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TECHNOLOGY tips Lindsay Reiten and Susanne Strachota

Promoting Statistical Literacy through Tuva

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ith political campaigns in full swing, we are reminded that promoting statistical literacy is a matter of equity, especially when it concerns providing access to individuals typically left out of the political process (Konold and Higgins 2003). In this article, we introduce an online tool that encourages students to engage in statistics and demonstrate how students can use this tool to develop and refine statistical literacy. Although many applications and programs can be used to analyze and display data, teachers and students do not always have access to these programs. Tuva (www.tuvalabs.com) is a new, free website developed and promoted by Tuva Labs. Edited by Steve Phelps Technology Tips offers a forum for innovative uses of technology in the teaching and learning of mathematics; it appears in every issue of Mathematics Teacher. Manuscripts for the department should be submitted via http://mt.msubmit.net. For more information, visit http://www.nctm.org/mtcalls.

Department editors Heather Lynn Johnson, heather.johnson@ ucdenver.edu, University of Colorado Denver; Steve Phelps, sphelps@madeiracityschools .org, Madeira High School, Cincinnati, Ohio; and Robert Lochel, [email protected], Hatboro-Horsham High School, Horsham, Pennsylvania

Fig. 1 Screen shot shows the initial image of the loaded data set.

Using open data sources, such as the U.S. Census and the Center for Educational Excellence in Alternative Settings, Tuva Labs has created online data sets that give students opportunities to explore real data around issues that are relevant to them and their communities. The data analysis capabilities of Tuva allow students to analyze, model, and predict with data, and to gain experience with data management, sampling methods, and issues of measurement variability, data quality, and reliability. With the free basic account, teachers have access to twenty-five data sets and are able to upload five of their own data sets. The premium account gives access to more than three hundred data sets, unlimited data set uploads, the ability to request data sets, and many more features. The premium account also gives teachers access to Tuva Collections. Collections are inquiry-based activities and lessons developed using authentic data. The collections are aligned to specific content standards (e.g., Common Core State Standards for Mathematical Practices [CCSSI 2010]) and span several content domains. For example, Model Shop uses data to introduce students to linear functions. We begin by introducing some of the features of Tuva using an activity from one of our classes. Then we will outline how to set up a free basic account.

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FEATURES OF TUVA Some of the features of Tuva can be illustrated in an activity we call “Supporting Your Argument,” which is based on an activity the second author used with her Algebra 2 and Data Analysis classes. It was inspired by arguments about bias in college admissions and was designed to embrace Cobb and McClain’s (2006) suggestion that students should be involved in activity that promotes an “investigative spirit and authentic practice of data analysis” (p. 176). In “Supporting Your Argument,” students explore a data set and various representations of the data. They are then asked to create and present a representation or two supporting their argument about whether one college’s admission process includes gender bias.

What does that case number represent in the context of this data? Additionally, by clicking on CASE CARD in the upper left-hand corner, students can explore how the data set is distributed by attributes. When viewing a particular case card, the associated

data point in the display and table is highlighted.

Changing Representations The Tuva feature that allows students to switch between and modify representations quickly promotes exploration of the data. Students become familiar

• Choose a random point or part of the representation and ask your partner what it is showing. • What story does this representation tell? What is this chart or graph representing? • Is this representation an appropriate way to present this data? • What would a representation look like that would (not) display a bias?

CHANGING REPRESENTATIONS

Exploring the Data When the data initially loads in Tuva, it is unsorted (see fig. 1). Students can begin exploring the raw data by clicking on TABLE VIEW below the graph. Doing so provides opportunities for students to talk with a partner about the raw data. For example, students may explore the table by discussing the following questions: • What does each row in the table represent? • What information is provided in the table? • Choose a random case number in the table. Clicking on a row in the table highlights the associated data point.

with the data, the functional differences between representations, and the affordances of the representations. Through the exploration process, students make sense of both the data and the purpose of each representation. Figure 1 highlights tools used for changing representations (area A). The user selects the type of representation the top row. The data are sorted by dragging and dropping the attributes (area B, listed on the left side of the screenshot) onto the graph or chart or by selecting the attributes in the table (C, at the bottom of the screenshot). Once activated, the name of an attribute turns from gray to teal (see fig. 2). You can also show or hide categories by clicking on the filter option button (fig. 1, area D) to the left of Sketch. The data can also be filtered by excluding specific cases or by keeping only specific cases. While exploring the data and various representations, it may be productive for students to discuss the following questions:

Fig. 2 This screen shot shows an example of a “No Bias” representation.

