Using a spreadsheet or other form of computer graphing package for data analysis is becoming a common activity in middle and high school math and science classes. As a mathematics teacher, I have helped many students make graphs for my own mathematics classes. As a technology specialist, I have assisted students in making thousands of charts, representing all kinds of data.

For several years, I assisted students in putting their data in a form the computer could understand, and in choosing the right kind of charts--line, histogram, pie, etc. This is probably the extent to which most students receive instruction in making charts. Many of the students' charts were for public display in the local science fair, to be viewed by parents, teachers, administrators, judges and community members. I was satisfied that students could create good looking charts, using standard schemes for labeling the axes and titling the chart (See Figure 1). My students, and the other teachers' students whom I was assisting were using technology to look at data in new ways, and analyzing and interpreting that data. We often rearranged data or transformed it, such as using moving averages or logarithmic transformations, and experimented with different types of charts. I thought my teaching was heading in the direction pointed to by state and national reform movements (NCTM, 1989; NCTM, 1992; NCTM,1996). I was satisfied that my students were effectively using technology to do mathematics.

Then a few years ago, I read an article in a computer magazine (unfortunately I've lost the source), that gave some valuable ideas on good style for charts in newspapers and magazines, that I thought I would try in my classroom. This article, more on desktop publishing than mathematics, provided me with one of the best teaching ideas I have ever used. Several excellent suggestions were given, but the simplest and most important was simply on how to title a chart.

Look at any of the charts in the local or national newspapers and you'll see that they are much flashier than what we would create in our mathematics or science classes. When we read a magazine or newspaper, it is rare to see a chart entitled X vs. Y, as we often do in a math class. What we are more likely to see is something like Unemployment is at its lowest rate in the last 10 years! (See Figure 2). As I was thinking of ways to make student's science fair projects stand out to the public and the judges, I thought this may be a way to grab the judges attention and give the students an edge over the competition.

I do not know for sure what effect these creative titles had on the judges, but I do know that it turned into one of the most enlightening teaching and learning experiences ever for both me and my students. The next day, after reading the article, I showed students some examples from Newsweek and USA Today and asked students to start titling their charts more like professional journalists. In essence, I asked them to draw conclusions based on the data in front of them, and write these conclusions in complete sentences. Asking students to draw conclusions from data is not a ground breaking idea. But using conclusions as chart titles and captions became one of the most important teaching and learning ideas I've yet to encounter. This may seem like an easy enough request, especially since many of these charts were created from science experiments using real data. But the sad fact was that the overwhelming majority of the students already had formed a conclusion before even looking at the charts. And even though they had formed conclusions which may have been supported by the chart, they could not think of creative titles for their charts. They could not put their conclusions into a concise sentence.

Students as young as seventh grade could label two columns of data such as "Lunch" and "Number of Students," and have the corresponding labels attached automatically to the spreadsheet chart (See Figure 1). And almost all could label the chart "Lunch versus Number of Students." Most students will easily be able to attain these levels of proficiency. But do not assume students can make inferences from the chart and data, just because they can make the chart. It was a shock to me that none of my students could immediately go to the next level and put into an actual sentence what the chart was telling them. And for some, this was after several years of making charts. This amazed me, these were very bright kids, and they had seen and made lots of charts and graphs in science and math classes. There were obviously some things I had mistaken about students' understanding.

I believe that mathematics teachers and writers of textbooks have a habit of making things too concise and abbreviated, to the great misfortune of many of our students. We use our own kind of mathematical communication, where we use hints to communicate, letting the reader or listener interpolate, extrapolate and discern all the implications of our hints. Should the reader not be able to understand what we intend, they are categorized as not quite as able as someone who may not think exactly the same as us. We use the same terseness with graphical information. How many times have we seen a teacher or text fail to label the axes of a graph? Example: How many times have we seen a bell curve drawn without labels attached? Can you remember what the axes represent? If we want to draw more students into mathematics classes and have them be successful, our job should be to remove the mystery of mathematics through better communication, and show students that math may not really be as hard as they thought.

Before we get to creating the titles of the charts, the labels of the axes must be mentioned. To facilitate students in the process of constructing colorful attention grabbing titles, I started asking students what the axes represented. It took me only short time to figure out that descriptive labels for the axes were a prerequisite for student understanding of the data. A typical conversation for labeling a graph as in Figure 1 might be as follows:

The Horizontal Axis

S: Lunches.

T: What does it tell us about lunches.

S: I don't know. It tells about lunches at school.

T: At our school?

S: Yes.

T: Do we serve this food at our school?

S: Yes.

T: Imagine I didn't know anything about the food at this school. I bring my own lunch everyday. How could you give the reader of your chart more information about the horizontal axis?

S: I don't know.

