Go out and collect a modest-sized, discrete dataset. Name lengths of all of the students in your classroom, say, or the number of people in each of their households.
This bar graph is only tangentially relevant, being more of a case-value plot of four different populations. But it breaks up a texty post. So deal with it.
Now play with that data.
If we add one or more new (hypothetical) cases, can we…
- Increase both the median and the mean?
- Decrease both the median and the mean?
- Increase the mean while decreasing the median?
- Vice versa?
- Increase the Mean Absolute Deviation (MAD) while decreasing the mean?
- Vice versa?
- Decrease both the MAD and the range?
- Decrease the MAD while increasing the range?
- Vice versa?
If we delete one or more actual cases, can we…
- [same list as before]
Thanks to Susan Friel, Connected Mathematics and tons of other creative folks for getting me started with this. Future elementary teachers to tackle this shortly. I’ll report back.
I could get myself in trouble here.
But I need to share.
Regular readers are aware that part of my professional time is spent working on a large-scale middle school curriculum project. The bulk of those on the project are university faculty members in fact and teachers in spirit. We do not work under a paradigm that puts a lot of value in the term proprietary.
We are respectful of intellectual property rights but we don’t spend a ton of time thinking about them. Fair use is an important phrase in this community and the idea that our own ideas might be used by others is a delightful one.
This will not be surprising to those who read stuff on the web. The blogosphere operates in a very similar vein; one which has even been formalized in Creative Commons licensing.
But that’s the development side of the curriculum. We create the intellectual property. A traditional publisher produces the text materials.
Publishers operate with a different world view. Content is money. Use of others’ intellectual property exposes one to lawsuits, except with meticulously obtained permissions, but those permissions are obtained through a legal department that is itself expensive. And obtaining permission may involve a fee.
As an illustration of this clash of world views in 21st century teaching, I offer an abridged list of permissionable selections from the previous version of the curriculum that the publisher would prefer to have removed from the next version. The list is much, much longer than the one reproduced below.
- Data from The Most Popular Colors by Type of Vehicle, 2001 Model Year
- Fastest Bicycle Speed
- Pet Incidence Trend Report
- Pizza Industry Facts
- Box Office Regional Analysis Map
- from “The Wizard of Oz”, the quote The sum of the square root of any two sides of an isosceles triangle is equal to the square root of the remaining side.
- Houston Rockets 2004 roster
- The Nuttiest Peanut Butter dataset
- Typical weights for tiger cubs, and
- Largest Hamster Litter on Record
I can’t quite decide whether this is a Truly Unfortunate Representation of Data. Help me out here.
The following is from an Educational Researcher article on the alignment between the math and English/language arts standards of various states and those of the Common Core State Standards (about which, more here).
The graphic (and several others like it) comes with the following disclaimer:
When reading these graphs, the representation of content emphasis is accurate at each column- by-row intersection, but the smoothing between rows and between columns is not meaningful because the data are nominal. (p. 107)
What this means is this, Because the data is categorical, we could really have put them in any order we like. As a consequence, any patterns (any patterns!) we see within each graph are simply artifacts of the order we chose. This smacks of TURD to me. But I stand ready to be convinced. Any takers?
Porter, A., McMaken, J., Hwang, J. & Yang, R. (2011). Common Core standards: The new U.S. intended curriculum. Educational researcher, 40, 103—116.
So here’s an interesting data representation. The New York Times invites readers to place a point on the graph below indicating their own emotional response to the news of the death of Osama Bin Laden (on the x-axis; right is positive, left is negative) and their feeling about the significance of the event (on the y-axis, up is more significant, down is less). In addition to plotting a point, readers are invited to leave a comment.
As you move your cursor around the graph, the comment associated with each point appears.
The critical thinking task is to predict the comments associated with the extremes-what did someone say who put his/her point in the upper right? What about the upper left? Each of the other corners? The origin? What about the people whose points are at the ends of each axis?
Caution! The task is harder than it seems.
And after you’ve messed around a bit, consider the profound difference between this rich and intriguing data representation and one I posted recently.
The New York Times, for at least the last 10 years, has been doing amazing graphic design work for data representation. The Walker Art Center here in the Twin Cities recently hosted a talk by Kevin Quealy of the graphics department at the Times. I was unable to attend, but it’s online.
I am dying for the end of the semester and having time to watch it.