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Compelling Spreadsheet Tips to Understanding Mathematics

By Wendy Petti





Additional Resources

* To Excel in the Classroom Is Elementary
This website offers an outstanding collection of spreadsheet ideas and information, including the ABCs of spreadsheets.
* Integrating Spreadsheets in the Classroom
* MathsNet A to Z of Spreadsheets
* Excel Tutorials for Beginners
 

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.

WHY USE SPREADSHEETS IN THE 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:

  • "I want to use spreadsheets to enhance the math curriculum rather than taking time away from math and getting too hung up on spreadsheet skills."
  • "Will too much use of spreadsheets erode math skills or hinder full understanding of the math concepts involved?"
  • "If I'm going to use spreadsheets, I need a collection of activities that are easy to implement and are kid-friendly and teacher-friendly."
  • "Is it worth the hassle to try something new?"
  • "Will my students be able to use spreadsheets to analyze data and solve problems they encounter in 'real life'?"
  • "Will I be able to use spreadsheets in ways that meet the needs of learners with a wide range of experience?"
  • "Time and computer access are issues for me."
  • "How will I troubleshoot problems if I'm not a spreadsheet expert?"

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

  • Spreadsheets are a powerful tool for exploring and constructing meaning in dynamic and creative ways. They empower students as they facilitate inquiry and analysis.
  • Students can experience elementary algebra in action as they create and use formulas and function tables.
  • Patterns, such as those in a multiplication grid, take on new meaning when students can extend a core 2x2 grid to any multiple with a few swipes of a mouse.
  • Probability experiments and other data can be instantly analyzed with dynamic graphs that adjust automatically as new data is entered.
  • Students can make predictions and formulate conjectures as they compare theoretical data with real-life data.

SUPPORTING RESEARCH

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."

EXPLORING AND CONSTRUCTING MEANING WITH SPREADSHEETS

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:

Exploring Patterns
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:

  • Using formulas to create and explore arithmetic, geometric, and special sequences: triangular, square, cube, and Fibonacci.
  • Linking formulas to explore the "grains of rice" story and compound interest.
  • Using formulas for measurement, money, time conversions, and instant-summing.
  • Sorting lists to alphabetize or organize by numerical value.
  • Dynamic magic squares.
  • Illustrating real-life data with bar, double bar, line, pie, and/or pictographs.
  • Using sliders and hidden formulas to create function machine puzzles.
  • Using sliders to create dynamic graphs (with lines or curves that move as the slider value changes): linear, quadratic, cubic, and sine.
  • Using random number generation and the frequency function, combined with a graph, to produce instant sets of 30 or more random rolls of dice pairs.
  • Using random number generation to create math bingo boards.
  • Using the average, median, mode, min and max functions to analyze data.
  • Using conditional functions to create a self-checking quiz (such as estimating the sum of four random 3-digit numbers).
  • Using conditional formatting in creating simple math games.
  • Discovering the square root of any number with two methods (guess-and-check and Babylonian/Newton).
  • Using a "brick wall" merge pattern and formulas to explore Pascal's triangle and its many properties.

Other Activity Ideas

  • Analyzing student growth data using filtering, sorting, graphing, functions.
  • Filtering a checklist of qualities of geometric shapes to identify terms sharing common features.
  • Combining autoshapes and other drawing tools with angled text to create geo-messages.
  • Using the comment feature combined with graphics to create pop-up mini-lessons.
  • Using internal hyperlinks to create tutorials or interactive math stories
  • Creating a game or puzzle sequence with levels by using the solution of each puzzle as the password to open the new level in a different password-protected workbook.

To demonstrate the last use, here's a puzzle:

Seven girls are on a bus.
Each girl has 7 bags.
In each bag, are 7 big cats.
Every big cat has 7 small cats.
Question: How many legs are on the bus?

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?

BIG IDEAS ABOUT SPREADSHEETS

To crystallize the many beneficial uses of spreadsheets into a few big ideas:

  • A spreadsheet is a tool for understanding and communicating mathematically.
  • We "talk math" with algebra and with formulas. In algebra, we explore and apply generalizations through the use of variables. In spreadsheets, we explore and apply generalizations through the use of formulas.
  • We use spreadsheets for real-life, meaningful inquiry.

IMPLEMENTING A SPREADSHEET PROGRAM

Let's keep these supporting ideas in mind as we use spreadsheets in the math program:

  • Keep the focus on the math.
  • Keep it simple.
  • If you're a "spreadsheet newbie" yourself, you might team up with a colleague to have an extra support person on hand during your first couple of spreadsheet activities.
  • It's easier to supervise ten teams of students, with each team sharing one computer, than it is to supervise 30 students, with each student working on his or her own project. The collaborative experience is good for students, too.
  • Students don't have to create everything from scratch. To "export" individual pages of the spreadsheet collection as ready-to-use or ready-to-adapt spreadsheet activities, follow the "export" instructions on the how-to page within the spreadsheet collection.
  • The whole class can sometimes share one computer.
  • Spreadsheet templates:
    • help make spreadsheets user-friendly.
    • keep the focus on the math. An empty Excel spreadsheet is not a thing of beauty. The cells and font are tiny and not kid-friendly. Create a format you like with large cells and font (You even could set up some column headings in the first row), and save it as a locked template. Younger students can open that template, resave it with their own name, and start entering data.
  • For collaborative spreadsheet creation and sharing, check out the spreadsheet area of Google Docs.

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
Education World®
Copyright © 2010 Education World

04/27/2010



 

 

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