T: Well suppose I look at the chart and I see the label "Lunches," does it mean the lunches served at all schools in the world, the lunches served in the state of Oregon, the lunches served at the state penitentiary in the month of August...

S: No, it means the lunches we serve at Silver Crest school.

T: Yes, very good. Could you repeat that for me one more time.

S: The lunches we serve at Silver Crest school.

T: I like it, use it for the label of the horizontal axis.

The Vertical Axis

S: Students.

T: Suppose I go over to the category for Turkey Tetrazzini. And go up, what does the chart tell me?

S: Forty students rated Turkey Tetrazzini as their top choice.

T: How many students?

S: Forty.

T: How many students rated mashed potatoes and gravy as their top choice?

S: 29.

T: How many students rated corn dogs as their top choice?

S: 10.

T: So what information is the vertical axis giving us?

S: The number of students.

T: The number of students that ...what?

S: The number of students that like a certain type of food.

T: Yes. But not just any food, it can't be a cup of coffee and pie can it?

S: No. (Exasperated sigh!) The number of students that picked a school lunch as their favorite.

T: Sounds good to me; use it for the title on the vertical axis.

The Title of the chart.

S: Lunches versus students.

T: No. I want something more descriptive, can you look at the chart and form a conclusion?

S: Students versus lunches?

T: No. I would like a complete sentence. The title must tell me more about the chart. Suppose the superintendent is going to use this chart to change the lunches offered to students next year. What would he think from looking at the chart.

S: That Turkey Tetrazzini was the favorite.

T: The favorite of whom, the cooks?

S: Noooo, (Another exasperated sigh!) the students .

T: Okay. You've drawn a conclusion. Could you put it into one complete sentence.

S: Turkey Tetrazzini was the students favorite lunch.

T: Lets get even more precise. Did all the students choose Turkey Tetrazzini as there favorite lunch?

S: Forty students did.

T: Can we work that into the title?

S: Forty students chose Turkey Tetrazzini as there favorite lunch .

T: Yes, now we are getting much closer. Is forty students more than for any of the other lunches?

S: Yes, How about 'More Students Prefer Turkey Tetrazzini Than Any Other Lunchí?

T: Excellent. I like that; put it on the chart and let's see how it works.

The student enters the title into the spreadsheet chart.

T: That looks good. I think we could get a little more precise. Which students' are we talking about?

S: Silver Crest students.

T: Yes, lets add that. And what type of lunches are we talking about home lunches? school lunches?

S: School lunches.

T: Okay. lets put that in and I think we have a winner!

Look at Figure 3 for the new version of the student chart. Having students verbalize and then put into writing their labels and titles, assists the students in developing their thoughts and interpreting what they see visually. Have students do this whenever possible and you will soon see some amazing results. I've often had students observe things in data which were not immediately obvious to me. You will get incredible creatively titles and students will begin to use several subtitles or captions to label their charts (See Figure 4).

The process of having students go to this next level of labeling charts may not be politically correct from a pure statistical point of view. We should probably let the reader of the chart form their own conclusions, without trying to influence them. But the purpose of this lesson is not to produce charts which will appear in a statistics book, the objective is to make students analyze, interpret and evaluate data. These strategies provide a fun way for students to accomplish this.

The question may arise what is different about using a spreadsheet to create these charts than using graph paper and colored markers? One obvious advantage is the ease with which we can rearrange the data, and look at different types of charts. If students have some given data that will remain in a certain original form, and they are required to created a specific type of chart such as a histogram, there really is not any difference, if your students can generate excellent charts the first time they attempt them. And do not misunderstand me, I believe making charts by hands is an invaluable experience, especially for elementary students. When you want your students to perform at a the next level of excellence, then using the spreadsheet has advantages over paper and pencil. This is simply because it is so easy to edit data and text when using a computer. And because it is so easy to edit charts and data, the teacher can generate discussion and conversations with students about that data, as in the example above. This additional discourse will lead students to a deeper understanding. While this discussion may have been possible before the use of spreadsheets, it would probably have occurred after students had already completed a chart, with no chance to make changes in their work. Using the methods suggested in this lesson will definitely take longer, some students may need at least one whole class period to think about appropriate labels for their data and chart. I prefer to provide as much time as necessary, making it clear that a certain level of performance is expected from all students, and nothing less will be accepted.

This technique for creating charts touches upon the difference between mathematics teachers that use technology, and teachers that use technology to teach mathematics. Before I started requiring more sophisticated labels and titles of my students, I used technology a lot in my mathematics classrooms to make charts. When realized that I was making unwarranted assumptions about students' understanding, I made a slight change in my teaching method by requiring creative titles and exact labels. I used technology as a tool, in this case the charting and editing features of computer spreadsheets, to help students gain valuable experience in taking data in both numerical and graphical form, and transforming it into our written and spoken language.

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