PROBLEM SOLVING || TECHNOLOGY TIPS

TECHNOLOGY TIPSAuthor(s): Karen Flanagan Hollebrands, Hollylynne Stohl, Mitch Stucker and Paul W. GosseSource: The Mathematics Teacher, Vol. 96, No. 8, PROBLEM SOLVING (NOVEMBER 2003), pp.598-603Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/20871439 .

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TECHNOLOGY TIPS

This

month's "Technology Tips" introduces Fathom Dynamic Statistics, which is a program

developed by Key Curriculum Press Technologies. This program allows users to explore data sets and statistical concepts by using dynamic tools. A full

description of the program and ordering informa tion can be found at www.keypress.com/fathom. In this tip, Mitch Stucker and Paul Gosse demonstrate how students can use the program to analyze a set of data that is included with the program. A tip from Hollylynne Stohl explains how to use Fathom when importing data sets. The "Surfing Note" this month is the Exploring Data Web site maintained

by Education Queensland. This site contains many data sets and activities that can be used in helping middle and secondary students learn about data

analysis and statistics.

How fast can you learn Fathom? Fast!

Fathom, from Key Curriculum Press, is a dynamic multirepresentational environment that is designed to enable students to explore data sets and statis tics concepts. The quickest way to become oriented to the Fathom environment is through one of its built-in data sets (users can also create or import data files). This tip uses the built-in census data for

Albuquerque, New Mexico. Start Fathom. You should see a blank screen and

toolbar, as shown in figure 1 (Stucker/Gosse). The toolbar shows (from left to right) the Selection Arrow,

as well as the New Collection Box, New Case Table, New Graph, New Summary Table, New Estimate, New Hypothesis Test, New Slider, and New Text icons.

Click File, Open, and select the Sample Docu ments folder. Since you want the census files

(although many other samples are included), choose the Census Files folder, as shown in figure 2

(Stucker/Gosse), and open the file named

NM_InclAlbuquerqPart203. A collection box with the file name appears in the Fathom window, as

displayed in figure 3 (Stucker/Gosse). On the Fathom screen, a data collection is repre

sented by a small box filled with gold balls, which

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Fig. 2 (Stucker/Gosse)

Edited by Karen Flanagan Hollebrands Karen_hollebrands@ncsu. edu

Campus Box 7801 North Carolina State University Raleigh, NC 27695-7801

Hollylynne Stohl [email protected] Campus Box 7801 North Carolina State University Raleigh, NC 27695-7801

This department offers a forum where teachers can share innovative classroom activities and ideas related to teach

ing and learning mathematics using technology. Ideas

using all types of classroom technology are welcome.

MATHEMATICS TEACHER



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represent ? collection of individual pieces of data. For those who are familiar with databases, each ball is similar to an individual record, which is called a Case, as in a database. Fathom's basic sets of data are stored in Collections, unlike the profes sional statistical packages, which store data in tables. Fathom uses this method to indicate that

tables, graphs, and so on, are simply different rep resentations of a collection of source data?a simple but powerful idea that reflects a multirepresenta tional emphasis in mathematics. When you double-click on the collection itself, a

Case Inspector window opens in the Fathom envi ronment. It allows users to read supplied background data on the file (Comments tab), see how the data set is displayed (Display tab), calculate defined measures that are applied to each case (Measures tab), or exam ine individual cases and their attributes in the data set (Cases tab). See figure 4 (Stucker/Gosse).

The Case Inspector window gives a lot of infor mation. For example, the status bar in this window shows that it is case 1 of 500. The Case tab shows all attributes and the values that they hold on a

case-by-case (record-by-record) basis. This census record includes 500 cases (people) and has several different attributes for each person. Some of these attributes are categorical data (for example, sex, race, and marital status), and some are continuous numerical data (for example, age and income). You can close the Case Inspector by clicking on the close button (X) in the upper-right corner of the Case

Inspector window. A Case Table is one representation of the collec

tion; it presents attributes for each case in a famil iar way. To view the Case Table, drag and drop a new Case Table to the screen, as shown in figure 5 (Stucker/Gosse). Dragging from an icon to the Fathom window creates that representation in the Fathom environment. The initial Case Table is

empty. Next, drag the name, which is a representa tion of the collection, from the Collection to the Case Table and drop it. As figure 6 (Stucker/Gosse)



Vol. 96, No. 8 ? November 2003



shows, the Case Table fills with data. You can drag attribute labels from one Fathom object to another in the same way.

