Background: The Emergence of Classroom Connectivity

Classroom Connectivity (CC) has been evolving on an exciting trajectory in recent years. Building on the success of outside-classroom technologies for learning about ideas, and connecting knowledge bases (e.g. Internet, WWW based courses, on-line tutors), new, and similarly powerful, inside-classroom technologies are becoming more stable, affordable, and effective. The success of such implementation is largely to do with the advances in wireless technology, ranging from Infrared and Bluetooth™, to faster network communications (802.11b/g). Such technology allows for “networks” to be integrated fast with little administration, logistical support or classroom destabilization (i.e. hardwiring networks together incurs direct and indirect costs both in time and money on facilities, re-fabrication of buildings, maintenance, dependence on mainframes, etc). Core examples of connectivity include:

1. Peer-peer devices, e.g. Palm/Cell Phones, where users can “beam” objects to each other;
2. Single-device connectivity, e.g. connecting a device to a computer, that is part of a wider established Network;
3. Local Wireless Networks, e.g. Texas Instruments (TI) Navigator Learning system, that wirelessly connects hand-held devices to one host “teacher” computer;
4. Wider Area Networks, Intranets and the Internet.

The use of the third example above will be the focus of this proposal. We detail the form and use of the system later. Our proposed work builds on several years of investigating and building prototypes of software in close collaboration with TI which led to the growth and commercialization of their product this Spring 2005. Our research work has predominantly been in local high school classrooms, with a second stream of piloting in low-risk upper level courses at UMass Dartmouth. We are now in a position to extend this work to a broader population of undergraduate students in mathematics classrooms across Campus. It is important to state at this point that the effectiveness of this technology is intimately bound up with the structure of the tasks designed to be used with the system, and its ability to enable students new ways to discover core mathematical ideas through leveraging their work from a private to a public, and more social, workspace. This has a huge impact on student affect and cognition, including participation and engagement as well as teacher efficacy, especially regarding the assessment of students’ knowledge.

Classroom Connectivity has earlier roots in more than a decade of classroom response systems, most notably ClassTalk™(Abrahamson, 2000), which enabled instructors to collect, aggregate and display student responses to questions (often as histograms), and, in so doing, create new levels of interaction in large classes in various domains (Burnstein & Lederman, 2001; Hake, 1998) and levels. See especially the review by Roschelle, Abrahamson & Penuil (2003) that shows remarkably consistent positive impacts across multiple domains and levels. This type of CC has been implemented in classes at UMass Amherst. The major new CC affordances beyond classroom response systems that we have studied are:

1. The mobility of multiple representations of mathematical objects (e.g. functions) and the ability to pass these bi-directionally and flexibly between teacher and students and among students, using multiple devices.
2. The ability to flexibly harvest, aggregate, manipulate and display to the whole classroom, representationally rich student constructions, and to broadcast mathematical objects to the class.
3. To do (2) in ways that respect and build upon naturally occurring social and participation structures.
4. The opportunity to engineer entirely novel classroom activities in concert with the mathematics to be taught and learned that both engages students in new and powerful ways, and to generate new forms of student responsibility and accountability that are intimately linked to intense mathematical activity.

Work-to-date has predominantly been in High School classrooms and so our activities have focused mainly on Algebra. The proposed work aims to build upon this work to create activities that are suitable for undergraduate mathematics courses, but still aims to attend to issues of participation and motivation that persist in higher education classrooms. In tertiary mathematics courses, e.g. Calculus, ideas become more abstract, and generalization from a few examples is a key issue: this becomes a big difficulty for students. Let us offer two examples from our present work, which aim to offer you a sense of how the system and content (i.e. CC) are tightly integrated.

Example 1: Linear Relationships. Here we ask students to move a cursor around a coordinate system on their hand-held device (see figure 1a) and to make a mark when their cursor is on a coordinate whose y-value is twice their x-value by pressing the “Mark” soft key on their hand-held device, which is connected to the wireless network. Their point is instantly sent to the teacher’s computer where a host software application is running. But each contribution appears simultaneously (see Figure 1b). So if this computer is connected to a video projector then each student can see their work “appear” and simultaneously compare it with each other’s contributions. In this example, a plot of points would hopefully appear, falling on the line Y=2X. Variation occurs via the contribution of each student; a natural consequence of the physical set-up of the classroom. Generalization occurs by students being able to observe, readily perceive via a visual stimulus, reflect and then discuss what they see in the public display.

Example 2: Functions and Geometry. In this example, we ask students to submit a linear equation that will construct a hypotenuse of a triangle with two other sides created by the teacher via two lines (i.e. Y= -4 and X=2). Variations of this could be for students to make a linear function, which has a slope equal to their group number, or which will form a triangle whose area is equal to twice their group number. Note: one can also hide the equations, forcing students to think about the algebraic form when only a visual representation can be seen in the public display. When the teacher has control over which representation to show, the focus of attention can be tightly controlled, forcing students to think more deeply about the mathematical ideas being investigated. Students’ names can also be hidden to preserve anonymity when needed.



The system also supports a standard response system, called “Quick Poll”, but in addition, enabling the teacher to send out (quickly) various types of response formats, including Likert-type scales (1=Poor to 7=Excellent), short, and open responses.

We are aiming to build on activities of these types for use in Pre-Calculus courses, especially those established for groups of students with disadvantaged backgrounds in mathematics (e.g. START program) as well as traditional Calculus courses. For example, one activity type would be to display a graph that represents the velocity of a ball being thrown off a building, and students could submit functions that they thought would represent graphs of the Position-Time graph. The initial height of the building is not given and students might realize that they can enter in any number for the height of the building, as the velocity of the ball is not dependant on this initial condition. This task allows students to naturally develop a family of possible answers (anti-derivatives) that could lead to interesting classroom discussions when they are projected publicly.

2. Goals of the Project

We will develop a set of activities that will be introduced into Impulse Calculus and Pre-Calculus (START program) in the Fall 2005, refined and then used to supplement or replace parts of the Pre-Calc and Calculus 1 courses in several sections offered in the Spring 2006. We have several professors who have agreed to do this for “test-purposes” and they will also help us refine and design more activities that exploit CC in powerful new ways. We will intervene in several classes during the course of the semester and collect data during these times.

We will collect video data of these classes. We will also interview a selection of students with varying degrees of proficiency with Calculator usage, to gather information on the impact of CC on their learning and engagement in class. We will also collect some assessment data to see if work with CC allows them to learn and retain knowledge for final exams.

All of this data will be used to build professional development resources for initial use on Campus and for wider dissemination system-wide. Faculty will not only have the opportunity to learn how to use the system with new mathematical activities but have extra resources to understand how the implementation of such materials impacts students’ learning.

So, in addition to our primary goal to develop new, innovative curriculum for undergraduate mathematics classes, we will also build a set of supporting resources for faculty development.