Math Relearning/Progressions/K-5 Data
These are my comments on the Common Core Math Progressions document Measurement & Data (data part): Grades K-5 (PDF).
line plot - Something I'll want to explore throughout this domain is the logic of the design of these different data displays. How necessary or flexible is the design? What does it accomplish? What data situations does each cover? Do the displays fall into families? What does each variation accomplish? Why do we order and place the elements as we do?
context - This seems like a very important point that I want to keep in mind.
Hmm, the GAISE report, another freely available document on conceptual math education. I feel like I should look for more of these. But maybe I shouldn't spend time on that and only collect them as they come up. I should at least keep a list of them on the website.
It would also be good to ask what kinds of steps are involved in moving from data collection to representation.
Also why do we pick out these features of the situation to represent in the display?
"greatest and least values" - What questions do we typically ask of data? Why these particular questions?
"fill in gaps" - Are there any categories that do act like numbers and would need to have gaps filled in? Letters come to mind maybe.
"dots will 'pile up'" - Dots are a form of tally, and shorthand for tallies are numbers, which suggests a table. So why do we make plots, graphs, and other such displays?
I'm listening to my Pandora math station, as usual, and the numbers song from Einstein on the Beach is on. It occurred to me that the numbers could have multiple meanings that change based on the context. It would be interesting to explore that technique with words other than numbers.
Where the Measurement Data Progression is heading
Thinking more about why we represent data visually, do we do much with treating graphs like geometric figures?
I guess I should get Tufte's quantitative information book to help me answer some of these questions.
"not in order to make any claims" - You have to know how to read graphs in order not to draw inappropriate conclusions from them.