A Case Table gives you a tablelike box in which

you can paste or drag data, label and enter data, or write formulas to calculate new data elements. Click to select the Case Table, and drag it somewhere convenient. Size it with the sizing handles to dis

play more of the attributes (column headings). By dragging the handles and making some selections

small, Fathom turns the selection into an icon that can save window space while still showing all active objects. Drag the handles of the Case Table to make it into an icon.

Suppose that you want to investigate the income of the cases (people) in the collection. Reopen the Case Table by dragging a corner to make it larger. Be sure that you can view the Income column head

ing. One way to investigate the income is to repre sent the data graphically. To create a graph, drag a New Graph box to the window in the same way that you previously dragged the Case Table. See

figure 7 (Stucker/Gosse). From the Case Table, drag the Income label and

drop it on the horizontal axis in the graph box. Fathom instantly produces a dot plot (the default

graph) with an accommodating scale. Scales in Fathom can be adjusted easily by grabbing either axis and dragging it. When your graph is selected, the status bar at the lower left of the Fathom window

gives valuable information about the collection that is relevant to the selected object. Clicking the drop down box in the upper-right-hand corner of the graph box shows several available plot types. We can

change the plot type easily. Choosing "histogram," for example, produces figure 8 (Stucker/Gosse).

To see more than one plot type at the same time, drag a new graph box into your environment and

change the type as desired. Figure 9 (Stucker/ Gosse) shows a box plot of the income data, in addition to a dot plot and a histogram.

Representations from the same source data in a collection are dynamically linked. Moving the

mouse over portions of any object or representation in a Fathom window produces specific information in the status bar on the bottom of the screen. For

example, move your mouse over the second quartile of the data on the box plot, and click to select that

quartile, as shown in figure 10 (Stucker/ Gosse). Data belonging in the second quartile become selected in every object or representation. Even the Case Table is indicating that cases 2 and 3 are two of the cases in the second quartile, whereas, for

example, case 5 is not. From the histogram, you can see that of the 343 cases where income is less than

$20,000, about 250 cases are highlighted in the

quartile group (of course, you can determine this number exactly, as well).

MATHEMATICS TEACHER



What happens if you bring a categorical attrib ute (for example, Sex) together with a continuous one (for example, Income)? Find the Sex label in

your Case Table, and drag it to the vertical axis of

your existing (or a new) box plot. Of course, you have two separate box plots (one for each category) in one graphical representation, as shown in figure 11 (Stucker/Gosse).

You can generate some interesting visual com

parisons. For example, selecting the second quartile on the Female portion of the dual box plot (you could have dual histograms by changing the plot type) now shows the location of only that group in the other representations, as figure 12 (Stucker/ Gosse) indicates. Case 3 is still now in this "fil tered" subgroup second quartile, but case 2 is not.

Create a new dot plot, drag the eduCode attrib ute from the Case Table to the horizontal axis of a

graph, and drag income to the vertical axis, as shown in figure 13 (Stucker/Gosse). Even though eduCode is a categorical variable, Fathom treats it as a numeric one, since the codes are numerals and have corresponding text codes in the eduText attrib ute. People with a higher level of education tend to have a higher income. Also, many people reported an income of zero. Compare the spread in this scatter

plot with the dot plot of income. Most of the cases have income of less than $40,000. If you look in the

scatterplot for the points above the $40,000 income

level, the data are more dispersed and tend to cor

respond to cases that also have an eduCode greater than 10 (that is, a high school diploma or GED), although many cases with an eduCode higher than 10 also have an income of less than $40,000.

This tip focused on the power of Fathom to quick ly and powerfully display and explore data using a

variety of graphs. Other real strengths in Fathom include exploring statistical calculations, modeling and generating statistical data, using and under

standing inferential statistics, and technical report writing?all of which are topics for another day.

