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1 FindArticles > Mathematics and Computer Education > Spring 2004 > Article > Print friendly Using Spreadsheets and Streaming Video for Developmental, Teacher Education, and General Education Mathematics Courses Shore, Mark A current project for the Allegany College of Maryland Mathematics Department is using spreadsheets in some of their General Education Mathematics courses. It is important to note that one of the key features of this project is that we do not require an introductory computer course as a prerequisite for any of the mathematics courses that will be or are currently using spreadsheets. In the mathematics courses for this project, students are not writing their own spreadsheets, but are using spreadsheets that have been developed for this project by the mathematics instructors at the college. However, students still learn basic functions for spreadsheets such as; how to navigate between spreadsheets, input data and formulas, copy and paste values, use spreadsheet functions such as Goal seek and Solver, and use Macros that have previously been written for this project. The students in the Mathematics for Elementary School Teacher courses will learn additional spreadsheet topics such as; inserting functions, and creating tables and graphs. Importantly, using the spreadsheets that have been developed for this project is not nearly as involved as the keystroke procedures students currently learn to operate graphing calculators. The goals of this two-year project are: 1. To supplement the instruction in developmental mathematics courses (Beginning and Intermediate Algebra) with spreadsheets; 2. To replace the use of graphing calculators in College Algebra and Statistics with spreadsheets; 3. To supplement the instruction in the Mathematics for Elementary School Teachers courses with spreadsheets and instruction on developing spreadsheets; 4. To complete the work of creating spreadsheets for these mathematics courses that are user friendly; 5. To create a minimum of 10-hours of streaming video for each of these courses for instruction and dissemination showing how to use spreadsheets for these courses; 6. To upload all video to the Internet and copy all video for each course onto CD's for every student enrolled in each course. Detailed Project Plan This project is adapted from a previous NSF project, Math Excel Mentor Lab project (MEMLP), from Northeastern University, grant number The Math Excel Mentor Lab was a project in 1992, and at that time, computer labs were not used as the primary teaching location. Therefore, spreadsheets were used as "support" for sections that were taught in a traditional classroom. The proposed project will use computers with previously developed user-friendly spreadsheets in the classroom. Therefore, spreadsheets will not merely be support for the course, but will be the main computational tool used in and out of class. For this reason, we will be setting up a computer classroom consisting of 18 desktop computers and a computer projection unit, for classroom demonstrations. The computer classroom will be arranged so that two students will work together at each computer. This will structure the classroom environment so that students will work together and we can accommodate up to 36 students in each class with these 18 computers. All tests for the mathematics courses for this project are on Blackboard (an online platform for classroom instruction and testing). Therefore, students take all tests in the testing lab, where they are individually tested. 1 of 6 8/31/08 3:26 PM

2 The Allegany College of Maryland project will use spreadsheets in Developmental Mathematics, Teacher Education mathematics courses, and lower-level General Education mathematics courses, thus testing the scope of which spreadsheets and streaming video are beneficial to mathematics instruction. Over a two-year period, this project will convert developmental, teacher education, and first level general education mathematics courses to using spreadsheets as the main instructional tool and streaming video (video help from the computer) to aid in instruction. These courses include the Developmental Mathematics courses (Beginning and Intermediate Algebra), College Algebra, Probability and Statistics, as well as the two Mathematics for Elementary School Teachers courses. Since we assume no prior knowledge of spreadsheets, the worksheets for each course will be written prior to offering the course. This will enable the students to utilize the power of spreadsheets without the need to learn intricate spreadsheet procedures. Formulas for calculations will be incorporated into passwordprotected cells so that typically students will not need to type in formulas. Button enabled macros have also been written so that multi step spreadsheet functions can be performed at the click of a button. Figure 1 shows the layout of a spreadsheet written for this project for College Algebra that will be used for analyzing data modeled by quadratic equations. Using the spreadsheet above, students can type in their x and y data points in the first two columns. The spreadsheet constantly updates the upper graph in yellow and the equation on the graph. When the student finishes entering their data, they then click the "Yes" button to copy the coefficients from the equation on the chart into cells D4, D5, and D6. If the student is not given data points and is instead given a quadratic equation, they would then type the values for a, b, and c into cells D4, D5, and D6. The x-intercepts and the vertex point (maximum or minimum point) for the model are automatically calculated. The data for the example given in the picture, gives the number of bacteria (in parts per million) in a water supply (y), after it has been treated with antibacterial material for (x) days. Students can then focus their attention on what the x-intercept and vertex point mean in terms of this problem situation and if a quadratic model is appropriate. Students can also determine the time(s) in which the number of bacteria in the water supply will be at a particular level (safe for consumption) by typing the y-value in cell E18. Using this same spreadsheet, students can make a table of values for the function by simply changing the "Start" and "Increment" values for the table in cells D15 and D16. This then automatically creates the table in columns C and D and the lower graph in green. On this one sheet students are able to model data, graphically see the difference between the actual data and the model (the upper graph on Figure 1), have the model solved for any y-value, make predictions to extrapolate future values, find minimums and maximums for the model, get a table of data based on the model, and graph the model (the lower graph on Figure 1). The quadratic model spreadsheet shown in Figure 1 is just one of the fifteen spreadsheets written for one of the courses in this project. Therefore, using the spreadsheets developed for this project, students are able to have the promise fulfilled that was imagined by educators in the 1990's, that students are able to easily see the relationship between the graph, table, and solutions of a model. Figure 2, below, shows an example of a project spreadsheet to be used in Statistics courses to analyze binomial distributions. Students enter the number of trials, the lower number of successes, the upper number of successes, and the probability of a success in cells B4, B5, B6, and B7. The spreadsheet then calculates the probability, the mean, standard deviation, variance, creates a binomial table (columns B and C), and graphs the binomial distribution for the data set. Students can easily see that the binomial distribution in Figure 2 is approximately normal and from experimentation students can determine the conditions in which a binomial distribution is approximately normal. All the topics studied in Statistics courses from probability to descriptive and inferential statistics are greatly enhanced by using spreadsheets. Also, students will almost certinally use spreadsheets in their career field to analyze data, not graphing calculators or pencil and paper. Using spreadsheets in Statistics frees the student from the procedures of calculating Z-scores, and looking up values in tables to understanding the concepts many students in statistics have trouble with such as; p-values, alpha levels, hypothesis tests, and correlation coefficients. Figure 2 is just one of seventeen spreadsheets written for Statistics. At this point, almost all the 2 of 6 8/31/08 3:26 PM

