General Observations The impact of the Tablet PC technology on our teaching styles and on the classroom environment have been quite surprising and unexpected. An immediate observation about the instruction within the classroom dealt with the simple fact that the instructor is constantly facing the students rather than having his back to the class while writing on the board. This simple change provides for a subtle but meaningful change in the relationship between the instructor and the students. In Differential Equations and in Calculus III, the instructors used semi-prepared notes, generated via LaTex and exported into DyKnow, that the students and instructors complete during the lectures. These notes are then made available online outside of class. Because the instructors are using digital technology during the lectures, more sophisticated notes, using images and different colors, can be generated. Additionally, using the replay option in DyKnow, students can replay the notes, stroke by stroke, so that they can follow the step-by-step process, which is much harder to do for static notes. The interactivity between the instructor and the student has improved the classroom discussions about the concepts being presented within the differential equations course. In this course, students learn several different techniques for solving differential equations. One of the key issues, then, for the students is to identify which technique is appropriate for a particular differential equation. Dr. Le frequently uses the interactivity capabilities of the Tablet PC and the DyKnow software to aide the learning process for identifying the appropriate technique for an equation. He will show the students a differential equation and ask them to select the appropriate solution technique via multiple choice. After displaying the class's responses, he can engage the students in discussions concerning why they chose a particular method. Dr. Le regularly used the polling capability of DyKnow to gauge student understanding of the lectures and could adjust the lecture notes based on this feedback, adding or deleting examples or further explanation, as indicated by the students input, providing for a much more dynamic and responsive lecture. For the Calculus III course, Dr. Burg uses Microsoft Math and Mathematica to visualize the curves and surfaces used within multi-variable Calculus. Microsoft Math is a pen-based math tool, that specializes in graphing implicit equations, parametric curves and 3D surfaces. Because it is pen-based, the student only needs to write the equation, without using any special templates or software-defined functions, so it is easy to learn and to use. Mathematica is a more powerful and more mature mathematical software suite and has many more features than Microsoft Math, including ContourPlot and VectorFieldPlot. However, it is much more difficult to learn. By having and using both software packages within the course and having the students use the software rather than observing the instructor's use of the software, students can learn the software more quickly and be more comfortable with it. The biggest impacts of the Tablet PC program within the University of Central Arkansas's Department of Mathematics were the use of semi-prepared notes within DyKnow, the use of worked homeworks and the increased integration of software and technology within the lectures. 1. Semi-Prepared Notes. Dr. Burg posted his notes online in PDF format and in the DyKnow format for the students in use in their studying. DyKnow has a replay button, which allows the students to watch the solution process step-by-step, later on when they are studying or working similar problems in homework. The unexpected consequence has been that a large portion of the students no longer take notes in class, since they will be available online. They prefer to pay attention to what the instructor is currently saying or teaching rather than focusing on copying down the notes, which prevents them from staying current with the derivations. Approximately 40% of the students indicated that their note-taking styles were altered dramatically because of the availability of online notes. 2. Worked Homeworks. During the last semester of the project (Spring 2009), Dr. Burg posted worked homeworks for the odd problems online. The answers to the odd problems were already provided by the book. Using DyKnow, Dr. Burg worked the odd problems, using the same methodology taught in class. Students repeatedly stated that they used the worked problems as guides for working the assigned even problems, significantly impacting their understanding of the skills being taught in class. 3. Software Integration. Because of the availability of the Tablet PCs, the use of Microsoft Math and Mathematica in Calculus III, Microsoft Excel in Differential Equations, and MatLab and Microsoft Visual C++ in Numerical Methods dramatically increased, affecting and altering the instruction in these courses. Students could use the software and follow the instructor's presentation by performing the tasks themselves, gaining confidence with the use of the software and using the software as an investigative tool.

Rationale Many high school and lower division mathematics courses use graphing calculators widely within their curriculum to investigate functions of one variable. However, multivariable calculus deals with functions of several variables which are graphically represented as curves and surfaces in 3D or higher dimensions and can not be visualized easily using graphing calculators. Additionally, the interactive capabilities of the Tablet PC can be useful in helping students through certain mathematical thought processes, such as the decision-making in choosing the best approach to solving a differential equation or in developing a logically, mathematically solid proof. The students in the multivariable calculus have responded almost unanimously that the Tablet PC is extremely helpful in visualizing and understanding functions of several variables, and the students in the abstract algebra sequence have expressed that they are understanding the material better using the technology.