Figures 2 and 3 represent the same data set. However, the two representations highlight different characteristics of the data. Understanding how and why each representation may support a particular argument is an important aspect of statistical literacy. Furthermore, students may construct confusing or inaccurate representations, providing an opportunity to discuss the ways in which data can be misrepresented, skewed, and in turn misunderstood. For example, a representation similar to the one shown in figure 2 might support a student’s argument that the admission process does not include gender bias because the percentage of females and males who were not admitted is about Vol. 110, No. 3 • October 2016 | MATHEMATICS TEACHER 229

Function

the orientation of a representation (i.e., vertical or horizontal) may or may not draw attention to different aspects of the data. Selecting the functions button (to the left of the filter icon in fig. 3) allows students to add different frequency counts, percentages, and reference lines. When applicable, the mean, median, mode, standard deviation, least squares line, and so on can also be displayed. Teachers and students can discuss how adding these features to a representation may aid interpretation. You can explore more features, such as video tutorials and information about webinars, at https://tuvalabs.com/ resources/. Now that we have introduced some of the features of Tuva, we walk through setting up a free basic account.

link to our data set). This option enables students to explore the data and create representations, but they are not able to save their work. Alternatively, teachers can have their students register with the appropriate class code for their teacher’s account. This second options allows the teacher to get the most out of Tuva by creating activities and worksheets in Tuva that are specific to a class. Also, with this option, students are able to save their work as they progress through the activities. For additional information about creating activities using Tuva, see https://tuvalabs.com/resources/ create_activities_with_tuva/.

REFERENCES

THE BASIC TEACHER ACCOUNT

Fig. 3 This screen shot shows an example of a “Bias” representation.

the same (i.e., 35.49 percent vs. 36.27 percent). Alternatively, a representation similar to the one shown in figure 3 might support an argument that the admission process includes gender bias. Students may further support this argument by highlighting Department C, where only 35 percent (i.e., 13/(13

+ 24)) of the males who applied were admitted, compared with 64 percent (38/(38 + 21)) of the females

Additional Features The ability to Swap X and Y Axes (see the bottom of fig. 3) provides an opportunity for students to discuss how altering

To start using Tuva, go to its website, https://tuvalabs.com, and create a free account or log in with an existing Google account.

Adding a Class Create a class by clicking the + Add Class tab on the right of your screen (see fig. 4). After you have selected the grade and named the class, Tuva generates a class code. You can find the class code on the right side of the class profile screen. Sharing the code with your students gives them access to any data you upload or activities you create for that class when they register.

Fig. 5 Six associated activities accompany the Viruses & Bacteria data set.

selecting the Viruses & Bacteria data set (see fig. 5) you have access to six existing activities (through View, Try it out, or Assign), or you can create your own activity based on the data set.

Uploading a Data Set To upload your own data set, click on the My Datasets tab located in the top navigation ribbon. Choose your file. Supported formats are .csv, .xls, and .xlsx. Cases are represented by row data; attributes are represented by the column information.

USING TUVA Now that you have a class set up, you can assign or create an activity tailored to your students and your learning goals. Step 1 is to choose a data set. You can either choose one of the free data sets or upload your own.

Using a Tuva Data Set Teachers can enroll students manually by clicking on Add Student and providing a username and password. Or, they may provide students with the Class Code for students to enroll themselves.

Fig. 4 Teachers can create pages for different classes.

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Click on Dataset (see fig. 4) and then click on Free in the upper right-hand corner. Tuva has more than three hundred data sets, twenty-five of which are available with the free account. The number of activities associated with a data set, the focus of the activities, and the intended target audience are displayed for each data set. For example, by

Fig. 6 Upload your own data set to Tuva.

For example, in our data set, we have 599 cases, representing the 599 applicants. The attributes are Department, Gender, and Admitted. Next, add a title, determine the privacy setting (i.e., “Only Me” or “Anyone with the link”), then click Upload (see fig. 6). You can also import a file directly from Google Drive™ or Dropbox®. Students do not need to create their own accounts in order to use Tuva. For example, teachers can share a data set or an activity with their students through a link (e.g., http://tinyurl.com/zjs5492 is a

Cobb, Paul, and Kay McClain. 2006. “Guiding Inquiry-Based Math Learning.” In The Cambridge Handbook of the Learning Sciences, edited by R. Keith Sawyer, pp. 171–85. New York: Cambridge University Press. Common Core State Standards Initiative (CCSSI). 2010. Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/wpcontent/uploads/Math_Standards.pdf Konold, Clifford, and Traci L. Higgins. 2003. “Reasoning about Data.” In A Research Companion to Principles and Standards for School Mathematics, edited by Jeremy Kilpatrick, W. Gary Martin, and Deborah Schifter, pp. 193–215. Reston, VA: National Council of Teachers of Mathematics. Tuva Labs. Tuva. https://tuvalabs.com/ LINDSAY REITEN, reiten@ wisc.edu, and SUSANNE STRACHOTA, sstrachota@ gmail.com, are doctoral candidates at University of Wisconsin-Madison. Reiten, a former middle school, high school and university lecturer, is interested in teacher education and supporting teachers in using and adapting technology activities in their classrooms. Before graduate school, Strachota taught high school math in Boston. She is interested in algebraic reasoning, specifically how students reason about functional relationships.

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