[email protected]

Highland High School Albuquerque, NM 87108

Palili). Goue. paulgosse@gov. ni. ca

Department of Education St. John's, NFA1B4J6



Vol. 96, No. 8 ? November 2003



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How to use Fathom when importing data from a Web site This month's "Surfing Note" highlights a Web site where you can find data sets that can easily be

imported using Fathom. Consider the data set in

figure 1 (Stohl), which contains information about the chirping rate of a cricket at various tempera tures. These data are located at exploringdata .cqu.edu.au/datasets/chirps.tab.

In Fathom, under the File menu, you can choose

Import from URL. You can enter the URL for the data set in the pop-up window that appears. See

figure 2 (Stohl). The data are automatically imported into a New

Collection. Fathom does its best to interpret the data into attributes and put the data values in

appropriate columns. In this case, the title and col umn headings for the data are on more than one line. The user should delete the first two rows in the Case Table, as in figure 3 (Stohl), by selecting the first two rows and choosing Delete Cases under the Edit menu. Then you can rename the attributes in the column header by double-clicking in column headers and typing a new name, as shown in fig ure 4 (Stohl).

The data are now ready to be analyzed with

graphs and statistics. Fathom makes obtaining real data from Internet sources as painless as possible. Whether a user chooses to import data through a

URL, as done in this tip, or to copy and paste tab delimited data from spreadsheets or Web pages, the

process of getting data in classroom-ready format is a lot easier with a tool like Fathom.

COEDTO^T"Technology Tips"

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Fig. 3 (Stohl)

602 MATHEMATICS TEACHER



Fig. 4 (Stohl)

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af L?tatv?n So you think the aeon, aadian and node era boring? Hill, aaybe. but there are interesting little side alleys to this topic that ore north exploring. Nroursi gf Sarud Visit here, and you ?ili learn about seat very useful statistics.

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rtoraal Plata Not included in Queensland syllabuses, e nomai plot of da toset thorn ot a glanes if a dotaset is approximately normally distributed. A very useful display to put in your display cabinet.

Surfing Note

Exploring Data

Exploringdata.cqu.edu.au The Exploring Data Web site contains many data sets and activities organized by topics. The topics include box plots, scatterplots, linear regression, hypothesis testing, and normal distribution. Each

category includes a review of concepts and proce dures, activities, and worksheets. A master list of data sets indicates the topics that are applicable to

study with each data set. These data sets can be

easily downloaded in three commonly used formats?

Excel files, NCSS files (a commonly used Statistical package in Queensland), and

tab-delimited, which can be used to transfer data to a graphing calculator with TI-Connect or

TI-GraphLink or can easily be imported into Fathom.

Mathematical Diversity MATHEMATICS

is a global endeavor. Different groups have responded to the challenge of learning, teaching, creating, and experiencing mathematics using distinct approaches. These differences in language, culture, ethnicity, talents, and needs present rewards and chal

lenges to the classroom teacher. In classrooms, varying perspectives yield important insights that motivate and enrich mathematical activity. What can we do to draw out and benefit from the diversity of human activity relating to mathematics?

We invite those with experience in diverse approaches to learning, teaching, creating, and experiencing mathematics to submit manu

scripts for a special focus issue on the human dimensions of mathematical diversity.

Seven double-spaced copies of the completed manuscript should be sent for review to the Mathematics Teacher, 1906 Association Drive, Reston, VA 20191

1502, no later than May 1, 2004. Please state clearly that the manuscript is being submitted for the 2005 focus issue on Human Dimensions of Mathematical

Diversity. No author identification should appear in the text of the manuscript. Guidelines for the preparation of manuscripts can be obtained from NCTM's Web site, www.nctm. org/mt/mt-info.htm. If you have any information or ideas related to this topic and would like to discuss them with a member of the Editorial Panel before preparing a manuscript, please send them to Jeffrey Choppin, [email protected]; Bonita G. Hayman, [email protected]; or Mariano (Rod) Rodrigues, [email protected]. Include your address, telephone number, and e-mail address. Someone will contact you after receiving your message.

Vol. 96, No. 8 ? November 2003 603



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PROBLEM SOLVING || TECHNOLOGY TIPS