I’d like to use my blog post this month to introduce CODAP and TUVA; more about them below.

As a math educator I’ve often considered the challenges of teaching statistics. Simply said, should we stress understanding statistics by examining relatively small data sets, calculating basic statistics (e.g. mean, median, mode, standard deviation, etc.), and examining the relationship between these basic statistics and the data set they represent?

Or, should we use larger data sets (real world data) and cloud-based data analysis tools to examine the relationship between the results of the data analysis and the data they ‘represent’?

You’ll notice, the end activity of both these approaches is to examine the data analysis and its relationship to the original data, but the latter ‘skips’ calculation or graphing by hand. Which should be preferred?

I prefer the latter; I’ve visited too many classrooms in which the teacher writes 5 numbers on the board and computes the mean to ‘find’ the center. Students can ‘see’ all 5 numbers and sense the center – without calculation. Many of the basic procedures used to calculate basic statistics precede understanding. This does not lead to inquiry or learning; I prefer students needing to grapple with and make sense of data – notice and wonder (see https://congruentthoughts.blog/2020/03/04/notice-wonder-with-padlet-dotstorming/). I’m more interested in stressing understanding first, then performing basic calculations (if necessary). Perhaps my primary objection concerns the data; it’s often a bunch of numbers, not data.

Of course, the comments above were meant to represent extreme positions; reality is somewhere in between. As we know the Common Core State Standards include basic calculations, interpretations, data analysis, and interpretation.

CODAP (Common Data Analysis Platform) addresses this by offering a data analysis tool for grades 6 through 14. And, it’s free; you can find it at https://codap.concord.org/

CODAP is easy to use; you can use your own data or the sample data sets; and/or explore the included classroom activities.

The following screen shot shows the data I chose (157 cases of roller coaster data with 15 variables), the ‘default’ scattergram, and the ‘suggested’ activities from ESTEEM (Enhancing Statistics Teachers Education with E-Modules from the Friday Institute of the College of Education at North Carolina State University). I apologize for the ‘crowded’ screen shot; you can display/hide any or all of these 3 elements when you’re in CODAP.

As an example, students can explore whether there is a relationship between the age of the roller coaster and its height, between the drop and the top speed, between the duration and the length, etc. My students make many conjectures, and then are able to ‘drag’ the variable titles to the axes and examine the results. There are, of course, more sophisticated ways to organize the data and observe the results. For example, it takes but a few seconds to create the following graph which separates the coasters into 3 age groups, colors them by type (wooden or steel) and plots their speed. What’s your conjecture(s) from this graph?

By simply dragging two variables (column headings in the data table) to the x and y-axes (x-axis: height, y-axis: top speed); you can immediately see the relationship between height of the roller coaster and top speed – no calculations, lots of visual data, lots to support exploration and generate conjectures.

CODAP is (to quote from their website) an interactive environment that encourages exploration, play, and puzzlement. Isn’t that what we what our students to do? I suggest you explore additional features of CODAP on your own at https://codap.concord.org/

Another web-based data analysis platform is TUVA which you can find at https://tuvalabs.com/

TUVA addresses the data analysis task by offering a library of instructional resources including standards-based lessons & activities, assessment tasks, data stories, etc. and the ability to enroll a class of students. And, of course, you can upload your own data too. Then, by using the dynamic software provided you can explore, analyze, and visual your data (graphs).

TUVA provides some data stories, usually interesting enough to engage students, and if you’re willing to pay for premium access, they also provide many more data sets and other advanced features. However, the ‘free stuff’ is a great place to start, though only 15 of the more than 400 datasets are free.

Each of the datasets has activities and data. One of my students’ favorites is Dogs with basic data (7 fields) for 197 breeds of dogs.

In just a few seconds (by dragging the life expectancy attribute to the vertical axis and the weight attribute to the horizontal axis, you immediately see the following scatter plot which can be used to discuss the apparent relationship (negative relationship; the heavier the dog the lower the life expectancy). Of course, there are many other activities (identified on the right side of the screen which have been created by teachers).

One of those activities is titled, “Finding the Median” which is composed of 4 steps and looks like it was submitted by a teacher. One of the steps (which does not require the student to compute but rather manipulate the graph) produces the following graph in which you can see the student is ‘encouraged’ to move one divider to the far right (to include all 197 cases) and move the other divider so that there are the ‘same number’ of cases to right and left (98 and 99 cases respectively). Then, of course, the discussion of the median follows.

If you’re interested in more strategies and examples from TUVA, go to https://tuvalabs.com/dashboard/. By the way, many of the data sets and instructional packages at TUVA connect science data and data analysis; they’re appropriate for STEM instruction and instructors.

My objective in this post was to introduce you to dynamic statistical packages which are freely available. CODAP and TUVA are easily accessible by students from a wide variety of grade levels. TUVA has many curated data sets (especially in the fee-based portion) while CODAP has some data and was designed, I think, for you to use your own data (by the way, the data you use can be imported in a variety of formats from many sources). More about data sources in my next blog post. TUVA has more graph types, while CODAP makes its graphs from dots (data points; so, for example, no pie charts). TUVA displays one graph at a time; while CODAP allows multiple graphs.

How do you approach statistics (measures of central tendency?) with your classes? Do you have an innovative approach for helping students understand and appreciate data? Tell us by making a comment.

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