Today I decided Alex was ready for some real data analysis. As a little side job, I’m in charge of the participant evaluation survey for SUUSI, our beloved family camp which we’ve attended every summer for seven years. I pulled out the data for the 39 respondents under the age of 18, to give Alex a manageable (and also personally meaningful) sample to work with.
I began the lesson by explaining that people look at data because there is a question they want answered. We make a graph or chart to put numbers into an organized arrangement that helps us figure out the answers to our questions.
I wrote a question down on a piece of paper: “Why do kids and teens come to SUUSI?” Then I gave her a list of reasons with counts after them, and asked her to think out how she could make a graph. Immediately she hit a road block: the first response option was selected by 37 people, and her graph paper wasn’t 37 squares high.
Her idea was that she could make a key linking each response option to a color. Then a too-tall bar could be split into two bars of the same color. We made a little rough sketch of how this would look and discussed whether it would be easy to interpret. (No.) She was surprised and impressed when I showed her that we could label the y-axis by 2′s, and from there she constructed a graph without difficulty.
When she was done, I showed her the question again and asked if she could use the graph to come up with answers. Here is her summary:
The main reasons kids come to SUUSI are friends and fun. Not many kids like the music at SUUSI. Tradition is reasonably popular as a reason to come to SUUSI. Different kids like different things about SUUSI.
Next I suggested we consider a more complicated question: “Do kids come to SUUSI for different reasons than teens do?” It seemed intuitively obvious to Alex that they do. I picked out a sample reason, “fun,” and wrote down that 13 kids and 20 teens had chosen that response.
“Teens like fun more than kids do?” Alex asked dubiously. Ah! No. In fact, only 13 kids answered the survey, compared to 26 teens. I drew little pie charts to illustrate the difference between 13/13 and 20/26, and she clearly understood the difficulty. I explained that to make the comparison fair we could convert the numbers to percentages, which she has some conceptual aquaintance with, and gave her a new set of results expressed that way.
Then we puzzled out how to draw the graph. Alex’s first thought was to shrink her first graph down so it only took up half the paper, so she could have one for teens and one for kids side-by-side. We drew a little sketch and considered whether that would be easy to interpret. (Maybe not.) I showed her how we could have side-by-side bars for each reason, and she went to work constructing her graph.
As she drew it, very carefully estimating where to draw each bar if one square equalled ten percent, we talked through the interpretation. What did the data show? Why might it be that way?
“Not many teens say they go to be with their families, but a lot of kids do,” Alex observed with surprise.
“Why do you think that is?”
“…Oh, because the teens don’t even stay with their families. They stay in the teen dorm and you only see them once a day to hug them.” (Alex is counting the days until she’s old enough for the teen dorm.) Similarly, she worked out that no kids say they go to SUUSI for the nightlife because nightlife doesn’t happen until kids are in bed.
When she finished the graph, once again I asked her to come up with some answers to our question. She surprised herself by coming up with a whole paragraph, which I wrote down for her:
Only teens like nightlife and music. Kids like nature trips and family a lot more. Teens like spiritual stuff more. Fun is more important to kids. Tradition is more important to teens. Friends are VERY important to both!
I did a lot more scaffolding in today’s lesson; i.e., showing her things she wouldn’t have been likely to hit on by herself. But she’s doing great with the main goals I had for this data analysis unit. She does a fine job of plotting points on a graph, given design guidance. She can read a graph well. And the most critical thing (which is missing from the lessons in her curriculum, incidentally): she’s beginning to develop an understanding that data analysis is organized around questions, and that you pick your choices to shed light on those questions.
?
I love it! What a great real-world way to illustrate and compare stats.
I really wish you’d taught the statistics and data analysis class during my master’s degree. Your explanations here are already head and shoulders above the sooooo dry, confusing and jargony descriptions of the 1000 year old anthropologist Professor.
The only thing that made that class interesting was learning that the professor had been kicked out of Kenya during colonial days for “mucking about with the native women” – supposedly he has many many decedents … Reconciling that story with the elderly man in the tweed jacket, corduroy pants, bald head and tendency to spit when he talked was mildly amusing…
*descendants…
I run into adults all the time who are still fuzzy on the idea that your data collection and analysis should be focused on the questions you want to answer.
Chad had just sent me a graph of the Pip’s weight by age, so I sent him this and he mentioned it on Twitter (in case you get new-to-you people coming by).
This is so awesome! I know CJ complains bitterly about how many of his high school students can’t construct or interpret a graph to save their lives.
I wish all kids were systematically taught this kind of data analysis. Maybe at some point you could get Alex to analyze a couple of news articles to learn to distinguish good and bad (deceptive) uses of statistics to answer or obfuscate questions. My favorite statistics text (http://www.amazon.com/Primer-Biostatistics-Stanton-A-Glantz/dp/0071379460) uses analysis from flawed biostatistics publications to teach proper use of statistical analysis.
This makes me happy. I like the part about starting with a question and then using the graph to help answer the question, and I especially like the part about figuring out why.
Hobbitbabe, I’ll admit that sometimes when I’m designing a lesson I think about what you might do.
Looking at the lessons in MEP (Alex’s back-up math curriculum while we wait for Beast Academy 3c), I am struck by how, even in an excellent math program, the lessons on data analysis are totally divorced from context. They try to make it relevant by having kids graph class data (weights, heights, even head circumference for everyone in the class), but there’s no indication of why you might care about everyone’s head circumference. You create a graph because, apparently, it’s what people do. Then you answer questions about the graph. But you don’t have a reason, which is a shame.
As a epidemiologist and stats person I love this lesson. Making it real makes things make so much more sense.
While I’m thinking of it, I’ll tell you one of the examples I use about explaining data. I heard this on NPR one morning when I lived in Ohio; I think in a story about how schoolkids were actually quite competent at the “basics” of calculations but needed to be challenged with the interpretation parts. I give it to university students or gifted teenagers with a framing of using it to ask younger kids to explain; this seems to make them feel competent and not condescended to.
Anyway, apparently a bunch of kids in a school were each given a spelling test and a length-of-foot measurement. A graph showed a positive correlation between spelling ability and foot size. Did it mean that big feet help people spell better? What else do yuo think it could mean? What else could you measure to help figure that out?