3 spreadsheets for College Algebra and Statistics have been written in a user-friendly format for this project. The teacher shortage that has encumbered public and private schools across much of the nation will continue to grow significantly in Maryland and the surrounding region. The Maryland State Department of Education estimated that Maryland hired a record 12,715 teachers to begin the school year, almost triple the number needed just eight years ago. These same trends are found nationwide. It is predicted that over the next ten years, the nation will need 2.2 million teachers. The proposed project hopes to insure that students enrolled in the Mathematics for Elementary School Teachers courses are experienced using the technological tools of our society when they become teachers. Students enrolled in the Mathematics for Elementary School Teachers courses will use spreadsheets developed to help elementary school children understand basic mathematical concepts such as fractions, percents, decimals, and graphs. Future elementary school teachers will also learn how to write their own spreadsheets to use when they become teachers. Students will also find and use spreadsheets that have been developed for teaching children mathematics that are currently available on the Internet. Streaming Video This project will also develop a minimum of 10 hours of streaming video for instruction on how to use the spreadsheets for each course. The project members will use Windows Media Encoder to capture the video of the instructions of how to use the spreadsheets. These videos will be recorded from the instructor's computer and illustrate with audio and video every action that the instructor makes. Therefore, these videos will show the spreadsheets as they are used to solve various real-life problems. Boster (2002) found that students who received instruction incorporating "video-on-demand" showed dramatic improvement. For this project each recorded video clip will be limited to 5 to 10 minutes with activities and practice problems for students at the end, a technique that matches research on best teaching practices (Brooks, 1997). Each video will also begin by showing the application of the material to be learned rather than the procedural skills, thus showing the "why" before showing the "how". An example of streaming videos made by the project team for College Algebra, which use graphing calculators, are available to view at (then click on "Online Video"). Research Support for the Use of Spreadsheets in Mathematics Research on the use of spreadsheets in mathematics has grown in interest for several reasons: * Students are much more likely to use spreadsheets in their future career rather than graphing calculators. * Spreadsheet programs such as Excel and Quattro Pro are often preloaded on computers before they are sold. * There are free spreadsheet programs on the Internet that can be downloaded such as Open Office and Office 602. * Most colleges and high schools now have several computer labs that have a spreadsheet application on them for students to use outside of class. * Almost every academic major requires both a science course and an introductory computer science course. In many science courses students use spreadsheets to analyze data, and in an introductory computer science course students learn key points in setting up spreadsheets. Therefore, taking a mathematics course that utilizes the power of spreadsheets will help integrate science and computer science courses. Research on the use of spreadsheets in mathematics courses shows promise and is a teaching and learning tool that should be investigated (Ozgun, 2002). "Spreadsheets build an ideal bridge between arithmetic and algebra and allow the students 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" (Friedlander, 1998, p. 383). Therefore, spreadsheets have become an important part of many different curriculums at different levels of education. Moreover, they have been used in education, especially 3 of 6 8/31/08 3:26 PM

