This project combines the dynamic geometry environment of The Geometer's Sketchpad® with haptic technology, particularly force feedback devices. The project is creating a series of geometric activities specifically focused on 2D figures and shapes as well as some simple 3D surfaces and solids, to enable users of various ages to explore the properties of these objects with various senses. The project combines these technology goals with learning goals that aim to provide better access to a wider variety of students, including underrepresented groups, in science, engineering, and mathematics. The Principal Investigator (PI) will conduct a series of informal after-school experiments at the James J. Kaput Center for Research and Innovation in Mathematics Education and then develop formal classroom interventions with primary school students in local schools. The PI will also extend these activities to engineering and mathematics undergraduate classrooms at the University of Massachusetts. The project will document, using data collected from the technological environment and other instruments, how students discover properties of mathematical objects within this new environment and develop formal argumentation, how this varies across age group, and how it can be integrated into formal classroom settings. The data will also be used to refine the design of the system.
The aim of the project is to discover what impact fusing a second modal input of feel to sight achieves in terms of engaging students of a variety of ages into exploring geometric concepts, and observe what kinds of mathematical activities can be designed that are significantly different to those using traditional forms of instruction. It will evaluate the practicality and educational benefits of integrating such technology. The project builds a new functionality on top of The Geometer's Sketchpad® software, and because of Sketchpad's huge impact and adoption by classrooms across the world holds the promise a potentially transformation of how mathematics, in particular geometric concepts, are understood by students.
Building on prior work, we developed a rich technological environment that combined the principles of dynamic geometry with haptic technologies. This enabled new ways of learning for a wide variety of students in the elementary and undergraduate grades. These were designed and tested in informal after-school settings including a local Boys and Girls club and several classrooms. We developed a set of activities that were implemented in 4th grade classrooms. The activity space examined a range of mathematics including exploration of 2D and 3D geometry configurations to enable users of various ages to explore the properties of these objects with various senses as well as concepts of number, multi-digit multiplication, estimation and area. Two primary technologies were utilized: 1. A force-feedback device called the Sensable PHANTOM® Omni device and 2. an implementation of a menu-free version of The Geometer’s Sketchpad® on the iPad. The first environment involves the use of an open source environment to set up a suite of solids and surfaces that students could manipulate through clicking and dragging but also experience force-feedback in terms of resistance to enable their exploration of particular mathematical attributes such as edges, vertices, faces, surface features, and planar intersection of solids. We introduced mathematics to young learners that are normally not presented until undergraduate courses but through working with STEM majors discovered similar approaches to our activities in both groups although the types of non-scholastic and scholastic language used were different. The second technology environment (Sketchpad Explorer) on the iPad involves the use of the computer software The Geometer’s Sketchpad® to design and build activities that are then transferred to the iPad for investigation by students. Here we combine the visual with the affordances of multi-touch in mathematically meaningful ways. Multi-touch enables multiple inputs either by a single user or multiple users that can lead to collaborative learning. In both environments we discovered that students of various ages could rapidly engage in mathematical activity through the use of multiple modalities that have profound opportunities in how we teach and learn mathematics in the future. We carefully analyzed how students come to understand mathematical phenomenon, reason, develop mathematical strategies, and establish formal arguments through collaborative work and structured activities. The result of such work has led to various contributions to the field of mathematics education including design principles for future curriculum designers, freely available software, curriculum materials and teacher support materials (co-developed with teachers). These are available for download at www.kaputcenter.umassd.edu/projects/haptic/. Apple has also recently bundled Sketchpad Explorer on their latest rollout of iPads and over 100,000 users have downloaded it.
