[Andee Rubin]

In trying to figure out how to support students’ understanding of covariation, I ran across the quadrant count ratio.  Have you ever considered adding it to CODAP?  It would be a simple addition to the “ruler” menu – it’s more intuitive than correlation coefficient because it doesn’t require fitting a line first, then seeing what the scatter is around the line.  Curious what you think.

[Bill Finzer]

Hi Andee,

No, we haven’t considered adding this measure or a visualization thereof. I think the wikipedia entry is helpful:

The QCR is not commonly used in the practice of statistics; rather, it is a useful tool in statistics education because it can be used as an intermediate step in the development of Pearson’s correlation coefficient.^[1]

I can see how it would be useful if one’s goal is to understand the meaning of the correlation coefficient as a numerical measure. You say that you think that not requiring the line makes it more intuitive. What are the conceptual difficulties you expect that it would help with?

Thanks for the question,

Bill

[Andee Rubin]

Yes, I had read the wikipedia entry after I saw a reference to this measure in an ICOTS paper (which wasn’t very good, other than introducing me to the measure).  I’m finding that students (and teachers) have very little understanding of what a correlation coefficient is – they just learn some rule of thumb about which values are “significant” and which ones aren’t.  In fact, I’m finding that students don’t really understand what a “least squares line” is either – they don’t understand the variability piece.  I’m developing a unit for 9th grade biology and want students to have strategies for looking at a graph and assessing whether there is a relationship between the two variables without having to plot a line.  Even more basic, students don’t really understand that an association means “as X gets larger, Y gets larger (or smaller),” so I’ve been working on some ways to help kids read scatterplots, which are somewhat of a mystery to them.  (They tend to read left to right as time, for example.)  So I want some way to talk to them about how strong the relationship is without getting in to plotting a line.

That’s a long answer – and I’m not sure I’m doing a great job of communicating my reasoning.  (I’m in the middle of teaching a workshop on data in Puerto Rico!).  If you’d like to talk more about it, perhaps we could Zoom sometime.

Andee

[Andee Rubin]

By the way, I’ve been working with Cliff on several visualization strategies to help kids parse scatterplots.  One involves coloring points and works really well in CODAP.  The other one would use binning – so it would be great to have a more robust binning capability…

[Heather Barker]

Andee

I teach introductory statistics students at the college level and introduce this idea as well, that they have usually seen before, thanks to high school teachers like you. But I think you’re right, that sometimes intuitively the idea of the strength of a linear relationship is lost.

I use CODAP as my primary teaching tool and I love to tell this story about my 7 year old son as an illustration of the power of data visualization. One day (as he often does) my son looked over my shoulder as I was preparing a lesson. I had a data set from the World Health Organization’s happiness report. This is a poll done by Gallup of several thousand people from many countries to measure different things about their life, GDP, healthy life expectancy, social support, happiness, etc.

I had the graph below open and told him that the bottom axis showed us how much money on average the people in a country make and the “sideways” axis is how long they can expect to live. I asked him what story he could tell me about how much money people make and how long they can expect to live. He thought for a moment and drew a circle around the dots between 7 and 9 on the x-axis and 45 to 65 on the y-axis. He said these people don’t make as much money and don’t live as long as these people (drew another imaginary circle from 10 to 12 on the x-axis and 65 to 80 on the y-axis). So I prodded and said well what does that mean? He said I guess that means a country that makes more money should live longer. And we discussed why that might be the case. He’s got it! That’s correlation from the mouth of a 1st grader. I think sometimes that by the time students have gotten into high school and college they have so many tools, it’s hard for them to step back and see the big picture.

Link to CODAP File

I would love to hear of any other data visualization techniques you use for kids. I also teach elementary education majors as they prepare to teach math. I love giving them tools they can use in the field.

[Heather Barker]

Andee

I teach introductory statistics at the university level, and run across the problem you shared as well. I love to tell this story about my 7 year old son interacting with CODAP and the power of data visualization.

While I was home preparing for a lesson recently my son looks over my shoulder and asked what I was doing. I had uploaded data from the World Happiness Report conducted by Gallup poll, that looks at hundreds of countries and evaluates things such as life expectancy, security, trust of government, happiness etc. Here’s a link to a CODAP page showing the 2019 data.  I had the graph below pulled up with GDP on the x-axis and life expectancy on the y. He’s never seen scatterplots. But I explained to him loosely how the bottom scored a country’s wealth and the side numbers scored how long they’d live. I asked him what he could say about these countries.

After a moment he uses his finger to make an imaginary circle around the dots between 7 and 9 on the x-axis and 45 to 60 on the y-axis. He said these people don’t have as much money and don’t live as long as these people (draws another circle around the dots from 10 to 12 and 70 to 80 on the x- and y-axes). I then prodded more and he said “well I guess the more money a country makes, they should live longer”. He’s in 1st grade, and he’s got it. Isn’t that what correlation is trying to tell us? I think sometimes our students get bogged down in the data analysis “tool box” they’ve been handed, and often miss the big picture of the story we can tell with the data.

I would love to see what you create with Cliff for young learners. I also teach the math classes for our elementary education majors and love to have things to share with them that they can use in their classes. Plus I love thinking about how young children learn, with those clean, clear minds.

[Dan Damelin]

Andee, I’d love to hear more about these strategies.

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