Impact on Teaching The multivariable Calculus course and the differential equations courses have previously been taught using a traditional lecture format, including the use of calculators by the students and some computer examples performed by the instructor using the video projector in the classroom. The abstract algebra sequence has used both traditional lecturing and one-on-one interaction between instructor and student when the students work on proofs and exercises in the classroom while the instructor travels around the classroom making comments about their work. For the multivariable Calculus course, the students and the instructor used the advanced graphing capabilities offered by the pen-based Microsoft Math software to investigate the properites of the functions visually. One successful class project was developed for the Calculus III course, introducing the students to quadratic surfaces in 3D, such as cones, spheres and paraboloids. For the differential equations course, the polling capabilities of the interactive tablet PCs and the DyKnow software was integrated within the instruction as the students learned how to determine which solution methodology was appropriate for a particular differential equation. A class demonstration/project based on Newton's Law of Cooling was performed, using a digital thermometer that recorded the data to a Microsoft Excel spreadsheet that was then analyzed by the students, using the Tablet PCs. Additionally, the usefulness of prepared and semi-prepared notes for improved instruction was invaluable, allowing students to focus on the lecture rather than on note-taking. For the abstract algebra course, the instructor tried several different approaches for using the Tablet PC within his instruction, eventually using it with a different projector, so that he could continue to use the white board for his lectures. Student exercises were displayed using the second projector, allowing the instructor to work one-on-one with the students. For the numerical methods course, the HP Tablet PCs were used for the lectures, using semi-prepared notes that are then posted online. Additionally, programming software such as MatLab and Microsoft Visual C++ are used during class time to assist the students with their comprehension of the numerical algorithms.

Quick Facts Department of Mathematics University of Central Arkansas Courses Impacted: MATH 2371 - Calculus III MATH 3331 - Differential Equations MATH 3360/3362 - Abstract Algebra I and II MATH 4340 - Numerical Methods MATH 6382 - Applied Math Seminar Number of Students Impacted: over a hundred students per year Number of Faculty Involved: 3 Future Courses to be Impacted: Math 1591 - Calculus I Math 1592 - Calculus II Math 6348 - Numerical Analysis This project was funded by a 2007 Hewlett-Packard Technology for Teaching grant.

Dr. Burg during a Multivariable Calculus Project Day "I am excited about our efforts to integrate the capabilities of the HP Tablet PC into the visualization aspects of our multivariable Calculus course. We are being more flexible with how the students use the technology for note-taking - some students only use the computer, while others only use pencil and paperwork. I even have some students who do not take any notes, but rather focus on listening and trying to comprehend the concepts. Presumably, they can use the completed notes that I post online for their review." - Dr. Clarence Burg, Project PI "I love the tablet PC's. [The instructor] was great about showing us step by step how to use them and the Math software, and I can't imagine learning this stuff without the hands-on visual aid it provides." - student in multivariable calculus. "I think that the digital classroom we are using in Abstract Algebra is very beneficial. Especially when doing proofs and stuff, because it helps you get a chance to try one of the proofs and get immediate feedback while remaining anonymous." - student in Abstract Algebra class. "[The interactive technology] shows me where I may be getting something wrong, and also shows me that some of the questions I have are the same things that other people are having trouble with." - student in Abstract Algebra class.

Use of Technology We are using DyKnow software during the lecture, to allow student/instructor interactions via polling and student feedback, and to present the material to the students through semi-prepared notes. After evaluating available software, we are using Microsoft Math to visualize the curves and surfaces in 3D and Mathematica and the TI Voyage 200 Calculator to evaluate the integrals used within the course. Three different styles are being used with the DyKnow software. For the multivariable Calculus course and for the differential equations course, the instructors are using the mathematical type-setting program LaTex to generate a polished PDF version of the notes. For the multivariable Calculus course, the PDF file is then converted to a DyKnow file and provided to the students as an incomplete set of notes to complete during the lecture. For the differential equations course, the instructor cuts and pastes from his prepared PDF file into the DyKnow file during the lecture so that the notes can be adjusted based the needs of the students. For the abstract algebra class, the DyKnow software is being used solely for student/teacher interactions, where the students submit the DyKnow panels to the instructor to be marked and evaluated. Observations about Multivariable Calculus Project on Quadratic Surfaces Project on Ellipsoidal Coordinates Project on Subatomic Forces Project on Gravitational Fields Observations about Differential Equations Observations about Abstract Algebra Example of Semi-Prepared Notes In Section 12.6 of our textbook, the students are introduced to the concept of the directional derivative. In preparing for class, Dr. Burg developed his semi-prepared lectures within LaTex. These are then converted to the native DyKnow format, which are used in class. The completed lecture notes are provided to the students both as a PDF document which is universally viewable and as a DyKnow document, which can be replayed by the students. Here are the documents for this section. LaTex File DyKnow File Completed PDF Document Completed DyKnow Document

