ETC 558 Scholarly Paper

                      Using Technology to Facilitate Learning Mathematics
         Recent research studies have shown that technology can greatly enhance instruction and facilitate learning mathematics.  Integrating technology into a mathematics classroom increases student motivation, improves conceptual understanding, and offers the opportunity to gain valuable social skills.
Pedagogy of Mathematics
      The earliest attempts at using technology in education were developed for the delivery of predetermined content (Hooper & Rieber, 1995). This was accomplished primarily through the use of teaching machines, television, and film. Drawing upon the behaviorist philosophy of B.F. Skinner, it was believed that students could retain information by presenting the concepts in small steps, requiring overt responses to frequent questions, and providing immediate feedback (Reiser, 1987).
Initial teaching methods divided mathematical concepts into specific skills with the goal of students achieving a certain level of proficiency (Wood, 2001). However, during the past 30 years there has been a shift towards having students take a more active role in learning (Hooper & Rieber, 1995). Current pedagogy now involves far more complex interaction and places students, instead of the teacher, at the center of instruction (Wood, 2001).
The National Council of Teachers of Mathematics (NCTM) has suggested emphasizing open-ended “real world” problems. The problems should incorporate working in small groups, connecting to other content domains, and using technology to allow students to explore interrelationships between concepts. Educational technology possesses the ability to facilitate this process by encouraging students to become engaged in meaningful cognitive activities  (Hooper & Rieber, 1995).
Teachers typically present concepts in discrete portions to promote transfer of learning and improve instructional efficiency. However, researchers argue that such a practice actually hinders learning. They claim that the solution lies with creating problems that utilize the students’ experiences, which makes the learning more personally relevant (Hooper & Rieber, 1995).
Computer Algebra System
Studies have shown that technology capable of transforming or translating information entered by a user facilitates learning mathematics (Forster, 2006). A computer algebra system (CAS) is a common form of classroom technology that consist of software programs designed to facilitate working with symbolic mathematical expressions. Having evolved from artificial intelligence research, it allows students to define, manipulate, compare, and visualize algebraic expressions (Computer, 2007). By initially freeing the student from having to learn how to perform mathematical manipulations by hand, they are able to focus on learning conceptual issues and as result, enhance their knowledge of solving equations. Furthermore, students can practice recognizing a sequence of algebraic manipulation without being consumed by paper and pencil errors (Heid & Edwards, 2001).
Students who use the CAS more than the common algorithmic procedures utilized in traditional classrooms achieve a greater conceptual understanding and have higher scores on knowledge assessments without a reduction in computational skills. However, using a CAS does not always lead to improved performance. Less positive outcomes will occur if a CAS is used primarily to increase the efficiency and speed of completing standard problem solving approaches. A CAS is most effectively utilized to explore and verify algebraic generalizations, instead of simply as a symbolic calculator (Hoyles & Noss, 2006).
Handheld CAS
A handheld calculator CAS has become widely prevalent in classrooms. Integrating CAS calculators can increase student interest, allow more time for experimentation and data analysis, promote higher level thinking, improve cooperation, and help facilitate teaching (Bowman & Koirala, 2000).   
By using a CAS calculator, graphs can be readily created, and calculations become faster and more accurate. Multiple examples can be quickly produced to support student inferences, allowing them to focus on properties and relationships (Forster, 2006). Research has demonstrated that the graphing calculator can also increase the time available for experimentation and data analysis. This allows students to broaden the scope of the experiment by examining additional variables, collect additional data, and conduct more thorough data analysis. (Bowman & Koirala, 2000).
CAS calculators also offer the potential to improve student interactions within cooperative groups. Studies have shown that less able students are able to keep pace with other students because they are not struggling with the mechanics of constructing a graph. This allows them to feel successful and improve their level of confidence. As a result, greater collaboration occurs and students are likely to offer support to individuals who typically have difficulty performing assigned tasks (Bowman & Koirala, 2000). This benefits the more capable students cognitively by the restructuring associated with teaching, and the less able students from the personalized assistance that they receive (Hooper & Rieber, 1995). By working together using graphing calculators, students have the ability to compare screen displays and share their information, both of which enhance communication (Forster, 2006).
Although a CAS calculator offers the potential to greatly enhance learning, it is imperative that the technology does not dominate any learning activity. If this were to occur, the objective and eventual outcome of the task would change, which would be detrimental to student learning (Fitzsimons, 2005). Students who become overly dependent upon the calculator tend to be weaker at mathematics and perform lower with the support of a CAS device (Stewart, Thomas, & Hannah, 2005).
New technological gadget
         Although a calculator is the most common form of CAS available, recent innovations offer the opportunity to expand the array of technological tools used within an educational setting. Using the Vernier Lab Pro, a wide variety of scientific sensors and electronic devices can be connected to calculators, personal digital assistants (PDA’s), computers, or can work as a stand-alone unit, to record experimental data. With over 50 sensors to choose from, the potential applications are limited only by the one’s creativity (Vernier, 2007).
         Some of the possible sensors include temperature, dissolved oxygen, gas pressure, pH, force, blood pressure, a spirometer to measure airflow or lung volume, and ultraviolet sensor. The sensor is automatically detected and available to use once it is plugged into the Lab Pro unit. The use can then begin transmitting data to a recording device, such as the graphing calculator (Vernier, 2007).
         There are a wide variety of applications for the large number of sensors that are available. For example, ultraviolet sensors could be used to measure the amount of radiation absorbed during a given duration of time. Students could then determine “safe” amounts of exposure to ultraviolet radiation and the effects of using sunscreen. Recording devices could be used to derive equations for calculating the amount of radiation a given individual absorbs after so many minutes in the sun. In addition, students could evaluate the effects of using various types of clothing, protective sunglasses, automobile glass, and so on. This experiment would be of particular interest to teenagers concerned about having tanned skin or for individuals living in states such as Arizona that receive increased amounts of sunlight exposure.
         Another set of experiments could be conducted using heart rate monitor and transmitter. Subjects could be led through a series of physical exercises. By wearing a heart monitor belt, data could be collected regarding the subject’s heart rate before, during, and after exercise. Students could determine how long it takes to fully recover after a given duration of exercise. In addition, the volume of oxygen intake and outtake could be measured throughout the experiment using a spirometer. This activity would be of particular interest to students who are involved in some type of physical activity or sport.
Conclusion
         Integrating technology into a mathematics classroom can greatly enhance and facilitate learning. As a high school math teacher, I am able to observe the positive reactions from students when incorporating technology into my lessons. Small group, real-life activities increase my students’ motivation dramatically. Many students begin independently exploring concepts in greater depth. For instance, using computerized stock market simulations in my high school consumer math class has prompted students to learn more about the economy, read financial reports, and investigate various stock performance indicators. Teaching within the context of the simulator has led to improved student learning.
         CAS calculators allow students to analyze data more thoroughly, promotes higher-level thinking, and improves cooperation with other individuals. My students have used CAS calculators to create models for real-world situations. Last year, I took a college algebra class to a nearby ski resort. Working in small groups, they used a global positioning system (GPS) to record the elevation at various points on the mountain. The students then used the calculator to construct a graph for the data and create a mathematical equation to estimate the elevation at any point on the mountain slope. Constructing an equation to model the data using paper-and-pencil would involve a tremendous amount of time due to the vast number of calculations. The activity reinforced valuable social skills and allowed students to utilize a wide variety of mathematical concepts when drawing conclusions and making generalizations.

Practicing teachers should know that there are numerous technological tools available that can improve student learning and lead to a more thorough understanding of mathematics.
         

         
References
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