Math Relearning/EngageNY/GK

These are my comments on EngageNY's Kindergarten modules.

Kindergarten is largely the same as pre-K, just moving a bit faster. This is because New York's pre-K standards are practically the same as the K standards. This actually makes it harder for me to work with in a short time frame because I don't want to replicate my efforts with pre-K, but I don't want to take too much time to sort out what's unique about Kindergarten. These comments will mostly document my false starts and other ideas I had but postponed.

At this point I'd like to note that the lesson objectives of this curriculum basically form a second set of standards. I might be even more interested in these than in the Common Core standards because, since they're meant for actual teaching, they're more granular, and they're specifically ordered to unfold the concepts logically.

But the lesson objectives aren't enough by themselves to give me the sense that I'm grasping everything. I want something I can read that will make me feel like every statement flows logically into the next. For that I need concepts and not just lists of tasks.

When I think about formalizing math concepts, these concept types seem important: objects, properties (of objects), relationships (among objects; relationships include things like equations), tasks (specific results to achieve using relationships), algorithms (procedures for carrying out tasks), capabilities (types of situations that particular relationships and tasks can address), applications (specific real-world situations to be solved with math). These form components of a system for doing math.

I think I'm enough of a visual learner that diagrams really would help me grasp this stuff. Right now the curriculum material feels like a wall of text. I'm thinking of extracting the relevant graphics from the lesson files and putting them in a new document listing the concepts.

I also think it would help me remember the concepts and piece them together if I had a name for each one. That would take a lot of work on top of all the work of discerning and spelling out the concepts, but it might be worthwhile.

Taking notes that simply copy from the source material feels like a waste of time, but it's helpful to have a streamlined set of information to examine and review, so maybe it is worth the time.

New propositional concepts from Module 1:

• A collection of objects can have attributes that allow it to be grouped with other collections, such as the quantity of objects they contain.

I'll dispense with the new propositional concepts for the rest of Kindergarten for now. It takes a little too much time to separate the new ones from the ones covered in pre-K. I might come back to it later.

One characteristic of this curriculum that makes the pre-K/K comparison harder is the ways the lesson objectives are worded and the tasks and concepts woven together as the lessons progress. To be honest it looks more like a tangle to me. I thought a more worthwhile use of my limited time on the material would be to tease the threads apart somewhat and separate them into more distinct strands, but that also ended up being too much work.

Each lesson objective has this general structure, possibly with some elements left out: Perform action A on object B within parameters C for purpose D. Several actions can be chained or simply collected within one lesson.

If I had lots more time, I might come up with a normalized version of these objectives that followed a small set of grammatical patterns and used a more controlled vocabulary. It would make the objectives and their progression a little easier to think about, but really it's overkill for what I need.

I did make a list of verbs, nouns, and modifiers the objectives used to see what basic tasks and objects the grade covered, and then I started writing a simplified set of tasks for it, but then I realized I was basically reproducing the Common Core standards, so I scrapped that idea. Instead I'll just review the standards.

I'll also review the sections of the Progressions that cover Kindergarten, and I'll do that for each later grade as I get to it. They seem to discuss most of the conceptual material I want to explore.