Investigating the Mathematics of Inaccessible Objects: Algebra Videos with iPads

Introduction

From fall 2010 to the present, the College of Education and Human Development (CEHD) at the University of Minnesota - Twin Cities has conducted one of the largest tablet initiatives in the world (Wagoner, Hoover, & Ernst, 2011). Just months after the launch of the first iPad, our college dean secured funding from an anonymous donor that allowed distribution of devices to each of the 450 entering first-year CEHD students. A goal of the initiative was to ensure technology and information access for all students, regardless of socio-economic status or background. First-year CEHD students complete most of their coursework in the department of Postsecondary Teaching and Learning (PsTL), which includes faculty from a wide range of disciplines including algebra, statistics, biology, physics, literature, history, psychology, sociology, art and performance, and public speaking. Twenty-seven of these instructors also received the iPad 1, and were asked to incorporate it into their teaching. This project has continued each year from 2010 to 2013 with device upgrades for the iPad 2, iPad 3 and the iPad mini. Each entering first-year student receives an iPad that they can use for academic and personal endeavors until they graduate or transfer out of the college.

The PsTL teaching landscape is complex and dynamic. Each fall, our faculty deliver team-taught interdisciplinary First-Year Inquiry seminars to 450 first-year students. These seminars focus on an annual “common book” that all students and faculty study, and on the theme, “how can one person make a difference?” Each spring, many faculty teach their disciplinary class as part of a learning community.

In this usage, a learning community refers to a form of organization in which a group of students co-enrolls in two or more classes as a cohort. The similar terms community of practice or community of inquiry refer to different forms of organization because they involve pedagogical goals that could easily occur within a single classroom. A learning community could seek to establish a community of practice amongst its students, but a community of practice could occur without the linked-class structure of a learning community. In the United States over the last two decades, learning communities that span disciplines have become a relatively commonplace curricular structure for first-year undergraduates because they tend to improve retention and student engagement outcomes, an effect that is amplified for students who are ethnically or culturally different from the campus majority (Jehangir, 2010; Tinto, Love, & Russo, 1994; Tinto, 2000).

The CEHD/PsTL iPad project is particularly tied to these two interdisciplinary endeavors, the fall term First-Year Inquiry class and spring term learning communities. Students receive their device as part of the First-Year Inquiry seminar. Faculty teaching a First-Year Inquiry seminar in the fall or a learning community in the spring are expected to incorporate the iPad into the class, in any manner that seems appropriate. Most PsTL faculty members devise assignments that help students integrate learning across disciplines. Most faculty either redesign their class or develop substantial amounts of new curriculum every year to accommodate changes in the common book or shifts to new disciplinary combinations of teaching teams.

The iPad video assignment was developed as an integrative assignment within a learning community in spring 2013 that was offered to students who were considering a major in elementary education. All students enrolled concurrently in college algebra and in a class introducing them to the discipline of education. The assignment took place in the college algebra class, but it was incorporated into classroom discussions in the elementary education class. The assignment was to visit the university’s Weisman Art Museum, select a compelling work of art, and make a video on the theme “How do the mathematical properties of the work of art contribute to its artistic feeling?” Our chapter focuses on an analysis of students’ mathematical choices recorded in the six iPad-based videos.