With all the math a busy teacher needs to cover, is there possibly room for one more thing? When you think of math and technology integration, do you think, "I'm going to take my students to some stimulating math Web sites!"? Or do you think, "Yay! We might have time to work on our spreadsheets today!"? (Uh-huh, I thought so!) A spreadsheet program might be one of the most underappreciated assets on nearly every computer. Let's take a look at what we can gain from using spreadsheets in our math program.
Of course, theres the obvious utility of a spreadsheet program as a "math assistant" of sorts: Two of the most common classroom uses of spreadsheets are to add columns of numbers, and to create graphs. But do those uses deepen our students' mathematical understanding or dilute it? The answer depends in part on when and how and why we use spreadsheets to "do the math" for us.
Issues and Concerns
Some of the concerns I've heard from teachers about the use of spreadsheets in the math classroom include:
Although this article might not be able to alleviate all concerns, let's look at a few of the ways in which the use of spreadsheets in the math program can deepen mathematical understanding, some activity ideas, and a few ideas for using spreadsheets successfully in the math program.
Benefits of Using Spreadsheets
Extensive research supports the use of spreadsheets in mathematics classrooms to empower student-centered learning.
J. C. Russell, in Spreadsheet Activities in Middle School Mathematics (NCTM, 1992), observed that a blank spreadsheet can be seen as a "student of the student," capable of being taught, as directed by the student. The act of teaching the computer to do something specific and meaningful with data helps a student clarify his or her own understanding of the problem.
Useful quotes and references are cited in Using Spreadsheets in Mathematics Education, ERIC Clearinghouse for Math, Science, and Environmental Education (Columbus, Ohio, 2000 - http://www.ericdigests.org/2003-1/math.htm).
The NCTM's 2000 Principles and Standards recommend that "students in grades 3-5 should also become familiar with technological tools such as dynamic geometry software and spreadsheets. They should learn to set up a simple spreadsheet and use it to pose and solve problems, examine data, and investigate patterns" (NCTM, 2000, p. 207).
Alex Friedlander, in "An EXCELlent Bridge to Algebra" (Mathematics Teacher, 1998, 91(50), 382-383), states: "Spreadsheets build an ideal bridge between arithmetic and algebra and allow the student free movement between the two worlds. Students look for patterns, construct algebraic expressions, generalize concepts, justify conjectures, and establish the equivalence of two models as intrinsic and meaningful needs rather than as arbitrary requirements posed by the teacher."
If we look at some of the specific mathematical inquiries that can be explored easily with spreadsheets, we begin to get a sense of their power and creative potential.
Its not within the scope of this article to provide a "how-to" tutorial on spreadsheets, but you'll get a sense of how formulas work by exploring some of the dynamic spreadsheet activities included in this spreadsheet file.
This is a downloadable spreadsheet file with many sample projects, a bit of hints on how-to help, and other resources. When you open the file, click "yes" to "enable macros" to get full use of all of the dynamic features of the activities.
Within this downloadable spreadsheet collection you'll find many mathematically interesting uses of spreadsheets:
We can extend patterns with a simple click-and-drag motion to create and explore arithmetic and geometric sequences. For example, if we type in two consecutive cells the numbers 1 and 4, and then highlight the cells and click and drag on the bottom right corner, when we release the mouse we'll see an extended pattern: 1471013.... When students get the motions down, they can experiment with any number of extended patterns and see if they can make predictions. For example, if our pattern begins with "14," what number will we find in cell M1? What if our pattern begins with "13" or "27," or "100150"?
We can extend other patterns besides numerical patterns. What happens if we try to extend a pattern of colored cells, or a pattern of letters?
Exploring Algebra through Formulas and Functions
Spreadsheet formulas bring algebra to life. Even young children can understand what variables are all about when they have a chance to play with them dynamically through spreadsheets. We can set up formulas ahead of time for students to explore, or we can guide students in creating and investigating their own formulas. Both approaches have value.
In the sample spreadsheet file, you'll find many uses of formulas to stimulate and facilitate mathematical inquiry:
Other Activity Ideas
To demonstrate the last use, here's a puzzle:
When you think you know the answer, you can find out if you're right by entering the digits of that number as the password to open this "bonus" spreadsheet.
If you enter the correct number of legs, the spreadsheet will open. If it doesn't open take another look at the puzzle and try again! Can you see how this could be one more fun mathematical use of spreadsheets?
To crystallize the many beneficial uses of spreadsheets into a few big ideas:
Let's keep these supporting ideas in mind as we use spreadsheets in the math program:
If all of those ideas aren't enough, check out the additional spreadsheet ideas, tutorials, and other resources in the sidebar to this article. Enjoy!
Article by Wendy Petti
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