Yesterday I came across a great resource from missCalcul8: an SBG wiki for noobs. (Thanks to yet another blog, The Space Between the Numbers, by Breedeen Murray, for the pointer.) It includes how-tos from some of the luminaries in this field, plus, joy of joys, actual lists of standards so that we can imagine what they’re really talking about. (She has also just posted a number of frightening skills lists on her own blog.)
For me, well, none of them are in statistics yet, but maybe that’s a place where I can contribute when I make that list.
So I tried to get started. One place to look for statistics standards is in the GAISE materials. That’s Guidelines for Assessment and Instruction in Statistics Education, put out by the American Statistical Association (ASA) and designed to elaborate on the NCTM Standards. These guidelines come in two downloadable pdf books, one for pre-college (that’s us!) and another for postsecondary. In our book, they define three levels, named A, B, and C. These do not correspond to elementary, middle, and secondary; many high-school students (not to mention adults, not to mention me) have not fully mastered the ideas in levels A and B.
Here is an excerpt from the overview (p 11):
Statistical problem solving is an investigative process that involves four components:
I. Formulate Questions
→ clarify the problem at hand
→ formulate one (or more) questions that can be answered with data
II. Collect Data
→ design a plan to collect appropriate data
→ employ the plan to collect the data
III. Analyze Data
→ select appropriate graphical and numerical methods
→ use these methods to analyze the data
IV. Interpret Results
→ interpret the analysis
→ relate the interpretation to the original question
This is a good start, but it has two problems: it needs more detail, and it doesn’t cover a lot of things I think are important (this latter is the vague issue I agonized over in a recent post). For more detail, we can dig deeper in the GAISE document or in a textbook. Under “Analyze Data,” we might have a standard something like,
- Create and interpret appropriate visualizations for comparing multiple sets of data
Which may still be too broad. This could include back-to-back stemplots, parallel box plots and histograms, and even two-way tables. I imagine that to become convinced of mastery, I’d have to ask too many questions. So maybe splitting “create” from “interpret” would help. But should I go further and split continuous (parallel box plots) from categorical (two-way tables and bar charts)? Of course there, part of the problem is that the kids need to decide what’s appropriate, right? Ack!
Then you try to decide where scatter plots live. That’s not really comparing two sets of data; it’s looking at the relationship between variables. Which is also true of a two-way table or ribbon chart—or, if you look at it right, a parallel box plot. (e.g., the one from a couple posts back, which shows the relationship between income and sex):
So maybe we should word them in terms of variables rather than data sets:
- Create appropriate visualizations for assessing the relationship between variables.
- Interpret visualizations that show the relationship between variables.
I like this better, although I still see them as kind of gigantic—but I hesitate to break them into tiny shards (like one per graph or table type). But should I anyway?
Writing this down is useful; maybe reading this will be amusing, if only in a Schadenfreude sort of way, for SBG veterans. If anyone has a good list, let me know.
I can extend this process to blanket much of GAISE and NCTM, and even traditional stats books, but it has its limitations, especially:
- Various standards documents direct the syllabus towards inferential statistics, which is great, but I want my course to have a bigger emphasis on modeling than the traditional course. That course often seems to treat least-squares regression as the exemplar, and then it’s a little divorced from the main thrust of the learning. So I have to decide what I care about in that area.
- Nothing seems to treat habits of mind and larger-scale understandings very deeply, and that’s what I care about most. If I care about it, I should assess it, right?
This last issue is the most troubling. I bet the luminaries have written about it, but I haven’t found it yet. Until I do, I’ll keep fretting. If nothing else, I know that in my situation, I can count on the kids to accept the idea that the list of standards is mutable, and we can work together throughout the year to come up with a fair one.