**Faculty Technology Group Grant - Activity Report**

Elizabeth Hamm, Integral Program

Ted Tsukahara, Integral Program

We used the iPads that we received from the FTG grant in many different capacities in the Integral Freshman Mathematics Tutorial during Academic Year 2012 – 2013. Early in the fall semester we used them to introduce the students to online resources and to show students copies of Greek manuscripts of Euclid’s *Elements*. This opened up questions about the use of diagrams in the text and gave the students a chance to see the Greek manuscripts. We also used the iPads to exhibit the five Euclidean solids using an App called ICross. This App displays the polyhedra and allows the user to manipulate and turn the solid figures. We found it effective to display the solids before the students worked through the mathematical constructions, since the constructions are difficult and they can be challenging to visualize. When discussing Ancient Greek astronomy, we used the iPads to display an image of the night sky from 120 A.D. By examining Ptolemy’s night sky, students were able to observe the differences between what Ptolemy saw and their own night sky. This was particularly useful in discussions about precession.

Alexis Doval, another FTG Grant recipient in the Integral Program, suggested several useful Apps. Additionally, we were pleased to receive suggestions for Apps from students. The Apps that we found to be most valuable include:

ICross – This App is useful in the study of solid geometry and the different polyhedra can be manipulated and turned. (Developed by Oleh Yudin.)

Stellarium – This App displays an image of the night sky for a given time. It gives one the option of displaying labels for various objects, such as planets, stars, and the ecliptic. (Developed by Noctua Software Ltd.)

Sky Sarari – This App is useful when observing the night sky since it helps in identifying objects. (Developed by Southern Stars.)

Ptolemy’s Universe – This App displays Ptolemaic and Copernican models. (Developed by Nelix.)

Geometry Pad – This App is useful for constructing and measuring geometric shapes. (Developed by ZonMobile.)

Additionally, one of us (Hamm) used the iPad in the Integral Sophomore Mathematics Tutorial to show animated models of Ptolemy’s astronomical theories. The iPad was used occasionally to display models in class, but it was especially effective in helping students visualize and comprehend the models in one-on-one conversations outside of class. Certain Apps, such as Ptolemy’s Universe, allow the user to adjust the parameters of a model, trace the path of a planet, or pause a model. The other (Tsukahara) did not teach the other section of Integral Sophomore Mathematics Tutorial but did experience some students in his Senior Language Tutorial using their iPads as a digital reader instead of paper editions adopted for the course. If the tutorial were to be scheduled in one of the smart classrooms, there is opportunity to compare alternative translations of non-English works.

While there were many ways in which the iPad was beneficial, there were also ways in which we hoped to use the iPad but chose not to do so. For example, we thought that the iPad could offer students a means to present a proposition that contained complex three-dimensional figures, such as those found in Book XII and XIII of the *Elements*; however, many of the Apps that we examined did not allow for a construction that was precise enough and even the use of stylist did not produce results that we were happy with. Although we did not use the iPad in presentations, we found it beneficial to examine some of the Apps that are currently available and this inspired us to think about other ways in which we can utilize technology in the classroom.

In sum, the iPads are a useful tool that has enhanced the mathematics curriculum in a few, important ways. We look forward to discovering new uses for this device in our courses.