Impact on Student Learning Originally, we planned to use the Tablet PCs for directed "discovery" projects within the multi-variable Calculus course, and to use this technology for greater student-instructor interactions in the three primary courses. Due to time constraints within the multivariable Calculus course and because of negative feedback from the students, the efforts to develop "discovery" projects was significantly reduced. These projects typically took twice as long as a typical lecture and the students did not learn the skills adequately, even though they may have understood the concepts better. The greater interactivity made available by the Tablet PCs and DyKnow was used widely within the Differential Equations course and the Abstract Algebra sequence, as a means to ask questions of the students and to administer quizzes, and this technology did have a positive impact on the student engagement and understanding of the material. In the Differential Equations course, the instructor used the interactive polling capabilities of DyKnow to gauge the level of student comprehension and to adjust his lectures accordingly. In the Abstract Algebra course, DyKnow was used to display student proofs which were invaluable for identifying common student difficulties and addressing them. The biggest impact, perhaps, of the Tablet PC on these courses was the use of the semi-prepared notes. Originally, these notes were developed as a means of reducing the amount of writing of definitions, theorems and problem statements, while requiring that the students follow along with the instructor with the derivations of formula, proofs of theorems and calculations of answers to problems. The instructors had to adjust their teaching styles to make sure that they thoroughly explained the theorems and definitions and give the students enough time in class to digest and comprehend these concepts. Eventually, many of the students changed their note-taking strategies, since the completed notes would be posted online after class. The students either stopped taking notes entirely, or only took sparse notes of critical details or unusual concepts. Thus, they were able to stay engage with the instructor during the lecture more readily. In addition, the use of the replay button on the DyKnow panels was an extremely useful tool for studying, especially in learning the step-by-step solution procedures required within Mathematics.

Summer Outreach Program During the summer of 2008, Dr. Burg taught Algebra II and Geometry concepts within UCA's Upward Bound program, and during the summer of 2009, Dr. Burg taught Algebra II for this program. The goal of the Upward Bound program is to provide academic support to high school students who are capable of succeeding in college but are at risk of not succeeding in high school due to a variety of academic and environmental factors. During the academic year, these students participate in afternoon and weekend tutoring and receive regular encouragement and motivation to continue in their studies. During the summer, they attend a five-week summer program and reside on campus at UCA. They take a wide variety of classes based on the courses that they will be taking in the fall semester, with the goal of prepping them for these courses. In 2008, Dr. Burg taught approximately 10 students in Algebra II and 10 students in Geometry; while during 2009, Dr. taught 11 students in Algebra II. The HP Tablet PC's were a big hit with the students. The students stayed engaged and motivated primarly because of the interactivity provided by the Tablet PC and the DyKnow software. After the instructor taught a concept, he would provide the students with one or two examples to complete, with the students knowing that the instructor would grab the panels at random and post them for class discussion. While they were working on them, he could provide individualized assistance. The students were almost always engaged with these exercises, hoping that their answers would be posted, even if they were incorrect. Further, the students quickly learned the DyKnow software and learned how to use the various highlighters and different colors to express themselves and to be creative. The Microsoft Math software was also a highlight for them as they could quickly enter a function and visualize its graph easily and with an extremely small learning curve. UCA Upward Bound Program

Contact Us Clarence Burg (multivariable calculus and numerical methods) clarenceb@uca.edu Long Le (Differential equations) Ramesh Garimella (Abstract Algebra) UCA Math Department

Software We regularly use the following software in this HP project: DyKnow - interactive lecturing and notetaking Microsoft Math 3.0 - excellent pen-based (tablet PC -based) math visualization software Mathematica - mature mathematical software system including many algebraic functions for solving Calculus problems and visualizing curves, surfaces, contours and vector fields MatLab - mathematical programming language used within Numerical Methods LaTex - mathematical type-setting program, which is an essential part of developing our math lecture notes.

This project supported in part by an HP Technology for Teaching grant.