Good Practice from Vesna Kilibarda, IU Northwest |
| Title | Active Participation in Mathematical Discovery |
| Course or Project | M436/T103 The Implementation
of Dynamic Geometry Software in a Problem-Based Learning and
Academic Service Learning Environment |
| Audience | Beginning undergraduates |
| Active | 2001, no longer active |
| Background Information | The purpose of our collaborative project (Dr. Besana and Dr. Kilibarda) was to use the dynamic geometry program, The Geometer’s Sketchpad, with its intrinsic invitation to an active, discovery-based learning environment as a means to provide a Problem-based Learning experience for in-service and pre-service teachers. The Academic Service Learning component of this project, as well as on-site workshops for teachers, have as a goal to positively influence current teaching practices in northwest Indiana. We targeted students in Introduction to Geometries, M436 and Mathematics for Elementary Teachers III, T103 at IUN as well as 40 northwest Indiana area teachers in the on-site workshops and through the Academic Service Learning component of the project. |
| Teaching Challenge | Historically, the middle school and high school geometry curriculum has been rigidly structured according to a deductive presentation of Euclid’s work, mostly through Hilbert’s revisitation (Hilbert, 1899). This traditional approach has produced generations of students who identify geometry as a closed branch of mathematics having its own peculiar language in which every question has a unique answer attainable through a compulsory series of steps, which are supposed to be passively absorbed from the all-knowing teacher and memorized for later assessment. Unfortunately, until recently, the college experience of future teachers reinforced sterile attitudes by reinforcing passive learning. New teachers were sent into classrooms ready to offer the same to younger generations. This cycle can and should be broken. A better approach is to integrate dynamic geometry software into a classroom environment structured with a Problem-Based Learning approach, incorporating an Academic Service Learning component. |
| Good Practice | The most relevant rationale
for the implementation of Problem-based Learning (PBL) and intensive
writing in undergraduate mathematics (or other courses) is the concrete
possibility of having the students experience, at an appropriate level,
the process of authentic mathematics creation. A course in which definitions
and theorems are not imposed from the outside as untouchable truths,
but are commonly agreed upon, revised at different stages, and modified
according to new contexts in which the mathematics maker is operating,
makes the excitement of discovery a reality.
To accomplish this, each unit of the course starts with the introduction of a problem. The problems are designed to challenge known notions, are open-ended and exploratory in nature, and require the use of models manipulatives, or technology. Students work in groups on the problem. The instructor listens and steers the discussion with carefully chosen questions. It is not uncommon for the students to raise and pursue issues which the teacher had not previously anticipated. Group work is followed by a discussion at the class level, which produces various solutions and/or opens more questions. Each student turns in a proposed written solution of the problem. A dialog between the instructor and each student ensues through repeated drafts of the assignment. When the class reaches a good understanding of the problem, a final draft is turned in and graded. The authors have a collection of anecdotal evidence of the excitement of the students. The open-ended nature of the problems utilized in the course encourages a diversity of learners' perspectives to flourish. The Geometer’s Sketchpad is particularly effective in introducing the modern notion of geometry as the study of invariant properties under a group of transformations. Students’ engagement with and ownership of abstract geometric ideas can be fostered through the use of Geometer’s Sketchpad. Geometer’s Sketchpad enriches the range and quality of active investigations by providing a view of geometric ideas from multiple perspectives and in a dynamic form. Drag a node in a Geometer’s Sketchpad environment and the construction on the screen changes, allowing an active approach to conjectures and discoveries. Mirror, Mirror on the Wall activity |
| Impact | Direct experience has shown us that the integration of Geometer’s Sketchpad with a Problem-based Learning approach deeply transforms learning in the geometry classroom. Long-term retention of material is achieved as a natural consequence of the empowerment that students experience and of the ownership of ideas that they develop. The ability to adapt to different learning styles is woven into the very fabric of the approach, as students set their own pace through discovery activities. |
| Assessment | The students completed three anonymous questionnaires at the beginning, in the middle, and at the end of the semester. All questionnaires were modeled on the Likert scale from 7 (strongly agree) to 1(strongly disagree). Teachers who attended the workshop completed an anonymous questionnaire as well. |
| Keywords | Collaboration/teamwork, problem-based learning, encouraging creativity |
| Technical Format | 2D Animation |
| Relevant URLs | http://www.samford.edu/pbl/ http://www.udel.edu/pbl/ http://www.imsa.edu/team/cpbl/ http://www.iun.edu/~mathvk/ |
Last updated:
4 May, 2007
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