Graphical Analysis for Windows
Workshop for Math and Science Teachers
The following excerpts from the North Carolina curriculum for math and science identify areas where the use of Graphical Analysis for Windows can help achieve these goals:
Mathematics Goals
The vision and philosophy described throughout this document are based on our goals in mathematics education for North Carolina students.
The six goals are for all students to develop:
· Strong mathematical problem solving and reasoning abilities;
· A firm grounding in essential mathematical concepts and skills, including computation and estimation;
· Connections within mathematics and with other disciplines;
· The ability to use appropriate tools including technology to solve mathematical problems;
· The ability to communicate their understanding of mathematics effectively; and
· Positive attitudes and beliefs about mathematics.
Science as Inquiry Strand- As a result of activities in grades 9 - 12, all students should develop:
· The ability to do scientific inquiry.
· Understanding about scientific inquiry.
· Abilities to perform safe and appropriate manipulation of materials, equipment, and technologies.
· Mastery of integrated process skills.
The essence of the inquiry process is to ask questions that stimulate students to think critically and to formulate their own questions. Observing, classifying, using numbers, plotting graphs, measuring, inferring, predicting, formulating models, interpreting data, hypothesizing, and experimenting help students to build knowledge and communicate what they have learned.
Workshop Agenda
¨ Opening the program and identifying and arranging the three windows
¨ Entering data, defining units, decimal places, etc.
¨ Importing data from TI calculators, copying from spreadsheets
¨ Scaling the graph, changing axes
¨ Adding a new data column and calculating the data to go in it
¨ Adding a new data set, plotting more than one data set on the same graph
¨ Curve fitting and identifying relationships
¨ Printing options
¨ Saving options
Open the program by going to start, data analysis tools, Graphical Analysis for Windows
Once the Welcome window is displayed, click on OK to enter the program..
Notice that the screen has three different windows. The active window is the one that has the bar colored or highlighted. Just click on the window you want when you need to change windows. With the data table window selected, you are ready to set up the columns to enter the data for the variables being studied. To label the columns, put the cursor into the gray area labeled X and double click. This opens the column options box to define the information about the variable.
Repeat with the Y variable column. Notice as you complete this, the axes are labeled and a title is put on the graph.
Enter the following data set:
Circumference (cm) / Radius (cm)62.7 / 10
50.2 / 8
31.5 / 5
75.4 / 12
44.0 / 7
188.3 / 30
94.1 / 15
25.1 / 4
Now choose data from the menu bar and sort data.
Data can also be imported from graphing calculators using a Graph-link cable connected to the calculator and the computer by going to file, Import from TI calculator
Data can be copied from spreadsheets or charts by highlighting the data, edit and copy, then switch to GA and edit and paste. Make sure you only highlight the part of the spreadsheet that contains data (no headings or text) and that you have data columns to accept the number of columns you want to paste. The cursor must be in the first cell in the data table when you paste the copied data.
Select the graph window by double clicking the mouse somewhere in the graph window. A graph options window will appear. This gives you more control on the appearance of the graph.
Choosing the More X-axis options or the More Y-axis options will let you change the way the axis is scaled as well as let you select what is to be plotted on each axis. This is where you would go if you had more than one data set and you wanted both data sets to be plotted on the same graph (this is usually on the more Y-axis options, assuming that both data sets had the same x variable).
You might want students to do something to the data for one of the variables and then replot the data. For example, suppose the shape of the graph indicates that the two variables might be inversely proportional. If you take the inverse of one of the variables and replot, the resulting graph should be linear if the two variables are indeed inversely proportional. This can be done quickly using this program and it encourages students to try a variety of things when looking for relationships.
To do this, you would select the data table window, click on Data from the menu bar, choose new column…calculated and this window appears
Once you have defined the formula, the data will be automatically entered into a new column in the data table. To replace one of the variables on the graph with this new data, double click on the label on the axis and replace the variable with the new column.
Let's try this with your data. Set up a new column to calculate diameter from the data you have entered. Replot the graph as diameter vs circumference.
New data sets can also be entered into the file. Choose Data from the menu bar, the New Data Set. This is helpful if students did more than one trial and wanted to compare results on the same graph.
One of the most powerful uses of this program is the curve-fitting option. You can use this to see how well the data fits a particular curve. From this, students can develop the mathematical relationships that models the data. With the graph window selected, choose Analyze, automatic curve fit, and then make your choice as to the relationship.
Apply a linear fit to the data you entered (Radius vs circumference). Does the slope have any significance? What if you reverse the axes and try a fit again? What about circumference vs diameter? Can you attach meaning to the slope? Is the y-intercept zero? Should it be?
There are several files that come with the program that you can use to tests these ideas more. First go to File and Open and open the file called temp.dat. Try a linear fit to this data. How well does it fit a straight line? What does the slope indicate? What about the y-intercept? Could you write the equation for the relationship between these two variables? Does it look familiar? Do you think students are more likely to remember the conversion formula by memorizing it or by constructing it from data they have collected?
Open the file called strobe.dat. What does the shape of the graph suggest? Try adding a new column that will calculate the square of time and then replot time squared on the x axis. Is it linear? Try a linear fit. Go back to the original graph by changing the x axis back to time and try a quadratic fit. What would you write as the equation for the relationship?
Open the file boyle.dat. What would you do to linearize the graph? Compare this to the file decay.dat. Are the both inverse relationships? Could you use this to help students see the difference between an inverse relationship and an exponential one?
The Text window is useful to help students describe the relationships they have identified from the data. It would also be a good place for students to write conclusions for lab reports or descriptions for how the data was collected. Any of the three windows can be closed or resized. To close a window, click on the box in the upper left-hand corner of the window, then choose close. To resize a window, move the cursor to the edge of the window until the cursor becomes an arrow pointing both ways. Click and drag the mouse until the window is the size you want.
You can also change the way the windows are arranged by choosing Window from the menu bar and arrange window.
To print, first choose file, then printer setup. Have students enter their name so when the graph prints, they can identify their work.
To save the file, notice that the default directory is g:\win_ga. Files can't be saved in this directory. Students should save as soon as they enter data into the data table, again after working with the graph, and again after they have completed the text box information. If you want to save the file to disk, then double click on a in the directory list. To save the file so that it can be accessed from any networked computer in school, save on g:\projects\your name\filename.dat. If you haven't created a folder on g:\project, you might want to do so to have easy access to student files. This can easily be done in Windows Explorer. Let me know if you need help doing this.