this question are 100 times more interesting to read than "I learned about least common multiples" but still has them using the vocabulary that I want them practicing.  I've recorded some of the most interesting responses, first to share back with students to model the types of answers I'm looking for, then to share with you because I've been meaning to write this post for a month!

Honors PreCalculus:

I wonder how a function is even or odd. 

I noticed that the graph had symmetry on the y-axis. 

South America must have the most drastic change in speed of rotation. 

I realized that different parts of the world spin slower than others depending on how close they are to the north/south pole. 

I wonder if I can find an easier way to calculate revolutions

I wonder about the guy who created pi, if he knew it would be used for this sort of stuff.

I noticed how easy it is to see the patterns on a graph

Class keeps getting more difficult every class/week, I like the challenge.

I noticed that the sin/cos graphs are like parabolas.

Fundamentals of Geometry:

I notice that this class teaches math differently than I'm used to learning. 

I notice that I remember some things from last year. 

Day 1: I wonder how difficult geometry will be. 

Day 3: I notice that geometry is easier than I thought.