In our technologically progressive society, new software, apps, and gadgets are constantly being introduced, ever widening the range of choices from which a teacher might select a technology for his or her classroom. With this prevalence of the latest and greatest technology, it is important for teachers to keep in mind that the most effective technology for demonstrating a given concept might be a familiar one. Spreadsheet software, like Excel or Numbers, is an excellent example of this. Although spreadsheet software has been around for years now, it still has useful capabilities that merit a place in a math classroom.
When one first thinks about spreadsheets, he or she probably thinks about a means by which to organize data entries, track a budget, or tally given quantities. If used in the classroom at all, spreadsheets are often limited to tasks similar to these, and they rarely find a place in math classes outside of statistics. But what if students could utilize spreadsheets to understand broader math concepts such as sequences and series or algebra?
By employing more of the features in software like Excel and Numbers, spreadsheets can find a place in a math classroom. For example, students might use Numbers to see the difference between a sequence of odd numbers and a series of odd numbers by first generating a column of counting numbers, 1 through a positive integer n. In the next column, the student could create a sequence of odd numbers by starting with 1 in the first cell of the column, and in the remaining cells in the column enter a formula such that the value of the cell equals the value of the previous cell plus 2. In the next column, partial sums of the series of odd numbers can be found by starting with 1 in the first cell, and in the remaining cells enter a formula such that the value of the cell equals the value of the previous cell plus that of the adjacent cell (which is the next odd number in the series). For clarity, see below:
As seen above, students can make conjectures about the explicit formula for the sequence of odd numbers, which we know to be Sn=2n-1, and test their conjectures in the spreadsheet.
Also, students can see the difference between the sequence and series of odd numbers by comparing the line graphs of each, as shown below. This might help students to recognize that the partial sum of the series of odds for a given integer n equals n^2.
A spreadsheet could also be used to graphically see the solution to an algebra problem. Take x^2-x+3 = x+2 for example. Students can create three columns, one for x, and one each for the left and right sides of the equation. Using formulas, a student can quickly generate a range of values for each side of the equation for given x values. A student can then create a line graph comparing the left and right sides of the equation. The solution to the equation will be where the two lines intersect, in this case, where x=1. This activity can help students graphically understand what it means for two functions to be equivalent for a given x value.
A noteworthy observation is that when using spreadsheets, there is typically multiple ways in which to achieve a given task. As a teacher, it is important to ensure that students employ correct mathematical reasoning when generating formulas and analyzing data. Further, by comparing results, students might be able to probe further into thinking about how their own solution works, and why their neighbor’s method might too. In this way, spreadsheets have the potential to satisfy Dick and Hollebrand’s (2011) stipulation that effective technology serves “to push our students’ mathematical thinking forward or to probe how students are thinking mathematically” (p. xi). However, in order to push or probe student thinking, the skills needed to manipulate the spreadsheet cannot overshadow the mathematical concepts presented (Niess, 2005). Thus, it is important for teachers to gradually build assignment complexity in order to keep students focused on the math.
Investigations like the ones described above only scratch the surface of the concepts that can be demonstrated with spreadsheets. So before you reach for the newest math app, explore the possibilities of the spreadsheet software you probably already have!
Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to
support reasoning and sense making. Reston, VA: National Council of Teachers of
Niess, Margaret L. (2005). Scaffolding math learning with spreadsheets. Learning and
Leading with Technology, 32(5), 24-25.