4 mathematics education, as a tool in helping students understand mathematical concepts such as plotting and exploring functions, probability and statistics, mathematical modeling, and geometric transformations (Ozgun, 2002). Relationships among different types of representation such as tables, equations, and graphs are more easily comprehendible when all representations are visible at once and linked to each other, i.e. when one makes a change in one representation, corresponding changes in other representations are presented simultaneously by the program (Ozgun, 2002). Moreover, spreadsheets allow students to focus on the mathematical reasoning by freeing them from the burden of calculations and algebraic manipulations (Ozgun, 2002). The use of spreadsheets in mathematics courses can greatly affect the dependence upon algebraic manipulation skills. Garfield (1995) states that technology is a driving force that has led to a shift in introductory courses from traditional views of teaching Statistics as a mathematical topic (with an emphasis on computation, formulas, and procedures) to the current emphasis on statistical reasoning and the ability to interpret, evaluate, and flexibly apply statistical ideas. Spreadsheets can have the same impact on Developmental Mathematics courses and other General Education mathematics courses. Pea (1987) argues that "intelligence is not a quality of the mind alone, but a product of the relation between mental structures and the tools provided by the culture." Educational research supports the use of spreadsheets both in K12, teacher education, and in professional development. Abramovich and Nabors (1997) describe how using spreadsheets helped seventh grade algebra students develop problemsolving skills. Molyneux-Hodgson (1999) states that the results of their study "suggest the possibility of enhancing students' capability to shift between a wider range of representations using the modeling approach embedded in computer environments such as a spreadsheet" (p. 1). Dudgale (1994) reports a project that involved experienced K-12 teachers in mathematical modeling and problem solving using spreadsheets and concludes that teachers developed models that exhibited a wide variety of mathematical topics and approaches in different grade levels. The National Council of Teachers of Mathematics (NCTM, 2000) suggests, "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 simple spreadsheets and use them to pose and solve problems, examine data, and investigate patterns" (p. 207). The use of spreadsheets for higher grade levels is also advocated by NTCM (2000): "The expanded class of functions available to high school students for mathematical modeling should provide them with a versatile and powerful means for analyzing and describing their world. With utilities for symbol manipulation, graphing, and curve fitting and with programmable software and spreadsheets to represent iterative processes, students can model and analyze a wide range of phenomena" (p. 297). While the gender gap for mathematics has narrowed over the past decade, the technology gender gap is still an area in which little improvement has been made (AAUW, 1998). We believe that this project will help narrow this gap, by giving all students more time using technology skills such as spreadsheets, and using streaming video. Relying on teacherdirected, whole-group, paper-and-pencil instruction, no longer meets the needs of students, especially students from culturally and linguistically diverse backgrounds (NCTM, 2000). References Abramovich, S. & Nabors, W. (1997). "Spreadsheets as generators of new meanings in middle school algebra". Computers in the Schools, 13 (1-2), American Association of University Women Educational Foundation (1998). Gender gaps: where schools still fail our children, executive summary. ISBN Boster, F., Meyer G., Roberto A., & Inge C. (2002). A report on the effect of the unitedstreaming application on educational performance. United Learning. August. Brooks, D. W., (1997). Web-teaching a guide to designing interactive teaching for the world wide web, Plenum Press, New York. 4 of 6 8/31/08 3:26 PM

5 Dugdale, S. (1994). "K-12 teachers' use of spreadsheets for mathematical modeling and problems solving". Journal of Computers in Mathematics and Science Teaching, 13 (1), Friedlander, Alex (1998). "An EXCELlent bridge in algebra". Mathematics Teacher, 91 (50), Garfield, J. (1995). "How students learn statistics". International Statistical Review, 63, Harris Interactive (2001). There's no place like home. April harrisinteractivc.com/news /allnewsbydate.asp?newsid=350 Molyneux-Hodgson, S., Rojano, T., Sutherland, R., & Ursini, S. (1999). "Mathematical modeling: the interaction of culture and practice". Educational Studies in Mathematics, 39 (1-3), National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author Ozgun-Koca, S. A. (2000). Using spreadsheets in mathematics education. Office of Educational Research and Improvement (ED), ERIC Accession No. ED Pea, R. (1987). Cognitive technologies for mathematics education. In A. Shoenfeld (Ed.), Cognitive science and mathematics education. Hillsdale: Lawrence Erlbaum Associates, pp Mark Shore Division Chair of Mathematics Allegany College of Maryland Willowbrook Road Cumberland, Maryland JoAnna Shore Department of Business Management Frostburg State University 101 Braddock Road Frostburg, Maryland Stacey Boggs Mathematics Department Allegany College of Maryland Willowbrook Road Cumberland Maryland of 6 8/31/08 3:26 PM

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