Here's what I wrote about in 2014:

**Making Sense of Complex Numbers **- I wrote a series of posts developing an argument against the idea that complex numbers were introduced for "whimsical" purposes. (

this, then

this) Teaching and reading about

elementary school math helped push me to the conclusion that rotations might be the best way into imaginary numbers. At the highest level of sophistication, though, complex numbers are

nothing more than points. So: start with rotations, end up with points.

**Exponents as Numbers - **Past research made me very familiar with the sorts of mistakes that kids make with exponents, but I didn't really have a prescription. I still don't, but a few posts this year brought me closer. I argued -- and I don't know if I still agree with this -- that a sophisticated understanding of exponents is closer to seeing exponents as a

number and not as an operation and certainly

not as an abbreviation. How do we help students see the sorts of numbers that exponents represent? I think geometric series are key. I argued that we could use this to give kids a sense of

what a "power" is. I then wrote about two lessons that show how I tried this in class last year. (

here and

here)

**Researchers and Teachers ***-* Some of the most fun I had this year was reading and writing about

*From The Ivory Tower to the Schoolhouse *with Raymond. (Thanks, Raymond!) The book is all about the ways university research does and doesn't make its influence felt in classrooms, and our posts

dug into these ideas. The trouble is that good ideas aren't always popular ones, and a lot has to do with the popularizer and the message. These sorts of concerns popped up when I

wrote about feedback and generally caused me to be

anxious about my own career.

***

This list is disparate. Does anything unify these concerns?

Besides for a pain-in-the-ass contrarian streak (but isn't every argument contrarian?) I think that my writing this year struggled mightily with the theory/practice divide. Teachers that I know (myself included) tend to seek activities and easily usable answers and resources. But on the topics that I've thought the most about -- proof, exponents, feedback, complex numbers -- I see the existing answers as inadequate. Teachers aren't theorists, though, and the way that we communicate is through easily usable activities and resources. (That is, sharing resources *is *teacher discourse.)

What will it be: essays or resources? This next year I'd like to do a better job with both.